Hybrid superconductor junctions with diluted PtNi ferromagnetic interlayer Taras Golod

Hybrid superconductor junctions with diluted PtNi ferromagnetic interlayer Taras Golod
Hybrid superconductor junctions with
diluted PtNi ferromagnetic interlayer
Taras Golod
Licentiate thesis in Physics
Akademik avhandling för avläggande
av filosofie licentiatexamen vid
Stockholms universitet
Department of Physics
Stockholm University
Stockholm, Sweden 2009
Hybrid superconductor junctions with diluted PtNi ferromagnetic interlayer
Taras Golod
Licentiate thesis in Physics
Department of Physics
Stockholm University
Sweden
c
Taras
Golod, 2009
ISBN 978-91-633-5099-3
Printed by: Universitetsservice US AB
Abstract
This thesis describes experimental investigation of thin films made of diluted
Pt1−x Nix ferromagnet alloy and Nb-Pt1−x Nix -Nb Josephson junctions.
Such Hybrid Superconductor-Ferromagnet (S-F) structures are of significant interest because of the new physics involved and possible applications in
low temperature and spintronic devices. In many cases, such devices require
components with small monodomain ferromagnetic layers and this, in turn,
requires development of specific nano-fabrication techniques.
Pt1−x Nix alloy is used as the ferromagnet layer due to very good solubility
of the two components which results in homogeneous diluted ferromagnet.
Systematic analysis of both chemical composition, and ferromagnetic properties of Pt1−x Nix thin films for Ni concentrations ranging between 0 and
∼ 70 at.% is performed.
The energy-dispersive X-ray spectroscopy (EDS) technique is employed
to study chemical composition of Pt1−x Nix thin films. To eliminate possible errors during EDS characterization, EDS is used with different electron
beam energies, different electron beam incident angles and on the free standing Pt0.60 Ni0.40 flakes. Ferromagnetic properties of Pt1−x Nix thin films are
analyzed by studying the anomalous Hall effect. The Curie temperature of
Pt1−x Nix films decreases in a non-linear manner with the Ni concentration
and has the onset at ∼ 27 at.% of Ni. It is observed that the critical concentration of Ni is lower and the Curie temperature is higher than it had been
observed early for the bulk PtNi alloys.
The 3D Focused Ion Beam nanosculpturing is used to fabricate nanoscale
S-F-S Josephson junctions providing the uniform, monodomain structure of
the ferromagnet layer within the junction. The detailed studies of S-F-S
Josephson junctions are carried out depending on the size of junction, thickness and composition of the ferromagnet layer.
The obtained Fraunhofer modulation of the critical current as a function
of in-plane magnetic field serves as evidence for uniformity of the junction
properties and monodomain structure of ferromagnet layer. The junction
critical current density decreases in spin glass state with increasing Ni concentration. In the ferromagnetic state the maximum current density of the
junction starts to increase. The latter is attributed to switching into the π
state as a function of Ni concentration. Simultaneously it is observed that the
critical current can completely disappear presumably as the result of stray
fields from the F layer in contact leads.
The Josephson junction is used as a phase sensitive detector for analysis
of vortex states in mesoscopic superconductors. By changing the bias current
at constant magnetic field the vortices can be manipulated and the system
can be switched between two consecutive vortex states. A mesoscopic superconductor can thus act as a memory cell in which the junction is used both
for reading and writing information (vortex).
iii
Keywords: Josephson effects, S-F-S Josephson junction, π state, Pt1−x Nix
ferromagnetic alloy, FIB nanosculpturing, EDS on a thin films, anodization,
vortex state.
iv
List of appended papers
Paper A. V. M. Krasnov, T. Golod, T. Bauch and P. Delsing, Anticorrelation
between temperature and fluctuations of the switching current in moderately damped Josephson junctions, Phys. Rev. B 76 224517 (2007)
Paper B. T. Golod, H. Frederiksen and V. M. Krasnov, Nb-PtNi-Nb Josephson
junctions made by 3D FIB nano-sculpturing, J. Phys.: Conf. Ser. 150
052062 (2009)
Paper C. A. Rydh, T. Golod and V. M. Krasnov, Field- and current controlled
switching between vortex states in a mesoscopic superconductor, J. Phys.:
Conf. Ser. 153 012027 (2009)
v
vi
Contents
Abstract
iii
List of appended papers
v
Acknowledgments
ix
1 Introduction
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Josephson effect . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 DC and AC Josephson effects . . . . . . . . . . . .
1.2.2 Proximity effect in S-N-S Josephson junctions . . .
1.2.3 Dynamics of Josephson junctions . . . . . . . . . .
1.2.4 Magnetic properties of Josephson junctions . . . . .
1.3 Introduction to ferromagnetism . . . . . . . . . . . . . . .
1.3.1 Basic concepts . . . . . . . . . . . . . . . . . . . . .
1.3.2 Anomalous Hall effect . . . . . . . . . . . . . . . .
1.3.3 Magnetism in thin film structures . . . . . . . . . .
1.3.4 Theory of PtNi alloys . . . . . . . . . . . . . . . . .
1.4 S-F-S Josephson junction . . . . . . . . . . . . . . . . . . .
1.4.1 Origin of order parameter oscillation in S-F bilayer
1.4.2 Theory of S-F-S π junction . . . . . . . . . . . . . .
1
1
5
5
5
7
9
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11
13
14
15
16
16
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2 Experimental methods
2.1 Sample fabrication . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Deposition of S-F-S multilayers and test ferromagnetic
single-layers . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Pattering of S-F-S multilayers and test ferromagnetic
single-layers . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 3D FIB nano-sculpturing . . . . . . . . . . . . . . . .
2.1.4 Anodization . . . . . . . . . . . . . . . . . . . . . . .
2.2 Sample characterization . . . . . . . . . . . . . . . . . . . .
2.2.1 EDS Characterization of PtNi thin films . . . . . . .
2.2.2 Low-temperature measurement setup . . . . . . . . .
vii
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23
28
33
34
34
36
3 Results and discussion
3.1 Chemical composition of PtNi thin films . . . . . . . . . . . .
3.2 Magnetic properties of PtNi thin films . . . . . . . . . . . . .
3.3 Characterization of S-F-S Josephson junctions . . . . . . . . .
39
39
47
54
4 Summary
67
5 Conclusions
69
6 Appendix
71
References
75
viii
Acknowledgments
First of all, I would like to thank my supervisor Vladimir Krasnov for his
support and advices. Special thanks to Andreas Rydh for his help with
measurements and fruitful discussions. I also thank Henrik Frederiksen for
helping out with EDS fabrication. I am grateful to Kjell Jansson and Osamu
Terasaki from Arrhenius Laboratory for helping with sample characterization.
I am grateful to all members of Experimental Condensed Matter Physics
group for their help and interesting discussions.
ix
Chapter 1
Introduction
The thesis is organized as follows: The introductory part starts with pointing
out the aim of this work. The next chapters provide some insight into the
physics of Josephson junctions, basics of magnetism, and physics of S-F-S
Josephson junctions. The experimental part goes through the sample fabrication and describes different experimental setups which were used during
this project. The experimental results and conclusions are presented at the
end.
1.1
Motivation
The important characteristic of superconducting state is the macroscopic
phase coherence of superconducting charge carriers (Cooper pairs). The
Cooper pair, formed by two electrons with opposite spins, has zero total spin
and therefore obeys Bose-Einstein statistic. The Cooper pairs are allowed
to be in the same lowest energetic level since the Pauli exclusion principle
does not apply to them. The quantum mechanics states that all particles
having the same energy will have the same phase velocity. Another important characteristic of the Cooper pairs is their relatively big size (about 10−4
cm) which is much bigger than average distance between pairs (the last is
of the order of interatomic distance). In other words, the wave functions of
the Cooper pairs are strongly overlap with each other. The result is that
all pairs are synchronized i.e. have not only the same velocity but also the
phases themselves are equal to each other at any points. Thus, such condensate of the Cooper pairs is coherent i.e. described by a common wave
function Ψ which is often called the order parameter. As a consequence, the
macroscopic quantities, such as current, can now explicitly depend on phase
of common wave function since such dependence does not disappear upon
summation over all particles. Such macroscopic coherence of superconducting condensate leads not only to infinite conductivity and Meissner effect but
also to very important coherent effects such as magnetic flux quantization
[1, 2] which implies that the magnetic flux passing through any area enclosed
2
CHAPTER 1. INTRODUCTION
by supercurrent is quantized with the magnetic flux quanta
π~c
Φ0 =
.
e
Another consequence of the phase coherence is appearance of the DC and AC
Josephson effects in superconducting weak links [3, 4]. The main idea of the
DC effect is that the some amount of supercurrent, Is , can flow through non
superconducting barrier between two superconductors without resistance.
The arrangement of two superconductors linked by a non superconducting
barrier is known as a Josephson junction. Such a current is driven by only
a phase difference between two superconductors. The maximum possible supercurrent through the junction is called the Josephson critical current, Ic ,
and depends on physical nature and dimensions of the junction. If the current through the Josephson junction exceeds the value of critical current, the
junction enters in the dynamic state and generates high frequency electromagnetic oscillations. This phenomena is know as the AC Josephson effect.
The interesting effect appears when a ferromagnet, which is characterized
by some exchange field, is used as a barrier in a Josephson junction. It is
well known that superconductivity and ferromagnetism are two competing
orders. Indeed, ferromagnetic order assumes similar orientation of electron
spins which is decremental for superconducting order with singlet spins of
electrons in Cooper pair. The problem of coexistence of these interactions
and their interplay is the subject of active research and will be discussed
more in the section 1.4.
One way to realize such interplay is to spatially separate the two interactions. In this case, the superconducting order parameter can penetrate into
the ferromagnet to some extent, due to a so-called proximity effect. The
main manifestation of the proximity effect in superconductor-ferromagnet
(S-F) structures is the damped oscillatory behavior of the superconducting
order parameter in F. As a result, the critical current of S-F-S Josephson
junction can change the sigh upon variation of temperature, F layer thickness or exchange energy of F layer [5]-[7]. Negative sign of the critical current
corresponds to the so-called π state and the junction is called π junction since
the change of the sign in Josephson current corresponds to the change of the
phase difference between two superconductors by π. In real experiment the
absolute value of critical current is measured. Thus, the transition from 0 to π
state results in non-monotonous behavior of the critical current with vanishing Ic at the transition point. The S-F-S systems provide unique opportunity
to study properties of superconducting electrons under the influence of an
exchange field acting on electron spins. It is possible to study the interplay
between superconductivity and magnetism in a controlled manner, since by
varying the layer thicknesses and (or) magnetic content of F layers one can
change the relative strength of the two competing orders.
S-F proximity structures has attractive interest also due to a possibility
to induce the spin triplet (p-wave) superconductivity in F materials [8, 9].
1.1. MOTIVATION
3
The Cooper pairs of conventional superconductors are in a singlet spin state
(two spins with opposite directions). It was predicted [10] that a triplet
Cooper pairs (two spins are pointed in the same direction) can be induced
in a ferromagnet adjacent to a conventional (singlet) superconductor.
Hybrid S-F structures are also actively studied as possible candidates for
future quantum electronics and spintronics. There are several suggestions
how S-F-S π junctions can be embedded into digital and quantum circuits as
stationary phase π shifters [11].
Another reason to study S-F systems is the possibility to achieve the absolute spin valve effect [12] with superconducting proximity structures. The
ordinary spin valve is a device consisting of two or more conducting magnetic
materials, that alternates its electrical resistance (from low to high or high to
low) depending on the alignment of the magnetic layers, in order to exploit
the giant magnetoresistive (GMR) effect [13]. The effect manifests itself as a
significant decrease in electrical resistance in the presence of magnetic field.
In the absence of an external magnetic field, the direction of magnetization
of adjacent F layers is antiparallel due to weak anti-ferromagnetic coupling
between layers. The result is high-resistance magnetic scattering. When an
external magnetic field is applied, the magnetization of the adjacent F layers is parallel. The result is lower magnetic scattering, and lower resistance.
The GMR has been widely used in reading heads of hard drives and magnetic
sensors.
An ideal F metal would have electrons with only one direction of spin.
There will be no current between two such metals if their magnetizations
are opposite. This is the absolute spin valve effect. The basic concepts of
ferromagnetism will be discussed in the section 1.3.1. However, conventional
F metals have electron states of both spin directions at the Fermi surface, so
that the absolute spin valve effect is impossible to achieve with such materials.
In [12] it was suggested to use the proximity effect minigap [14] induced in a
normal metal (N) by an adjacent superconductor to achieve the absolute spin
valve effect. The suggested device consists of two S-N-F structures with N
parts connected by insulating barrier. The S will induce the minigap in the
N metal and the tunneling current between N parts of two S-N-F structures
will have a jump at the threshold voltage eVth = (∆1 + ∆2 ), where ∆1(2)
are the minigaps in N parts of each structure. The F part, on the other
hand, will induce magnetic correlations in the N part resulting in a shift
of the gap edges for opposite spin directions due to exchange energy of the
ferromagnet. Then, the tunneling current between N parts will have jumps at
different threshold voltages depending on which spin components contribute
to the current. In the voltage interval between these threshold voltages, the
tunneling current jumps from zero to a finite value differently for parallel
and antiparallel orientations of magnetizations in these two structures. The
N metal is needed only to physically separate the F and S so that neither F
suppresses the superconductivity nor S the ferromagnetism. Note that the
4
CHAPTER 1. INTRODUCTION
N metal should be in clean limit in order to realize such device. In principle,
S-N-F structure can be replaced by S-F structure with diluted F in which
the superconducting state coexists with ferromagnetic.
Both hybrid S-F-S and spin-valve devices put strong constrains on the F
layer. Technologically the F layer should be thick enough, ∼ 10nm, to form
a uniform Josephson barrier without defects such as pin-holes. However, in
conventional strong ferromagnets like Ni, Fe, etc., the coherence length is
. 1nm [8]. This in turn requires that the F layer is made of a weak, diluted
F alloy, to allow a significant supercurrent [6]. Even more requirements are
imposed on spin-valve devices, which require monodomain F components
with uniform spin polarization. This can only be achieved by decreasing the
size of the F layers and by using the shape anisotropy. However, this puts
additional demands on the nano-scale spatial homogeneity of the F-alloys.
Another reason for decreasing the total area of S-F-S junctions is a very small
resistance per unit area, which require SQUID measurements [6].
The PtNi alloy, studied here, is probably one of the best candidates for the
F-material in nano-scale S-F devices because Pt and Ni form a solid solution
in any proportion [15], unlike CuNi and many other Ni and Fe based alloys,
which are prone to phase segregation [16]. The onset of ferromagnetism in
bulk Pt1−x Nix at room T occurs at x ≃ 40 at.% Ni [15, 17]. Increased interest
to PtNi alloys in recent years is associated with its magnetic and catalytic
properties and because of earlier controversies about its chemical stability.
The magnetic properties of bulk PtNi alloy will be discussed in section 1.3.4.
In this work nano-scale S-F-S Nb-Pt1−x Nix -Nb junctions are fabricated
by 3D Focused Ion Beam (FIB) nano-sculpturing, which allows fabrication
of junctions with area down to ∼ 70 × 80 nm2 . The Pt1−x Nix alloys with
the Ni concentration ranging from 0 to 70 at.% are used as F material. The
nanometer size of the junctions both facilitates the mono-domain state in the
F-barrier and allows measurements with conventional technique due to sufficiently large junction resistance. To characterize the Pt1−x Nix thin films, I
study the anomalous Hall effect and perform nano-scale analysis of chemical
composition of the Pt1−x Nix thin films by means of energy dispersive X-ray
spectroscopy (EDS). To characterize the fabricated junctions I perform the
following measurements: current-voltage, field and temperature dependence
of critical current and dependence of critical current on Ni concentration
and barrier layer thickness. It is observed that the Curie temperature of the
Pt1−x Nix thin films decreases in a non-linear manner with Ni concentration
and that the critical current density of the Nb-Pt1−x Nix -Nb junctions decreases non-monotonously with increasing Ni concentration, which may be
due to switching into the π state [6].
5
1.2. JOSEPHSON EFFECT
1.2
1.2.1
Josephson effect
DC and AC Josephson effects
As it was mentioned in section 1.1, some supercurrent can exist between two
superconductors separated by a weak link (normal metal, insulator, semiconductor, superconductor with smaller critical temperature (Tc ), geometrical
constriction) and its value is proportional to the sine of the difference
ϕ = θ1 − θ2
(1.1)
of the phases of the superconductor order parameters Ψ1 = |Ψ1 | exp (iθ1 ) and
Ψ2 = |Ψ2 | exp (iθ2 )
Is = Ic sin ϕ.
(1.2)
This is the DC Josephson effect. With a fixed DC voltage V across the
junction (voltage biased junction), the phase ϕ will vary linearly with time
and the current will oscillate with amplitude Is and frequency proprtional to
V
dϕ
2e
= V.
(1.3)
dt
~
This is the AC Josephson effect. This result is a consequence of the quantum
mechanical principle that the time derivative of the phase is proportional
to the energy of a state. Thus, the time derivative of a phase difference is
proportional to the voltage in a charged system.
The equation (1.2) is the simplest and commonly used current-phase relation to describe ordinary Josephson junctions. There are several general
properties of the current-phase relation: if there is no current across the junction, Is = 0, then the phase difference ϕ = 0; Is is 2π periodic function since
a change of phase by 2π in any of the electrodes is not accompanied by a
change in their physical state; changing the direction of a supercurrent flow
across the junction must cause a change of the sign of the phase difference,
therefore Is (ϕ) = −Is (−ϕ) [18].
1.2.2
Proximity effect in S-N-S Josephson junctions
Consider a junction with a normal metal (N) as a barrier layer. In this case
Cooper pairs can penetrate the normal metal to some distance ξn known as
the coherent length. If the electron motion is diffusive, the normal metal
is ”dirty” (ln ≪ ξn ), this distance is proportional to the thermal diffusion
length scale
p
ξn(dirty) = ~D/kB T ,
(1.4)
where D = 13 vF ln is the diffusion coefficient, ln is the electron mean free path
and vF is Fermi velocity. In the case of a ”clean” normal metal (ln ≫ ξn )
the corresponding characteristic distance is
ξn(clean) = ~vF /2πkB T.
(1.5)
6
CHAPTER 1. INTRODUCTION
Therefore, superconductivity may be induced in the normal metal and this
phenomena is called the proximity effect. The induced superconducting wave
function exponentially decays in normal metal
Ψ = Ψ0 exp (−x/ξn ),
where Ψ0 is order parameter at S-N interface. The wave functions of superconducting electrodes interfere in the region of their overlap, with the
consequence that phase coherence is established between superconductors.
Fig.1.1 shows the decay of order parameters of left and right superconductors into the N barrier layer. The jumps at the left and right S-N interfaces
are due to an interface transparency γB = Rb σn /ξn , where Rb is the S-N
boundary resistance per unit area and σn is the conductivity of N layer [19].
S
N
S
Fig. 1.1. Schematic of the proximity effect in S-N-S Josephson junction. The solid line
represents the decay of order parameter into the N metal. The jump at the S-N interface
is due to interface transparency.
A unique characteristic of the superconducting proximity effect is the Andreev reflection revealed at the microscopic level. A.F. Andreev [20] demonstrated how single-electron states of the normal metal are converted into
Cooper pairs and also explained the conversion at the interface of the dissipative electrical current into the non-dissipative supercurrent. An electron in
the barrier layer with energy lower than the superconducting energy gap can
not enter into the superconductor. In this case, the electron will penetrate
into superconductor but with another electron from the normal metal, with
opposite spin, in order to build a Cooper pair. The second electron leaves a
hole below the Fermi level in the normal electrode. In order to satisfy the
conservation laws this hole must have exactly the same energy as the first
electron and its momentum must have the same value but opposite direction
(since the hole’s mass is negative). Thus, a charge 2e is carried away, but all
the energy is returned back when an electron diffuses through the interface.
7
1.2. JOSEPHSON EFFECT
The hole is consequently Andreev reflected at the second interface and is
converted back to an electron, leading to the destruction of a Cooper pair.
As a result of this cycle, a pair of correlated electrons is transferred from one
superconductor to another.
1.2.3
Dynamics of Josephson junctions
Supercurrent can flow through a Josephson junction either by tunneling
through an insulating barrier or by diffusing through a normal barrier (proximity effect). Consider a Josephson junction connected to a DC current
source. Slowly increase the current and measure the resulting voltage across
the junction.
For I = Is ≤ Ic , the voltage across the junction is zero and only the
supercurrent flows across the junction. The phase changes from ϕ = 0 at
Is = 0 to ϕ = π/2 at Is = Ic . Since the supercurrent is dissipationless, the
energy will be stored in the supercurrent in the junction during increasing
the current from 0 to Ic . This energy is given by the time integral of the
voltage, according to general expressio (1.3), times the current (1.2)
E = Ej (1 − cos ϕ) .
(1.6)
Here Ej = ~Ic /2e = Φ0 Ic /2π is called the Josephson coupling energy.
When I > Ic , a quasiparticle (normal) current can flow across the junction
by tunneling of unpaired electrons from one electrode to the other (if the
barrier is insulator) or by the flow of unpaired electrons in the barrier (if it
is a normal metal). This current is often approximated by an ohmic relation
In = V /R in case of S-N-S type of junction. To complete the picture one
should also consider a displacement current Id = C dV
due to capacitance C
dt
between electrodes (junction capacitance).
The dynamics of Josephson junction is described by the so-called resistively and capacitively shunted junction (RCSJ) model. The RCSJ model
combines the channels described above for the supercurrent, the normal current and the displacement current into a circuit model. An equivalent circuit
for this model is shown in Fig. 1.2 (left). Since the channels are parallel, the
total current will be the sum of the currents from all three channels
I = Ic sin ϕ +
V
dV
+C
.
R
dt
Using the AC Josephson relation this expression can be rewritten as
I = Ic sin ϕ +
~ dϕ ~C d2 ϕ
+
.
2eR dt
2e dt2
This equation describes the phase dynamics of the Josephson junction.
(1.7)
8
CHAPTER 1. INTRODUCTION
When C is small, the voltage across the junction at I > Ic can be found
from (1.7) (without last term) and (1.3). This voltage is periodic function of
time
I 2 − Ic2
V (t) = R
,
I + Ic cos ωt
p
where ω = 2eR I 2 − Ic2 /~.
2E j
0
I=0
Π
2Π
Ωp
3Π
4Π
j
I=0.5Ic
I=Ic
I=1.5Ic
Fig. 1.2. (Left) Equivalent circuit diagram for the RCSJ model. From left to right are the
supercurrent, capacitive and resistive channels. (Right) Washboard potential of the RCSJ
model for the different bias currents.
The equation (1.7) can be considered as equation of motion of a damped
and driven pendulum were C represents moment of inertia, 1/R represents
damping and Ic represents gravitation. The applied current I is the driving
force. The natural frequency of the motion, which is, in case of Josephson
junction, called Jospehson plasma frequency, and given by
ωp (0) = (2eIc /~C)1/2 .
This expression is only valid in the absence of applied current. At the finite
bias current, the plasma frequency is ωp (I) = ωp (0)(1 − ( IIc )2 )1/4 .
Qualitative insight into the junction dynamics can be obtained from the
so-called tilted washboard model (Fig. 1.2 (right)). It is also convenient to
consider the equation (1.7) as equation of motion of a particle with a position
given by ϕ, mass given by C and a velocity given by ϕ̇. The particle moves
in the potential, given by (1.6) minus the energy done by the current source
Esource = ~I
ϕ, and is subjected to the viscous drag force given by the conduc2e
tance 1/R. The bias current, I, corresponds to the external force, which tilts
the potential. The kinetic energy of such particle is equal to energy CV 2 /2
stored in the capacitive channel when there is a time-varying voltage across
the junction. In the case when I < Ic , the particle is confined to one of the
1.2. JOSEPHSON EFFECT
9
potential minima, where it oscillates back and force at the plasma frequency.
The time average of dϕ
, and hence the time averaged voltage, is zero in this
dt
state. The local minima in the washboard potential disappear and ϕ evolves
in time when the current I exceed Ic . The dynamic case is associated with
a finite voltage across the junction which increases with increasing bias current. The particle becomes retrapped in one of the minima of the washboard
when the bias current is reduced from above Ic . The current, at which it
retrapps, Ir , depends on the inertial term given by C. There are two types of
junction namely overdamped and underdamped junctions. The particle has
small mass, and thus small inertia, in the overdamped case and it becomes
immediately retrapped at the current Ir = Ic . In contrast, it is necessary to
reduce the current to a retrapping current Ir < Ic in the underdamped case.
The particle now has a large mass and can overshoot the minimum. This
leads to a hysteretic current-voltage (I-V) curve for an underdamped junction. The McCumber parameter, βc , is a measure of the degree of damping
in a junction
2e
βc = Ic R2 C.
~
The junction is overdamped when β . 1. In opposite (underdamped) case,
the energy stored in the capacitor must be taken into account [21].
1.2.4
Magnetic properties of Josephson junctions
The important characteristic of a superconductor is that it screens magnetic
fields. The applied field will only penetrate a very short distance, known
as the London penetration depth λ, into the superconductor, which is the
characteristic length over which the magnetic field decays exponentially. If a
Josephson junction is placed in an external magnetic field, its dynamics will
be altered because the field will penetrate a distance λJ into the junction.
λJ is a Josephson penetration depth and is given by
s
r
Φ0 c
Φ0
λJ =
[Si
units:
λ
=
],
(1.8)
J
8π 2 Jc d magn
2πJc µ0 d magn
where Jc is the critical current density and d magn is the so-called magnetic
thickness. λJ ≫ λ since the Josephson currents are much weaker than the
ordinary superconducting screening currents. λJ is very important characteristic since it determines the ”magnetic size” of the junction. When the
length of the junction is smaller than λJ , the field will penetrate the junction
uniformly and the junction is called ”short”. If the length is bigger than λJ ,
the flux dynamics of the junction starts to be important and the junction is
called ”long”.
Consider the ”short” thin film type of Josephson junction. The junction
is formed by two thin films which are separated by a barrier layer in a place
10
CHAPTER 1. INTRODUCTION
H
0
x
t
dl
Imax/Ic
1
L
x+Dx
d1
B
z
y
d2
x
-3
-2
-1
0
1
2
Φ/Φ0
Fig. 1.3. (Left) Josephson junction in the magnetic field H0 . The thicknesses of two superconducting electrodes are d1 and d2 . (Right) Simulated, according to (1.17), dependence
of the maximum supercurrent on the external magnetic field.
where they overlap each other. The external magnetic field, H0 , is applied
in y-axis direction perpendicular to the junction side L as it is shown in Fig.
1.3 (left). The thicknesses of two thin films, d1(2) , are of the order of λ . In
this case the field will completely penetrate superconducting electrodes and
the supercurrent density in electrodes is given by the quantum-generalized
second London equation [21]
c
Φ0
J1(2) =
∇θ1(2) − A ,
(1.9)
4πλ2 2π
where A is the magnetic vector potential. In the presence of field B in the
barrier, the phase difference will have a gradient along the junction length
L and can be found by integration of equation (1.9) over the infinitesimal
contour of length 2dl, covering the barrier of thickness t ≪ d1(2) (Fig. 1.3
(left))
Z
Z
∇θ1 dl +
∇θ2 dl = θ1 (x) − θ1 (x + ∆x) + θ2 (x + ∆x) − θ2 (x) =
C1
C2
2π
=
Φ0
4πλ2
[J2 − J1 ] + Bt ∆x.
c
Taking into account expression (1.1) and definition of derivative one can find
dϕ(x)
2π 4πλ2
=
[J2 − J1 ] + Bt .
(1.10)
dx
Φ0
c
c
J1(2) can be found from the Maxwell’s equation J1(2) = 4π
rotH1(2) , where
H1(2) is the field in the electrodes 1 and 2 and is given by the second London
equation for magnetic field in the electrodes 1 and 2
H1(2) + λ2 rot rotH1(2) = 0.
(1.11)
1.3. INTRODUCTION TO FERROMAGNETISM
11
Taking into account the symmetry of the problem (H1(2) changes only in
z-axis direction), the equation (1.11) can be rewritten as
d 2H1(2) (z)
H1(2) (z)
=
.
dz
λ2
(1.12)
Using the boundary conditions H1(2) (0) = B and H1 (d1 ) = H2 (−d2 ) = H0 ,
J1(2) can be calculated
h
i
h
i
z
d1(2) ∓z
d1(2)
c ±H0 cosh λ ∓ B cosh
cosech λ
λ
J1(2) =
,
(1.13)
4πλ
and
dϕ(x)
2π
=
(BΛ − H0 S) .
(1.14)
dx
Φ0
Here Λ = t + λ coth dλ1 + λ coth dλ2 and S = λ cosech dλ1 + λ cosech dλ2 .
When d1(2) . λ, screening by electrodes is weak, B ≈ H0 , and (1.14) can be
simplified
dϕ(x)
2πH0 magn
=
d
,
(1.15)
dx
Φ0
where
d
magn
d1
d2
= t + λ tanh
+ λ tanh
2λ
2λ
(1.16)
is magnetic thickness for thin films. Therefore thin film junctions are less
sensitive to magnetic field [22].
0
The integration of (1.15) gives ϕ(x) = 2πH
d magn x + C, and, using DC
Φ0
Josephson relation, the total maximum supercurrent through the junction is
sin(πΦ/Φ0 ) ,
Imax = Ic (1.17)
πΦ/Φ0 where Φ = H0 Ld magn is the total magnetic flux through the junction. Imax
is the periodic function of Φ/Φ0 and is equal to zero when the total magnetic
flux is equal to an integer number of Φ0 . Such diffraction pattern is called
the Fraunhofer pattern (Fig. 1.3 (right)) in analogy to diffraction of light
through a slit.
1.3
1.3.1
Introduction to ferromagnetism
Basic concepts
Ferromagnetism is magnetically ordered state in which most of atomic magnetic moments are oriented in one direction. Consequently, the ferromagnetic state is characterized by a net spontaneous magnetization M i.e. a
12
CHAPTER 1. INTRODUCTION
magnetization even in zero external field. Ferromagnetism occurs at temperature below the so-called Curie temperature, TCurie , in the absence of
external field. Upon application of a weak magnetic field, the magnetization increases rapidly to a high value called the saturation magnetization.
Ferromagnets tend to stay magnetized to some extent after being subjected
to an external magnetic field. This tendency to ”remember their magnetic
history” is called hysteresis. The fraction of the saturation magnetization
which is retained when the driving field is removed is called the remanence
of the material.
The first, successful, attempt to explain magnetic ordering was made by P.
Weiss. He postulated that a ferromagnet is composed of small, spontaneously
magnetized, regions (domains) and the total magnetic moment is the vector
sum of the magnetic moments of the individual domains. Each domain is
spontaneously magnetized because of a strong internal (molecular) magnetic
field which is proportional to M. The effective field acting on any magnetic
moment within the domain may be written as H = H0 + αM, where H0 is
external field and αM is the Weiss molecular field.
A quantitative description of ferromagnetism requires a quantum theory
treatment. The important consequence of the Pauli exclusion principle is the
dependence of the energy of a system of fermions (electrons) on the total spin
of the system. This can be explained by existence of an additional exchange
interaction. The exchange interaction appears when the wave functions of
neighboring electrons overlap (direct exchange). The exact expression for
an exchange interaction can not be obtained even in the simplest case of
two-electron system. There are different approximations to the exchange
interactions exist. One of the simplest is the Heisenberg Hamiltonian
X
Hex = −
Jij Si Sj .
i6=j
This interaction favors parallel orientation of the spin magnetic moments Si
and Sj if the parameter Jij > 0 and antiparallel spin orientation if Jij < 0.
The exchange interaction has an electrostatic origin and depends on the
mutual spin orientation of the electrons in the system, and is responsible for
the magnetic ordering.
Magnetic ordering occurs only in materials which have unfilled electron
shell (orbital) in the atoms. Only non saturated internal electronic shells
(i.e. those protected to form chemical bonds by shells further out from the
nucleus) can remain unfilled when an atom incorporated in a multiatomic
system. Such unfilled shell creates a non-zero total magnetic moment. The
total magnetic moment is the sum of the spin and the orbital momentum of
the electrons. For 3d transition metals, such as Ni, Fe, Co, etc., the total
magnetic moment is largely determined by the spin moment.
There are two models of magnetism. The first assumes that the magnetic
electrons are localized at the atomic sites, and can be found in states that are
1.3. INTRODUCTION TO FERROMAGNETISM
13
similar to the free atom. This is the model of magnetism of localized electrons. On the other hand, the model of itinerant electrons considers that the
magnetic electrons are the conduction electrons which are totally delocalize,
and free to travel anywhere in the sample. In this case, the magnetic moment
carried by a magnetic atom differs markedly from the free atom. The first
model well describes the rare earth metals (4f) while second is appropriate
in case of metals and alloys of the 3d transition series.
The magnetic moments of the rare earth metals are associated both with
the spin and the orbital angular momentum of the f electrons. The f electrons have small spatial extension making them weakly sensitive to their
local environment. The s or d electrons delocalize to some extent to become
conduction electrons. Typically, the spatial extension of f electrons is far less
than the interatomic distances, and correspondingly there can be no direct interaction between 4f electrons of different atoms. Rather, it is the conduction
electrons which couple the magnetic moments. The conduction electron is
polarized when interacting with a localized magnetic moment. The electron
passes to the next localized magnetic moment and interacts with it. Thus
the two localized magnetic moments are correlated. This type of indirect
exchange mechanism is called the Ruderman-Kittel-Kasuya-Yosida (RKKY)
exchange.
In case of 3d transition metals, the localized magnetic moment is carried
by d electrons. These electrons are not very much affected by the lattice,
but they overlap a little with the orbitals of neighboring atoms forming a
conduction band. The ferromagnetic state arises from a difference in the
occupation of the bands with spin up and down. This can happen in some
cases when energy is minimized upon transferring of some electrons from
one spin state to the other. The main reason for this comes from the Pauli
exclusion principle, which postulates that two electrons with the same spin
can never be in the same ”place” at the same time. This means that two
electrons with opposite spins will repel each other more than two electrons
with the same spin, as the latter feel each other less because they can never
be in the same place. The criterion for instability with respect to ferromagnetism is IN(EF ) > 1, where I is the difference in repulsion energy between
electrons with opposite spins and electrons with the same spin direction and
N(EF ) is the density of electron states at the Fermi level. This criterion
is called Stoner’s criterion. Note that this criterion shows that strength of
ferromagnetic metals is largely depend on the density of states at the Fermi
level [23].
1.3.2
Anomalous Hall effect
In ferromagnetic materials, the Hall resistivity includes an additional contribution, known as the anomalous Hall effect. The magnetic induction
B = H0 + 4πM should be in use when considering the Hall effect in magnetic
14
CHAPTER 1. INTRODUCTION
materials. The Hall field of ferromagnet plate, in external magnetic field,
H0 , perpendicular to the plate surface (z-direction), can be written as
Ey = RBz Jx + Ra 4πMz Jx ,
(1.18)
where Jx is the density of the current along the plate length, M is spontaneous magnetization of ferromagnet, R and Ra are normal (Lorenz force on
charge carrier) and anomalous (proportional to the sample magnetization)
Hall coefficients respectively. The Hall resistivity is given by ρH = Ey /Jx .
The first term in (1.18) describes the normal Hall effect. The contribution
in the Hall field, which is proportional to M, is called the anomalous Hall
effect. The coefficient Ra is one to two orders bigger than R and has strong
temperature dependence. In alloys, the magnitude and sign of Ra depend on
the concentration of components. In general, the sign of Ra can be different
from the sign of R. The presence of external field, in the anomalous Hall
effect, is needed only to magnetize the sample. The anomalous Hall effect
can be observed even without external magnetic field in case of monodomain
sample.
1.3.3
Magnetism in thin film structures
The magnetism of metals is very sensitive to the local atomic environment.
This environment influences both the strength and sign of the exchange interaction, and it determines the local anisotropy of the material. The atomic
environment at the surface of a material, or at the interface between two different materials, is strongly modified in comparison to the bulk material. At
a surface the number of neighbors is reduced and, moreover, the symmetry
is not the same as for the bulk material. Obviously, any surface effect may
have a substantial impact on the properties of a thin film.
The magnetic moment of ferromagnetic transition metals is predicted to
be higher at the surface than in the bulk. This is due to a narrowing of the
d-band because of the lower number of atom’s neighbours. This results in
an increase of the density of states N(EF ) at the Fermi level. In the transition metals which are characterized by itinerant magnetism, the increase of
N(EF ) leads to an increase of the surface magnetism (Stoner criterion).
The magnetic properties of the thin films may also depend on the nature of the substrate. If the cell matching between the substrate and the
deposited film is not perfect, both materials will be deformed depending on
their respective rigidities and thicknesses. This results in a variation of the
cell parameter of the deposited material causing a change in its magnetic
properties. Contraction of the cell results in a reduction in the magnetic
moment while a dilation of the cell tends to increase the magnetic moment.
1.3. INTRODUCTION TO FERROMAGNETISM
15
The choice of substrate can also influence the electronic structure of the deposited film. Certain substrates have little or no direct electronic interaction
with the deposited films, while the use of others leads to hybridization effects
between the electrons of the magnetic film and those of the substrate.
The ordering temperature of ferromagnetic materials (the Curie
temperature) is given by
TC = J0 S(S+1)/3kB ,
where S is the value of an individual atom’s spin, and J0 is the sum of the
exchange interactions with all neighbours. According to this expression, TC
is proportional to the number of neighbours. Therefore, one can expect a
reduction in the ordering temperature at the surface of a ferromagnetic material. This is true in a number of real cases, where one then refers to the
creation of dead layers at interfaces and surfaces. However, in certain cases,
the dominant effect is not a reduction but an increase in the ordering temperature at the surface. For transition metals, this is again due to increase
of N(EF ). This strengthens the magnetic stability at the surface according
to the Stoner criterion.
Magnetic anisotropy is the dependence of the magnetic energy of a
system on the direction of magnetization within the sample. Thin films
show very large anisotropy phenomena. The main reason for this is that
their shape usually favors an orientation of magnetization within the plane
in order to minimize the energy. This energy is often described by a uniaxial
anisotropy
E = −K cos2 θ,
where θ is the angle between the magnetization and the normal to the plane
of the sample. By definition, a positive value of K implies an easy axis
of magnetization perpendicular to the plane of the sample (θ = 0) while a
negative value of K corresponds to an easy plane of magnetization (θ = π/2).
There are different sources of magnetic anisotropy in thin films. They can be
divided into two groups, those concerning the volume of the material (Kv ),
and those concerning its surface or interface (Ks ). The anisotropy of a thin
film of thickness t is given by K = Kv + Ks /t. The reorientation of the
easy axis of magnetization from in the plane to the direction perpendicular
to the plane, as a function of the film thickness, has been observed in a large
number of transition metal thin films and multilayers [24, 23].
1.3.4
Theory of PtNi alloys
The choice of the ferromagnet layer has a great impact on current transport
characteristics of S-F-S junctions. PtNi alloys are also interesting because
16
CHAPTER 1. INTRODUCTION
of their magnetic and catalytic properties. Magnetic moment distribution
in bulk PtNi alloys has been studied quite exhaustively by the high field
susceptibility measurements [16] and by neutron scattering experiments [25].
It was observed that the PtNi alloys have a spatially homogeneous moment
distribution. This is in sharp contrast to CuNi and many other nickel alloys
which exhibit ferromagnetic clustering. The bulk PtNi alloy can exist in
two phases: chemically disordered face centered cubic (fcc), with Pt and Ni
atoms randomly distributed over the crystal lattice, and chemically ordered
face centered tetragonal (fct) or fcc depending on Ni concentration. The
concentration dependence of the magnetic moment and Curie temperature
is different for the ordered and disordered alloys, particularly at the lower Ni
concentrations.
Both experimental and theoretical analysis of local magnetic moment
for disordered alloys show that the magnetization decreases monotonically
with increasing Pt concentration. The zero temperature magnetization vanishes at around 60 at.% concentration of Pt. The structure is fcc without
any distortion for all Pt concentrations but any short-ranged ordering has
a great impact on the local Ni magnetic moment. The magnetism of Ni in
alloys strongly depends on its near environment. For example, if Ni is not
surrounded by at least six other Ni in a fcc lattice, then it loses its magnetic moment altogether at any temperature. Thus the effect of environment
should be taking into account while considering the local magnetic moment
of Ni [17].
There is a tetragonal distortion of the lattice in ordered alloys at about
50 at.% concentration of Pt. The tetragonal distortion increases the Ni-Ni
distance leading to a self-dilution in this system. This results in vanishing of
the local magnetic moment on Ni at this Pt concentration as it was experimentally observed in [26, 17]. However, the theoretical analysis given in [17]
predict reasonably large magnetic moments on Ni at 75 at.% concentration
of Pt. The alloy at this concentration has fcc structure without tetragonal
distortion.
1.4
1.4.1
S-F-S Josephson junction
Origin of order parameter oscillation in S-F bilayer
Superconducting correlations induced in the ferromagnet differ from those in
S-N proximity systems. In a normal metal, the destruction of Cooper pairs
is due to thermal fluctuations (characteristic energy E = kB T ). In case of
S-F system, there is one more depairing factor in the ferromagnet, namely
exchange energy Eex . Exchange energy will try to orient all spins in one
direction. This will destroy the Cooper pair which forms from electrons with
17
1.4. S-F-S JOSEPHSON JUNCTION
opposite spins. Thus the length scale, on which the Cooper pair can penetrate
the ferromagnet, is also affected by Eex . Moreover, the superconducting order
parameter displays oscillatory behavior under the influence of the exchange
energy of ferromagnet.
The exchange energy is the main depairing factor if TCurie is much higher
than superconducting critical temperature Tc (Eex ≫ kB T ). In this case and
for a ”dirty” ferromagnet, the Cooper pair can penetrate the ferromagnet at
distance ξF1 = (~D/Eex )1/2 . Here D is the diffusion coefficient in ferromagnet
layer. The order parameter will oscillate with oscillation period 2πξF2 , where
ξF2 = ξF1 .
In case of Eex > kB T , ξF1 and ξF2 are not equal and can be written as [6]
ξF1,2 =
s
~D
2
(πkB T ) +
2
Eex
1/2
.
(1.19)
± πkB T
The expression (1.19) is valid for a ”dirty” ferromagnet.
A qualitative picture of appearance of the order parameter oscillation can
be obtained for ”clean” metals in framework of quantum mechanics. In the S-
S
F
(a)
p1
p1
p2
- pF
pF
Dp
- p+
F
p2
p+
Dp
F
z
S
x
h
F
(b)
p1
- pF
p1
p2
pF
- pF -Dp
p2
pF -Dp
Fig. 1.4. Appearance of the nonzero net momentum in ferromagnet close to S-F interface
under exchange field h. (a) and (b) correspond to different spin configurations of electrons
in pair. Adapted from [27].
18
CHAPTER 1. INTRODUCTION
F bilayer the correlated electrons in the pair, having opposite spin directions,
experience the exchange field of the ferromagnet, resulting in appearance of
net nonzero momentum △Q of the Cooper pair [27]. Consider the Cooper
pair formed by two electrons with opposite (lying on the Fermi surface)
momentums pF and −pF , so that the total momentum of the pair equal to
zero. The Cooper pair inside the ferromagnet, can be described by
 R

Z
i
Ψ(r) = C exp 
p(r) dr ,
(1.20)
~
0
where p(r) is momentum of the Cooper pair and the integral is from position
at S-F interface (r = 0) to arbitrary point R inside the ferromagnet. Under
the influence of Zeeman interaction only, the single particle Hamiltonian for
electron with a spin can be written as
p̂2
e~
−
(σ̂ · h),
2m 2mc
where h is the exchange field. In semiclassical approximation, this Hamiltonian can be replaced with two classical Hamiltonians for electrons with spin
up and spin down
Ĥ =
p2
p2
− Eex ,
H↓ =
+ Eex .
(1.21)
2m
2m
In one dimension case, the electrons, forming the Cooper pair, may change
their momentums in x direction only. According to (1.21), the spin up electron in the pair lowers its energy by Eex and the spin down electron raises
its energy by the same amount upon entering the F region. In order for
each electron to conserve its total energy, and thus keep the Copper pair, the
spin up electron must increase its kinetic energy while the spin down must
decrease. Consider the case when electron with momentum p1 has a spin
down and electron with momentum p2 has a spin up (Fig. 1.4 (a)). Then,
the kinetic energies for electrons with momentums p1 = −pF and p2 = pF in
F region should be written as
H↑ =
(−pF + △p1 )2
(−pF )2
=
− Eex
2m
2m
(1.22)
(pF + △p2 )2
(pF )2
↑
E2 =
=
+ Eex ,
2m
2m
where pF is the Fermi momentum. From (1.22), each electron acquires a
positive gain of momentum △p1,2 = Eex /υF so that that the Cooper pair,
as whole, acquires the momentum △Q = 2Eex /υF . As a result it starts to
move in positive direction from S-F interface. According to (1.20), the wave
function of pair acquires additional exponential factor and can be written as
i2Eex
Ψa (x) = ΨF (x) exp
x ,
~υF
E1↓ =
1.4. S-F-S JOSEPHSON JUNCTION
19
where ΨF (x) = Ψ0 exp (−x/ξF1 ) describes damping of superconductor order
parameter by analogy with the S-N proximity effect and Ψ0 is order parameter at the S-F interface.
In opposite case, the electron with momentum p1 has the spin up and
electron with momentum p2 has the spin down (Fig. 1.4 (b)). In this case,
both electrons acquire a negative gain of momentum △p1,2 = −Eex /υF . The
Cooper pair, as whole, acquires the momentum △Q = −2Eex /υF and the
wave function can be written as
i2Eex
Ψb (x) = ΨF (x) exp −
x .
~υF
Since states Ψa (x) and Ψb (x) are equally probable, the real state will be
superposition of these states
1
x
2Eex
Ψ(x) = (Ψa (x) + Ψb (x)) = Ψ0 exp −
cos
x .
2
ξF1
~υF
The real part of the superconducting order parameter is decaying oscillatory
function (Fig. 1.5). The wavelength of such oscillations is
λ=
π~υF
Eex
which gives for clean ferromagnet ξF2 = ~υF /2Eex .
One should bear in mind that the picture described above is purely qualitative. It implies continuity of the order parameter at the S-F interface.
This corresponds to a very weak ferromagnet with extremely small exchange
energy. Other drawbacks are temperature independence and describing the
Cooper pair by the common wave function. To get more correct picture one
should consider correlation of independent electrons rather than the Cooper
pair as one whole.
1.4.2
Theory of S-F-S π junction
To describe the relevant experimental situation one needs to use a microscopic approach. The main objects of this approach are the Bogoliubov-de
Gennes equations or the Green’s function technique which describe correlation between electrons with parallel and antiparallel spins. These equations
can be reduced to Eilenberger [28] equations by averaging with respect to
relative electron motion in the pair. The Eilenberger equations can be further simplified to Usadel [29] equations in case when the electron mean free
path is small (diffusive approximation) and the ferromagnet is unperturbed
by the proximity with the superconductor (the pairing potential ∆ is absent
in the ferromagnet).
20
CHAPTER 1. INTRODUCTION
F
S
l
Fig. 1.5. Schematic of the order parameter oscillations in S-F bilayer. The real part of the
order parameter is decaying oscillatory function.
In the ”clean” limit the critical current of S-F-S junction can be written
as [30]
π∆2 |sin (4Eex tf /~υF )|
Ic Rn =
,
(1.23)
4e
4Eex tf /~υF
whereas in case of diffusive (”dirty”) limit, the critical current is given by
π∆2 cos(2y) sinh(2y) + sin(2y) cosh(2y) Ic Rn =
4y
(1.24)
,
4eTc cosh(4y) − cos(4y)
where y = tf /ξF , tf is ferromagnet barrier layer thickness, Rn is the normal
state resistance of the junction and ξF ≡ ξF2 = (~D/Eex )1/2 [31]. In the
”clean” limit critical current decay as ξF /tf while in diffusive limit it decays
exponentially as e−tf /ξF .
Chapter 2
Experimental methods
2.1
2.1.1
Sample fabrication
Deposition of S-F-S multilayers and test ferromagnetic single-layers
All multilayered structures and single films used in this work were deposited
by DC magnetron sputtering. Sputtering is the most widely used laboratory
technique for preparing thin films. The majority of sputtering machines
works with a base pressure of 10−8 to 10−6 mbar. An inert gas, usually Ar,
is introduced into the chamber in a controlled manner, and maintained at a
pressure between 5 · 10−4 and 2 · 10−2 mbar. The gas is ionized in a strong
electric field creating a plasma. The positive Ar ions are attracted towards a
target of the material to be deposited. The bombardment of the target with
these relatively heavy ions results in atoms being torn out of the target, i.e.
sputtered away. These atoms travel through the plasma and the neutral gas,
and condense on a wafer. In the case of metallic targets, the ions are attracted
to the target by applying a constant negative voltage to the target (DC
sputtering). In magnetron sputtering systems, the field lines of permanent
magnets placed behind the target act to channel the electric charges, and
thus concentrate the plasma in the vicinity of the target, resulting in an
increased sputtering rate.
Before starting the sputtering process, the oxidized 2” Si wafer was cleaned
in oxygen plasma over 10 minutes with the RF power of 50 W in order to remove organic contamination and therefore to improve the adhesion between
wafer and material to be sputtered. The Nb-Pt1−x Nix -Nb-Pt1−x Nix multilayers were sputtered in a single vacuum cycle with the base pressure about
10−6 mbar. The Ar pressure was maintained at 9.3 · 10−3 and 6.7 · 10−3 mbar
during Nb and Pt1−x Nix sputtering respectively. This provides mean free
path about 2.3 cm for Nb and 3.2 cm for Pt1−x Nix . The lower and upper Nb
layers were sputtered with the smallest distance (6 cm) between the 6” Nb
target and wafer and the DC power of 0.35 kW for over 3 min. 15 sec. and
22
CHAPTER 2. EXPERIMENTAL METHODS
5 min. for lower and upper layers respectively. The Nb deposition rate was
estimated prior, using the lift-off process, to 11.5 Å/sec. Thus the thicknesses
of lower and upper layers of Nb expected to be 225 and 350 nm respectively.
The smallest distance between the target and wafer during deposition and
high deposition rate for Nb were chosen to provide the highest Tc .
The layers of Pt1−x Nix were sputtered at the maximum distance (10 cm)
from the 1.5” target to the wafer and the DC power of 0.05 kW with sputtering rate of 1.67 Å/sec for over 3 minutes.
The edge of the 2” wafer was positioned just under the target center. This
does not cause any problems with uniformity on Nb deposition, since the
target is large (6” diameter). On the other hand, such off-axis displacement
creates the thickness gradient from 20 nm to 30 nm, in the middle of wafer, for
Pt1−x Nix , since the target is only 1,5” diameter. Therefore, S-F-S junctions
with different F-layer thickness, but the same Ni-content could be made later
on from different parts of the same wafer.
Fig. 2.1. (Left) SEM image of the deposited Nb-Pt1−x Nix -Nb-Pt1−x Nix multilayer side
view. The picture was taken at the angle of 59◦ from the normal to the sample surface.
The thicknesses of lower and upper layers of Nb are ∼ 225 and 350 nm respectively. (Right)
Profile of the electrodes made from the deposited multilayer structure. The total thickness
of deposited multilayer structure is close to 600 nm from which the thickness of Pt1−x Nix
layers can be estimated to ∼ 12.5 nm.
The left panel in Fig. 2.1 shows the Scanning Electron Microscope (SEM)
image of the deposited multilayer side view from which it can be verified
the thicknesses of upper and lower layers of Nb. The right panel in Fig.
2.1 shows the profile of six electrodes made from the deposited multilayer
structure (details of the multilayer pattering will be discussed in the next
sections). The profile was measured by KLA Tencor P-15 surface profiler
which has vertical resolution up to 0.1 Å. The measured sample was taken
2.1. SAMPLE FABRICATION
23
from the edge of wafer where Pt thickness expected to be less than 20 nm.
The total thickness of deposited multilayer structure is close to 600 nm which
is in agreement with calculated thickness.
Due to large cost of Pt, it was not possible to make a separate target for
each PtNi concentration. Instead, to vary the composition of the Pt1−x Nix
alloys, the corresponding number of rectangular shaped Ni segments were
symmetrically attached on top of the pure Pt sputtering target. Fig. 2.2
shows the Pt target with attached eight Ni segments installed in the magnetron sputter Nordiko 2000 [32]. Each rectangle covers about 7.4 % of the
total Pt target area from which the material is effectively sputtered. This
area is confined within the erosion track with diameter of 19.5 mm, in the
middle, and width of 7 mm as it is shown in Fig. 2.3. Since the erosion is
not uniform over the width, the effective width was taken to be half of the
real width. One should bear in mind that it is very difficult to calculate,
or even estimate, how the Ni affects the magnetic field and thereby the deposition rate. The real concentration of Ni in the film deposited from the
target, shown in Fig. 2.2, corresponds to about 54 at.% of Ni. The details
of determination of Ni concentration will be discussed in section 3.1.
The deposited structure consists of two Nb layers separated by Pt1−x Nix
layer. One additional layer of Pt1−x Nix was deposited on top of the upper
Nb layer. The schematic of the structure is shown in Fig. 2.4(1). The
intermediate layer of Pt1−x Nix was used as the junction barrier, while the
upper layer was employed for improving adhesion with bonding contacts. At
the beginning of this work, I used Au, instead of Pt1−x Nix , as the contact
layer (upper layer). However, it was turned out that the deposition of Au
on top of Nb-Pt1−x Nix -Nb trilayer is inadmissible in case when anodization
is needed (see section 2.1.4).
In addition, test Pt1−x Nix single-layers were deposited on oxidized Si
wafer for analysis of ferromagnetic properties of Pt1−x Nix alloys. Deposition
was made at the same conditions as for the Pt1−x Nix layers implemented
in Nb-Pt1−x Nix -Nb-Pt1−x Nix multilayer used for junction fabrication. The
thicknesses of sputtered Pt1−x Nix single layers were in the range between 50
and 100 nm depending on the place on the wafer.
2.1.2
Pattering of S-F-S multilayers and test ferromagnetic single-layers
The deposited structures were patterned with standard photolithography, reactive ion etching and Ar+ milling (Fig. 2.4). Photolithography is a process
when light transfers the pattern from the original mask onto the substrate
which is coated with a light sensitive layer (photoresist). This layer absorbs
the light at the particular wavelength and undergoes a photochemical reaction. Before starting photolithography process, a dicing saw was used to cut
the wafer on chips with a size of 5 by 5 mm. Then the sample was spin
24
CHAPTER 2. EXPERIMENTAL METHODS
Fig. 2.2. Pt target with 8 attached rectangular shaped Ni segments providing the total
effective deposition area of Ni about 59.2 %.
Fig. 2.3. 1.5 inch Pt target. The position of rectangular shaped Ni segment with the size
4.5 × 14 mm is shown schematically. The erosion track has the diameter of 19.5 mm, in the
middle, (shown by blue circle) and width of 7 mm. The rectangular shaped Ni segment
covers ∼ 7.4% of the total Pt target area from which the material is effectively sputtered.
The region, from which the material is effectively sputtered, is confined within two dashed
circles.
25
2.1. SAMPLE FABRICATION
coated with positive photoresist for 1 min. at 4000 rpm and soft-baked on a
hotplate for 1 min. at 90◦ C. During soft-baking, solvents evaporate from the
photoresist. After exposure with UV light (λ ∼ 365 nm), irradiated areas of
photoresist were dissolved in developer. In order to remove residue of irradiated photoresist, the sample was cleaned in oxygen plasma over 20 seconds
with the RF power of 100 W.
The etching of Pt1−x Nix layers was done by Ar+ milling in chemically
assisted ion beam etcher (CAIBE). In this process, the argon ions, generated
and accelerated in the ion source, reach the sample and physically mill the
unprotected by photoresist areas of the sample. Since the electrons, created
1
5
Nb
PtNi
2
6
SiO2
7
3
8
4
9
Fig. 2.4. 1. Sputtering of the Nb-Pt1−x Nix -Nb-Pt1−x Nix multilayer, 2. Spin coating with
the positive photoresist, 3. Exposure with UV light, 4. Development, 5. Ar+ milling of
the upper Pt1−x Nix layer, 6. CF4 RIE etching of the upper Nb layer, 7. Ar+ milling of
the lower Pt1−x Nix layer, 8. CF4 RIE etching of the lower Nb layer, 9. Removal of the
residual photoresist.
during ionization of argon gas, also hit the sample causing heating of photoresist one should be very careful with milling time. Long milling time causes
the problem with the following removal of unexposed photoresist. During
the Ar+ milling, the Ar gas was added into the process independently of ion
beam, increasing the number of ions bombarding the sample. The process
pressure was about 2 · 10−4 mbar. With the Ar ion beam current of 6.4 mA
and accelerating voltage of 500 V, 20-30 nm of Pt1−x Nix was etched in about
10 minutes.
In principle, 225 and 350 nm of Nb can also be milled in CAIBE, but long
time needed to do this will cause the hardening of photoresist which will be
impossible to remove afterwards. For this reason, the etching of Nb layers
was done in the Inductively Coupled Plasma/Reactive Ion Etcher (ICP/RIE)
with a process gas of tetrafluoromethane (CF4 ) mixed with oxygen in proportion 20 to 1.
26
CHAPTER 2. EXPERIMENTAL METHODS
In this system, the plasma is generated near the bottom electrode and
in the upper part of the chamber independent of each other. The RF power
applied to a bottom electrode is capacitively coupled, and offset by a self
generated DC-bias. The RF power applied to a water-cooled antenna, winded
around the ceramic part of the chamber, couples to the plasma inductively.
The vertical electric field near the bottom electrode provides directionality
for anisotropic etching. The RF power of 100 W was applied to the antenna
and 55 W was applied to the sample stage (bottom electrode). Fig. 2.5
shows the ICP/RIE Oxford Plasmalab System 100 [32].
Fig. 2.5. The Oxford Plasmalab 100 ICP/RIE is equipped with one load-lock serving two
process chambers. The plasma is generated near the bottom electrode (sample stage) and
in the upper part of the chamber independent of each other. The process chambers are
equipped with the laser interferometer endpoint system.
The CF4 ICP/RIE combines physical etching (milling) by F+ and chemical etching by chemical reaction with F atoms. In CF4 plasma, F atoms are
formed by electron impact dissociation of CF4 . The combination of physical etching with chemical provides high anisotropy (contribution of physical
etching) and high etching rate (contribution of chemical etching). The chemical etching also provides high material selectivity of the etching process. The
etching was done over 5 and 7 minutes for lower and upper layer of Nb respectively with the process pressure of 80 mtorr. The process chamber is
equipped with the laser interferometer endpoint detector. It can work in two
modes, either in the ”reflectance mode” or in the ”interferometric mode”.
In the ”reflectance mode”, one can measure the intensity changes of light
27
2.1. SAMPLE FABRICATION
b)
PtNi
SiO2
50 mm
a)
I XX
VH
c)
Y
Z
5 mm
H
X
or
Fig. 2.6. a) Pattern of six electrodes on the chip with size ∼ 5 × 5mm2 . Each electrode
is the Nb-Pt1−x Nix -Nb-Pt1−x Nix multilayered structure deposited on the SiO2 wafer. b)
20 times magnified central part of the chip. The width of the electrodes in the middle of
the chip ∼ 6µm. c) Pattern for the Hall effect measurements. The pattern is the single
layer of Pt1−x Nix deposited on the SiO2 wafer. The current is applied along the sample
and voltage is measured in the transverse direction.
reflected from the sample surface during etching. In the ”interferometric
mode”, the interference signals from two interfaces (e.g. the top of a transparent layer and its bottom) are monitored. The system is also equipped with
CCD camera allowing accurate laser beam positioning. During the etching
of Nb, the ”reflectance mode” was used. Since the intensity of reflected light
from Nb is different from light reflected from Pt1−x Nix and SiO2 , the etching
can be precisely stopped when Nb is etched away completely. This prevents
undesired additional undercut of Nb layer.
Finally, after all layers were etched, the unexposed photoresist was removed in acetone. In order to remove residue of photoresist, the sample was
cleaned in oxygen plasma over 1 minute with the RF power of 100 W or in
ultrasonic bench. Six electrodes with the width ∼ 6µm were made on each
chip.
To do magnetic characterization of the Pt1−x Nix alloys, the test Pt1−x Nix
single-layers were pattered, to be able to measure Hall voltage, with photolithography and Ar+ milling. The schematics of Hall measurement and
electrodes patterns are depicted in Fig. 2.6.
28
CHAPTER 2. EXPERIMENTAL METHODS
The rest of fabrication processing of Nb-Pt1−x Nix -Nb-Pt1−x Nix multilayers was performed in the dual beam Scanning Electron Microscope-Focused
Ion Beam (SEM-FIB) workstation.
2.1.3
3D FIB nano-sculpturing
The FIB workstation is a very versatile and powerful tool for micro and
nano fabrication. In a typical FIB system a focused ion beam ejected from a
liquid metal ion source (Ga). The Ga+ ions are emitted and accelerated by
extractor voltage applied between liquid gallium source and cathode. The
ions are shaped into a beam by a number of electrostatic lenses and apertures
and focused onto the sample surface. The ions penetrate into the sample and
knock out the uppermost ions from the sample surface. The schematic of an
ion column is shown in the inset of Fig. 2.7. Alignment of the ion optics and
positioning of the beam is completely computer controlled which facilitates
easy handling. Characteristics of milling or deposition are defined using the
built-in software so the desired pattern may have basically any shape and
can just be drawn as the image on a computer screen. Milling is performed
by sputtering the material with the high energy (30 keV) Ga+ ions. The
milling rate is determined by the ion beam current.
In the FIB chamber there can also be one or several gas injection systems (GIS) that can be used either for deposition or increasing the milling
rate. The inset of Fig. 2.7 shows the schematic of typical dual beam SEMFIB workstation equipped with one GIS. The ion beam can also be used
for imaging, providing an ion induced secondary electron image of the sample. The image is produced by the electron contrast due to differences in
crystallographic orientation, topography etc. However, imagining leads to
implantation of Ga+ and milling of the sample so care has to be taken not
to etch away or destroy delicate feature during viewing.
During this work I used the FEI Nova 200 Dual Beam system which is
the FIB system combined with SEM. The main panel of Fig. 2.7 shows the
FEI Nova 200 system at AlbaNova nanofabrication laboratory. The sample
is loaded directly into the vacuum chamber via the side door. The system
is equipped with one GIS for deposition of Pt. There are two detectors in
this system, namely through-the-lens detector (TLD) and Everhart Thornely
detector (ETD). The TLD uses secondary and backscatter electrons (SE
and BE). It is mounted within the lens and therefore collects electrons from
immediately over the scanned area of the sample. The ETD is mounted
in the chamber above and to one side of the sample. It uses SE and BE
generated for collection outside of the lens. The ETD has worse resolution
but can provide better topography imaging. In additional, there is the CCD
camera installed inside the chamber. The working pressure for SEM is ∼
10−5 mbar and for FIB is ∼ 10−6 mbar. The ion beam current in this system
can be changed in steps from 1 pA to 20 nA by using a number of different
2.1. SAMPLE FABRICATION
29
Fig. 2.7. The main panel shows the FEI Nova 200 Dual Beam system. The electron gun
is pointed normal to the sample surface while ion gun is tilted over 52◦ from electron gun.
The system is equipped with one GIS for deposition of Pt. The inset shows the schematic
of typical dual beam system with one GIS. The main components of ion column are liquid
Ga ion source, cathode to extract the ions from the source and the number of apertures
and magnetic lenses to shape the ions into the beam.
apertures. Depending on the ion beam current, the milling spot size ranging
from 6 nm to 150 nm. The ion and electron guns are tilted with respect to
each other at the angle of 52◦ . The FIB-SEM allows the SEM to perform
imaging and the FIB to perform milling simultaneously or sequentially. Thus
the sample can be imaged during preparation without any damage. For the
FEI Nova 200, the sample stage can be tilted from −10◦ to 59◦ . Rotation of
±180◦ about an axis normal to the sample stage is also possible.
For 3D FIB nano-sculpturing [33] we used the custom-built 45◦ wedge
holder. The ion beam is perpendicular to the sample surface when the sample
stage is tilted over 7◦ as it shown in the left panel of Fig. 2.8. The ion beam
becomes parallel to the sample surface by rotating the sample stage over 180◦
and tilting over 7◦ (see the right panel of Fig. 2.8).
Both pictures shown in Fig. 2.8 are taken by the CCD camera inside
the chamber. In the right corner, of both of these pictures, is the tilted FIB
column and next to the left is the vertical SEM column. The sample was
30
CHAPTER 2. EXPERIMENTAL METHODS
Pt
x
Ni
1-
x
Fig. 2.8. (Left) Position of the sample holder for narrowing of electrode. The sample is
mounted on the side of the 45◦ wedge holder. In the right corner is the tilted FIB column
and next to the left is the vertical SEM column. The picture is taken by the CCD camera
inside the chamber. The ion beam is normal to the sample surface at the sample stage tilt
of 7◦ . (Right) Position of the sample holder for making the side cuts into the electrode.
The sample stage is rotated over 180◦ in respect to the position shown in the left panel
and tilted to the same angle of 7◦ . At this position the ion beam is parallel to the sample
surface
Nb
Nb
Fig. 2.9. The mail panel shows the FIB image of the junction top view after the second
top cut. First, the electrode was narrowed from ∼ 6µm to ∼ 0.8µm with the FIB current
of 100 pA and then to the final junction width of ∼ 206 nm with the FIB current of 10 pA.
The inset shows the schematic of the junction side view before the side cuts were made.
2.1. SAMPLE FABRICATION
31
glued on one of the side of the 45◦ wedge holder by a silver paint and then
the electrodes were grounded to the holder either by silver paint or wedge
bonded using aluminium or gold wires.
The sculpturing of the junction was performed in the following sequence.
First, the electrodes were narrowed from ∼ 6µm to ∼ 0.5µm with the FIB
current of 100 pA (milling spot size ∼ 20 nm), accelerating voltage 30 kV
and with the position of ion beam perpendicular to the sample surface. The
high current was used to decrease the milling time. The milling rate was
estimated to ∼ 23.5 nm/s for ion beam current of 100 pA. It is convenient
to describe the milling rate in Volume per Dose (m3 /C) which is calculated
V olume
as Volume per Dose = Beam current
= 2.35 · 10−10 m3 /C.
×Time
Then the electrodes were narrowed further to the final size (the junction
width) ranging from ∼ 80 nm to 300 nm with the ion beam current of 10 pA
(milling spot size ∼ 6 nm) and accelerating voltage 30 kV, see Fig. 2.9. Using
the smaller ion beam current allows longer time for imagining the sample
without serious damage. Hence, it allows better focusing and compensation
Fig. 2.10. The main panel shows the SEM image of the junction side view after the side
cuts were made. The junction has the length ∼ 230 nm. The left and right cuts are
overmilled into the upper and lower Nb layers respectively for ∼ 50 nm and left side cut
into SiO2 /Si for ∼ 100 nm. The inset shows the schematic of the junction side view. The
arrow indicates the direction of supercurrent. The layer of Ptx Ni1−x sandwiched between
two Nb layers and enclosed between left and right side cuts serves as a Josephson junction
barrier. The Ptx Ni1−x layer on top of upper Nb layer serves to improve adhesion with
bonding contacts.
32
CHAPTER 2. EXPERIMENTAL METHODS
for astigmatism. Another advantage of using smaller ion beam current is
better resolution because of the smaller spot size. From the other side it is
ineffective to perform the narrowing in one step with the ion beam current of
10 pA because of the long milling time due to low milling rate. The milling
rate for current of 10 pA is ∼ 3.0 nm/s and calculated Volume per Dose is
2.96 · 10−10 m3 /C. The small difference in Volume per Dose for 100 and 10
pA is probably because of the actual ion beam current was less than 100 pA.
The time required for narrowing of one electrode to the final junction
width is about two hours, in case of using only ion beam of 10 pA, in compare
to about 15 minutes in case of stepwise narrowing.
The side cuts were made with the ion beam close to be parallel to the
sample surface with the ion beam current of 10 pA. The distance between
two side cuts, which determine the junction length, varied from ∼ 70 nm to
1500 nm for different junctions.
Fig. 2.10 shows the SEM image of the junction side view with distance
between two side cuts ∼ 230 nm. The arrow in the inset of Fig. 2.10 schematically indicates the direction of supercurrent so that the intermediate layer
of Ptx Ni1−x , enclosed between two side cuts, forms the Josephson junction
barrier. Fig. 2.11 shows the SEM top image of the same junction as it is
shown in Fig. 2.10. The junction has the width ∼ 160 nm.
Fig. 2.11. SEM image (main panel) and schematic (inset) of the junction top view after
the side cuts were made. The junction is the same as it is depicted in Fig. 2.10. The
width of the junction is ∼ 160 nm.
2.1. SAMPLE FABRICATION
33
The small undercut of the upper Nb layer can appear since the ion beam is
not perfectly parallel to the sample surface. In order to avoid such undercuts
the side cut must overmill into the upper Nb layer by the value which is
depend on the actual alignment of the ion beam and the junction width. The
minimum overmill distance is given by a = tan α · b, where b is a junction
width and α is an angle between ion beam and normal to the junction side.
The left and right cuts of the Junction shown in Fig. 2.10 are overmilled into
the upper and lower Nb layers respectively for ∼ 50 nm. The left side cut is
also overmilled into SiO2 /Si for ∼ 100 nm. The effect of undercut of the Nb
layer and the way how to get rid of it will be discussed in section 3.3.
Fig. 2.12 shows the SEM image of typical chip, which is ready for measurements, where the junction is made in the middle of each electrode. In
total, there are six junctions made on one chip. Therefore junctions with the
same properties can be made with different geometries.
Fig. 2.12. SEM image of the chip with six junctions on it. Each junction is made in the
middle of each electrode.
2.1.4
Anodization
In order to eliminate possible short circuits of the junction due to resputtered conducting materials (mostly Nb) during FIB etching, some junctions
were anodized. Anodization is an electrolytic process in which a metal, in
our case multilayer of Nb-Pt1−x Nix -Nb-Pt1−x Nix , serves as the anode in a
34
CHAPTER 2. EXPERIMENTAL METHODS
suitable electrolyte. When a current passes through the film in the electrolytic solution, the surface of the film is converted to its oxide form. This
oxidation progresses from the solution inward, towards the metal, with the
final thickness determined by the applied voltage [34]. Prior anodization,
all electrodes with Josephson junction on a chip was short-circuited so that
anodization was performed simultaneously, for all junctions. The electrolytic
solution of ammonium pentaborate (165 gr.) with ethylene glycol (1120 ml.)
and deionized water (760 ml.) was used.
The anodization process proceeded as follows:
1. The cathode in the electrolytic solution was grounded while the sample
(anode) was connected to a power supply;
2. The voltage from the power supply was ramped, from 0 V to 16 V,
maintaining the initial constant current of about 10 mA through the
sample. The overall ramp time was approximately 1 min;
3. The voltage was holding constant at 16 V. During the voltage hold
time, the current through the sample dropped exponentially as the
oxide layer densified;
4. When the current level reached the value of about 0.2 mA, the power
supply was abruptly switched off.
The total immersion time was approximately 15 min.
As it was mentioned in section 2.1.1, the anodization is inadmissible in
case of having the Au as contact layer. The reason for this is that the used
electrolytic solution has etching influence on Au. The result of etching of
Au by electrolytic solution is destroying of junction. Fig. 2.13 shows the
junction with Au on top of Nb-Pt1−x Nix -Nb trilayer after anodization.
2.2
2.2.1
Sample characterization
EDS Characterization of PtNi thin films
To characterize the Pt1−x Nix thin films, I studied the anomalous Hall effect
and performed an analysis of chemical composition of single-layer Pt1−x Nix
thin films by means of energy dispersive X-ray spectroscopy (EDS). The
experimental setup for the anomalous Hall effect measurements is roughly
the same as for junction characterization and will be described in the next
subsection while in this subsection I will briefly describe EDS technique [35].
The EDS is add-on that can be used for analytical microscopy in both
SEM and Transmission Electron Microscope (TEM). When used in TEM the
resolution cab nearly as good as the spot size, i.e. a couple of nm. For SEM
on the other hand, the resolution is in the order of µm since the electrons can
2.2. SAMPLE CHARACTERIZATION
35
Fig. 2.13. SEM image of the sample with Au as contact layer after anodization. The used
electrolytic solution etched Au and destroyed the junction.
be scattered around the volume much larger than the spot size, and X-rays
generated can easily reach the specimen surface. During this work I used the
JEOL JSM-7000F system which is the high resolution SEM equipped with
energy dispersive and wavelength dispersive spectrometers.
When an incident electron hits the specimen, it causes an inner shell
electron to be ejected from the specimen atom. An electron from an outer
shell then jumps to the inner shell. The difference in energy between the
shells is sent out as an X-ray. The different X-ray peak can be seen in a
EDS spectrum. The K-peak indicates that the first ejected electron originated to the K-shell, the L-peak means the L-shell and so on. The indices
α, β... indicate from where the second electron jumps. Since each element
has a unique electronic structure, the series of generated X-ray photons are
characteristic of the particular element emitting the X-rays. The intensity of
the X-rays is proportional to number of atoms generating the X-rays. Note,
that not only the characteristic X-rays are generated when the electron beam
hits the sample. There are also secondary electrons and backscattered electrons. At the surface of the sample, X-rays emission is enhanced by scattered
electrons from below. Moreover, those X-rays produced at depth of analytical volume must pass through a certain distance within the sample and risk
being absorbed. The escape energy of an element is the energy threshold
needed to initiate inner sphere ionization and generate characteristic X-rays.
36
CHAPTER 2. EXPERIMENTAL METHODS
In addition to incident electrons, other X-rays can also exceed this threshold. Ionizing X-rays can be generated by ionization of other elements with
higher escape energy. All these factors should be taken into account while
processing the measured data.
In SEM-based EDS system, the generated X-rays are detected by a lithium
drifted silicon (Si(Li)) detector. When an X-ray strikes the detector, it will
generate a photoelectron within the body of the Si. As this photoelectron
travels through the Si, it generates electron-hole pairs (every 3.8 eV). The
electrons and holes are attracted to opposite ends of the detector with the
aid of a strong electric field. The size of the current pulse thus generated
depends on the number of electron-hole pairs created, which in turn depends
on the energy of the incoming X-ray. The pulses are then stored in a multichannel analyzer where each channel represents a certain amplitude interval
of the pulses. Thus, an X-ray spectrum can be acquired giving information
on the elemental composition of the material under examination. In a spectrum, the exponentially decreasing energy known as the Bremsstrahlug can
be seen. This is background X-rays produced by inelastic scattering (loss of
energy) of the primary electron beam in the specimen. It covers a range of
energies up to the energy of the electron beam. For SEM analysis, this is the
background in the spectrum above which rise the characteristic peaks from
the elements.
Electron probe microanalysis has traditionally been used as a bulk analytical technique for the characterization of samples with the spatial resolution
∼ 1µm. Successful utilization of the technique requires an interplay between
the heterogeneity of the sample, the beam energy, and the X-ray energies.
Typical beam energies of 10-30 keV have excitation depth of 1-5 µm, lower
beam energies (5-10 keV) have excitation depth of 0.1-1 µm, and ultra-low
energies (below 5 keV) have excitation depth of 0.05-0.1 µm. However at such
low energies, quantitative complexities arise due to fewer X-ray lines available. When analyzing a thin film specimen with a thickness of the order of
hundred nanometers or less, incident electrons penetrate into the substrate.
In this case, the EDS analysis becomes a complicated task. The characteristic X-ray intensity from the thin film can be influenced by the parasitic
signal from the substrate [36, 37].
2.2.2
Low-temperature measurement setup
All measurements during this work were carried out using either a liquid
helium (He) dewar (left panel in Fig. 2.14) or cryogen-free magnet system
(right panel in Fig. 2.14) with a flowing gas insert. The sample was glued on
the chip holder by a silver paint and then wedge bonded using aluminium or
gold wires. The chip holder layout is designed so that it is always possible
to do a four point measurement of all six junctions in one cooling cycle.
The chip holder was mounted on a dipstick and then fixed in a gas flow
37
2.2. SAMPLE CHARACTERIZATION
dipstick
GAS
RESERVOIR
dry pump
gas flow insert
MEASUREMENT
SYSTEM
DRY
PUMP
COMPRESSOR
magnet
sample
Sample
Magnet
Needle valve
Fig. 2.14. The low-temperature setup involving the liquid helium dewar (left panel) and
cryogen-free system (right panel).
insert. In case of using the dewar, the gas flow insert was cooled in 4 He
dewar under continuous pumping. In such a refrigerator a small fraction of
the liquid 4 He from the main bath flows through a suitable flow impedance
into the insert. The sample is located in the vapour above the liquid 4 He.
The continuous pumping of the 4 He vapour allows to reach the temperature
about 1.6 K. In this case, the 4 He is pumped away to atmosphere. When
the dewar was used, the superconducting solenoid mounted on the insert or
built-in superconducting magnet was used for magnetic field measurements.
In case of using the cryogen-free magnet system, the 4 He is pumped to the gas
reservoir from which it condensed back into a helium pot and then trough the
needle valve into a sample space. In the later case, there is no waste of helium.
The system, used in this work, is equipped with 17 T superconducting magnet
and utilizes a pair of two stage cryocoolers to produce temperature of around
4.2 K at the magnet and allow operation of the gas flow insert between 1.6
K and room temperature. To determine the magnetic field, the Hall probe
was installed close to the sample.
For current-voltage (I-V) measurements I used four point contact method.
It means that the measurement of the voltage and applying of the current
were done at the different contacts. By using this method I measured only the
voltage across the junction and not the voltage across the contact resistance
of the probes and oxide layer.
The measured samples were always current biased. All I-V measurements
38
CHAPTER 2. EXPERIMENTAL METHODS
ADC
PXI
preamplifier
ADC
PC
-
+
preamplifier
LabVIEW
-
+
RSER
RS
JJ
Fig. 2.15. Diagram of the I-V measurement setup. RSER is the series resistance and RS is
the resistor used to measure the current.
were performed using real-time PCI eXtensions for Instrumentation (PXI)
system which is a rugged PC-based platform. The instrumentation is integrated by means of a LabVIEW-based measurement program. An arbitrary
waveform generator was used as a current source. The sample voltage was
measured using the 24-bit analog-to-digital converter. The software-based
lock-in amplifier was used to extract the resistance from I-V signal. The PXI
system allows to measure simultaneously different samples or/and to measure the signal from the sample and e.g. the signal from the Hall probe. A
schematic of the measurement setup is shown in Fig. 2.15. The biasing is
done by connecting a series resistor, another smaller resistor (100Ω) is used
in order to read out the current flowing through the circuit by measuring the
voltage. Both current (indirectly) and voltage is measured by using battery
driven differential preamplifiers. Simultaneously the Hall probe is current
biased and the voltage signal is used to calculate the magnetic field at the
sample.
Chapter 3
Results and discussion
3.1
Chemical composition of PtNi thin films
The study of chemical composition of thin films by EDS is not an easy task as
it seems to be at the first sigh. The reason for this is the presence of a thick
substrate material underneath analyzed thin film and small film thickness in
comparison to the whole analytical volume.
The typical spectrums for 5 keV and 15 keV electron beam voltages are
shown in Fig. 3.1 and Fig. 3.2 respectively. The capital letters indicate the
peaks which are used for determination of Ni, Pt, Si and O concentrations.
The spectrums were taken from the film with the thickness of 50 nm and
which was deposited from the target with 44.4 % Ni area. The incident
electron beam in this case was normal to the surface. The integrated peak
intensity is measured from each elemental peak in the sample and then the
background is removed (by digital filtering). This value from the sample is
then normalized to known standard values for each element. The treatment
of measured X-ray spectrum is usually done by the special software. In this
work INCA software was used. This software takes into account the so-called
matrix effect, i.e. the combined effect of all components of the sample other
than the desired on the measurement result. These effects will be different
for different accelerating voltages and correspondingly for different analytical
volumes. Thus it is important to know exactly the size and shape of the
analytical volume. The extended algorithm of Pouchou and Pichoir (XPP)
[38] is used to make the corrections for the effect on
• the electron interaction (depth of electron penetration and fraction of
backscattered electrons) with the sample (atomic number correction);
• the absorption of the emitted X-rays in the sample which reduces measured intensity;
• the fluorescence of secondary X-rays which increases measured intensity.
40
CHAPTER 3. RESULTS AND DISCUSSION
Pt
Ni LE
O
Ni LD
Si
Fig. 3.1. X-ray energy spectrum of the PtNi thin film with 44.4 % of Ni target area and
for the incident electron beam energy 5 keV. The capital letters indicate the peaks which
are used for determination of Ni, Pt, Si and O concentrations. The arrow indicates the
possible Si induced secondary fluorescence of Ni.
The silicon and oxygen signals on the spectrums shown in Fig. 3.1 and
Fig. 3.2 are coming from the oxidized Si wafer while carbon is due to contamination in the SEM. The Si peak become much stronger for 15 keV electron
beam. In this case the interaction volume mostly confined in the Si wafer.
From Fig. 3.1, the Si induced fluorescence effect (indicated by the arrow)
can be seen. In this case, the Ni Lα (0.85 keV) and Ni Lβ (0.87 keV) peaks
are used to estimate the Ni concentration. For electron beam energy 15 keV
(Fig. 3.2), the Si induced fluorescence effect can be neglected since the Ni
Kα (7.48 keV) and Ni Kβ (8.26 keV) peaks are used for determination of Ni
concentration.
Fig. 3.3 shows the dependence of Ni concentration of PtNi thin films on
the relative Ni target area. The thicknesses of PtNi are ranging from 50 to
100 nm. The error in Ni target area was taken ∼5 %. There are two sources
for this error. First, the exact size of Ni segment can slightly vary between
different segments and second, the erosion track of the target is not well
defined so there can be an error in track diameter. Both the Ni segment size
and the erosion track diameter were used in the determination of Ni target
area (see section 2.1.1).
Since the quantitative analysis routine, XPP, assumes that the material,
under examination, is a bulk material which is alloy rather than layered struc-
41
3.1. CHEMICAL COMPOSITION OF PTNI THIN FILMS
Si
O
Pt
Ni KDNi KE
Fig. 3.2. X-ray energy spectrum of PtNi thin film with 44.4 % of Ni target area and for
incident electron beam energy 15 keV. The capital letters indicate the peaks which are
used for determination of Ni, Pt, Si and O concentrations.
ture (Pt1−x Nix alloy on Si/SiO2 wafer), two different cases were considered.
First, it was assumed that the sample is only Pt1−x Nix alloy (Fig. 3.3(a))
and second the sample was considered to be the mixture of Pt1−x Nix alloy
with C, O and Si (Fig. 3.3(b)). From comparison of Fig. 3.3(a) and Fig.
60
Ni at.%
50
electron beam energy:
5 keV
10 keV
15 keV
30 keV
70
60
50
Ni at.%
70
40
30
40
30
20
20
0
0
10
20
30
40
50
60
Ni-target area (%)
70
(b)
10
(a)
10
0
electrone beam energy:
(including effect of C, O and Si)
5 keV
10 keV
15 keV
30 keV
80
0
10 20 30 40 50 60 70 80
Ni-target area (%)
Fig. 3.3. EDS measured Ni concentration of the PtNi thin films as a function of the
relative Ni target area for different electron beam energies. (a) the sample is considered as
bulk PtNi alloy and (b) the sample is considered as mixture of PtNi alloy with C, O and
Si. The dashed lines represent linear fit to Ni concentrations at different electron beam
energies with twice of concentration weight for 5 keV and thrice for 15 and 30 keV.
42
CHAPTER 3. RESULTS AND DISCUSSION
3.3(b) it is seen that the difference between the two cases is rather small.
The Ni concentration in at.% corresponds to Ni target area in % (see Fig.
2.3) for the electron beam energy of 5 keV. The Ni concentration is higher
than Ni target area for the beam energy of 10 keV and lower for the beam
energies of 15 and 30 keV. The difference in estimated Ni concentrations
between different electron beam energies is clearly seen for higher Ni target
areas. This difference can be due to the following reasons
• effect of the substrate which can provoke error in the correction of
secondary fluorescence by Si;
• change in the yield of backscattered electrons in the film due to the
film/substrate interface;
• secondary fluorescence of Ni by Pt in the film.
All these factors will give the rise to the error in XPP correction.
One possible reason for different Ni concentrations depending on electron
beam energy is the error in fluorescence correction. The fluorescence effect of
Si expect to be less in case of PtNi alloy on Si/SiO2 substrate in comparison
to the bulk Pt/Ni/Si/SiO2 alloy. In case of PtNi alloy on Si/SiO2 the amount
of X-rays which can cause secondary fluorescence is less due to energy loss at
the film/substrate interface. For higher electron beam energies the Si induced
fluorescence can be neglected while the error in fluorescence correction can
be important for lower beam energies. On the other hand, the change in
Ni concentration is rather small when we ignore the presence of Si/SiO2 at
all (see Fig. 3.3(a) and Fig. 3.3(b)). This implies that the difference
in measured Ni concentrations for different electron beam energies
can be only partly explained by the error in correction of Si induced
secondary fluorescence.
The conversion of the characteristic X-rays into the composition can only
be made correctly if it is exactly known, where the X-rays are being produced.
The generation of X-rays as a function of depth z is represented by the Xray depth distribution function φ(ρz), where ρ is the density of a sample
material. This function describes the volume and shape of analytical volume
[36]. The shape of the φ(ρz) curve for the thin film is different from that
for the bulk standard, because the scattering of incident electrons at the
film/substrate interface is different from the scattering in the bulk specimen.
The backscattered electron yield at the film/substrate interface increases with
the atomic number of the substrate. Therefore, the X-ray production in the
film increases [39].
At beam energy of 5 keV, most of analytical volume is confined in the
film and not in the substrate. This can be seen in both Fig. 3.4(a) and
3.5(a) where the amount of Ni and Pt is much larger than the amount of Si
and O. There will be a lack of electrons at the film/substrate interface, and
3.1. CHEMICAL COMPOSITION OF PTNI THIN FILMS
43
consequently a lack of backscattering electrons, due to low energy of incident
electrons. Thus the effect of backscattering electrons will be less seen for
beam energy of 5 keV.
For electron energies of 15 keV and higher, the analytical volume is confined much deeper in the Si substrate as it can be seen from Fig. 3.4(b)
and 3.5(b) where the amount of Si is larger than all other elements. In this
case the probability for high energy incident electrons to be reflected at the
film/substrate interface is quite small. Moreover, the probability to be excited by backscattering electrons is higher for less energetic Pt M lines than
for high energetic Ni K lines. Those two types of lines are used to estimate
the Ni and Pt concentrations for electron beam energies of 15 and 30 keV.
However, at intermediate electron beam energies such as 10 keV, the analytical volume is enough confined within PtNi thin film. There are considerable amount of backscattering electrons from the film/substrate interface
with high enough energy. In this case the probability to have overestimated
value of concentration is higher for Ni since less energetic L lines are used for
quantitative analysis.
From the discussion above the following conclusions can be made. For
very low electron beam energies, the effect of the backscattering electrons
from the film/substrate interface is small simply due to lack of these electrons. At high electron beam energies, this effect is also small and has more
influence on the Pt concentration leading to slightly overestimated Pt concentration. However, for electron beam energy about 10 keV, the
effect of backscattering electrons from the film/substrate interface
is substantial and can lead to overestimated Ni concentration.
In order to further investigate the effect of the substrate on actual Ni
concentration, the dependence of Ni concentration on an angle of incidence
of electron beam was studied. Fig. 3.4 shows the dependence of Ni, Pt, Si
and O concentrations on the deviation angle from the normal to the surface
for thin film deposited from the target covered by 44.4 % of Ni. The results
are presented for the electron beam energies of 5 keV (Fig. 3.4 (a)) and 15
keV (Fig. 3.4 (b)).
The Ni concentration remains almost the same for different angles and
for different beam energies while the Pt concentration is not constant for the
electron beam energy of 5 keV. The contents of Si and O vary with electron
beam incident angle for both beam energies. The increase of oxygen contents
and decrease of Si with increasing the angle is expected since the interaction
volume will be now confined more in SiO2 layer than in Si. The increase of
oxygen is not proportional to decrease of Si for the electron beam energy of
5 keV. In this case, the Pt concentration decreases while Ni concentration
remains the same. Since the PtNi alloy is expected to be homogeneous,
the Pt and Ni concentrations should follow the same trend. In order to
understand whether this difference is due to error in correction procedure or
caused by change in angle, in Fig. 3.5 I plot the area of elemental peaks from
CHAPTER 3. RESULTS AND DISCUSSION
45
40
35
30
25
20
15
10
5
0
(a) (5 keV)
Pt
60
(b) (15 keV)
Si
50
Ni
40
O
at.%
at.%
44
30
O
20
Si
10
0
10
20
30
Pt
0
40
0
Ni
Deviation angle (degree)
10
20
30
40
Deviation angle (degree)
Fig. 3.4. Concentration of the thin film elements (Pt and Ni) and the substrate elements
(Si and O) as a function of electron beam incident angle for the electron beam energies of
5 keV (a) and 15 keV (b). The Ni concentration of the sample correspond to 44.4 % of
the relative Ni target area.
500
Pt
250
150
Ni
100
50
O
0
Si
0
10
Si
105
90
400
200
20
30
Deviation angle (degree)
Peak area (a.u.)
Peak area (a.u.)
(a) (5 keV)
(b) (15 keV)
300
7
6
200
0
10 20 30 40
Pt
100
0
40
0
10
20
30
O
Ni
40
Deviation angle (degree)
Fig. 3.5. Spectrum peak area of the thin film elements (Pt and Ni) and the substrate
elements (Si and O) as a function of electron beam incident angle for electron beam
energies of 5 keV (a) and 15 keV (b). The Ni concentration of the sample correspond
to 44.4 % of the relative Ni target area. The increase of Pt and Ni concentrations with
angle is due to increase of the analytical volume within the PtNi film. This change of the
analytical volume for high electron beam energies can be approximated by cos of deviation
angle as it is shown by solid lines in the inset.
3.1. CHEMICAL COMPOSITION OF PTNI THIN FILMS
45
the spectrum as a function of electron beam incident angle. Here the same
spectrum was used as in Fig. 3.4 but no correction was made to the data.
The correction is needed to get concentrations in the at.%.
The concentrations of Pt, Ni and O increase with increasing of angle while
the Si content has trend to decreases for electron beam energy of 5 keV. This
behavior is plausible since, as it was mentioned above, upon increasing the
angle, the interaction volume is confined more in PtNi/SiO2 layer and less in
Si. Such predictable behavior can be considered as evidence for presence of
an artifact in correction procedure for 5 keV which gives the Ni concentration
in at.% shown in Fig. 3.4 (a).
Similar dependence of Pt, Ni and O contents on the beam angle can
be seen for electron beam energy of 15 keV (Fig. 3.5 (b)) although less
pronounced than for 5 keV. This is because for higher energies the PtNi/SiO2
layer is very small part of the total interaction volume and it is not so sensitive
to changing the angle. The small increase of Pt and Ni concentrations is
well described by increase of the analytical volume within the PtNi film.
This change of the analytical volume for high electron beam energies can be
approximated by cosine of the deviation angle (solid lines in the inset of Fig.
3.5 (b)). The Si content for 15 keV behaves in a strange manner. It increases
with increasing of angle up to 20 degree and then starts to decreases for
30 and 40 degrees. This is somewhat surprising since one would expect the
continuous reduction of Si content with angle. It would probably require the
XPP correction in order to get correct qualitative picture in case of 15 keV
accelerating voltage.
In order to completely eliminate the effect of the substrate on the determination of Ni concentration, the dependence of Ni concentration on electron
beam energy for free standing PtNi flakes was studied. To do this, the PtNi
film was scratched and spread on the carbon substrate. Fig. 3.6 shows SEM
images of the flakes from which the EDS spectrums were taken. The film has
the thickness of 50 nm with the Ni concentration corresponds to 44.4 % of
the relative Ni target area.
Fig. 3.7 shows the average value of Ni and Pt concentrations, measured
in different places on different PtNi flakes, as a function of electron beam
energy. The difference in Ni (Pt) concentration between different
beam energies can not be attributed to the substrate effect but
rather can be explained by the error in correction of Ni X-ray
absorption in the film [37].
From the discussion above it becomes clear that the conventional quantitative correction for bulk specimen analysis can not be applied to the thin
film when using low electron beam energies. The XPP correction procedure
seems to work properly for the electron beam energies of 15 and 30 keV.
For the electron beam energies above 10 keV one can neglect the Si induce
secondary fluorescence effect. For electron beam energy of 10 keV, the effect
of backscattering electrons from the film/substrate interface is substantial
46
CHAPTER 3. RESULTS AND DISCUSSION
Fig. 3.6. SEM images of the PtNi flakes with the thickness of 50 nm scratched from the
PtNi thin film. The EDS spectrums were taken from different places on each flake. The
Ni concentration corresponds to 44.4 % of the relative Ni target area.
60
Pt
57
Ni at.%
54
51
48
45
42
Ni
39
5
10
15
20
Electron beam energy (keV)
Fig. 3.7. EDS measured average value of the Ni and Pt concentrations of the PtNi flakes
as a function of electron beam energy. The PtNi flakes were scratched from the film with
the Ni concentration corresponds to 44.4 % of the relative Ni target area and are shown
in Fig. 3.6.
3.2. MAGNETIC PROPERTIES OF PTNI THIN FILMS
47
and can lead to overestimated Ni concentration. The absorption probability
of light Ni L series, which are used for determination of Ni concentration in
case of low beam energies, is much higher than absorption probability of high
energy Ni K series. In general, the absorption is very difficult to correct when
working with a light elements. The error in X-ray absorption correction is
smaller at higher beam energies. It is also more difficult to correctly compensate the secondary fluorescence of very light Ni L series by Pt (in case of
low electron beam energy) than secondary fluorescence of Pt by Ni K series
(in case of high electron beam energy). In what follows, Ni concentrations
are obtained from the linear fit to EDS data at electron beam energies of 5,
10, 15 and 30 keV but with two times larger weight for 5 keV and three times
for 15 and 30 keV (dashed line in Fig. 3.3(b)). From the fit, the actual Ni
concentration is ∼1.1 times smaller than the relative Ni target area.
3.2
Magnetic properties of PtNi thin films
Magnetic properties of thin films can be quite different from that for the bulk
material. To characterize the ferromagnetic barrier layer in S-F-S Josephson
junction, I studied thin PtNi films with the thicknesses of 50-100 nm and
the Ni concentrations of 13, 27, 40 and 67 %. In order to measure the Hall
resistance, a magnetic filed was applied perpendicular to the thin film and
Hall voltage (VH ) was measured in transverse direction at constant current
bias in longitudinal direction (Ixx ) (see Fig. 2.6).
Fig. 3.8 shows the temperature dependence of the measured Hall resistances, RH , for films with the Ni concentrations of 13, 27, 40 and 67 at.%
and for two opposite field directions perpendicular to the film. The applied
field was ±0.1 T for the samples with 13, 27 and 40 at.% of Ni and ±0.15
T for the sample with 67 at.% of Ni. RH contains both longitudinal and
Hall contributions. Up to the Curie temperature, the longitudinal part is
dominant in RH since there is no difference between different field orientations. At the Curie temperature one can clearly see the onset of additional
contribution to RH from the anomalous Hall effect. This is true for 27, 40
and 67 at.% of Ni. Depending on the orientation of applied magnetic field,
the contribution to RH can be either positive (open circles in Fig. 3.8) or
negative (full squares in Fig. 3.8). As it was mentioned in section 1.3.2, the
anomalous Hall resistance has strong temperature dependence. The anomalous Hall resistance for the sample with 67 at.% of Ni (Fig. 3.9) is saturated
at T < 150 K after which the trend is the same for different field orientations.
Fig. 3.9 shows the temperature dependence of the pure Hall resistance,
∗
RH
, normalized by the absolute value of applied perpendicular magnetic
∗
field, for films with the Ni concentrations of 13, 27, 40 and 67 at.%. RH
was
determined as
[RH (H + ) − RH (H − )]
∗
RH
=
,
2
48
CHAPTER 3. RESULTS AND DISCUSSION
0
50
0,0024 a)
100
150
0
Pt0.87Ni0.13
100
200
300
b)
Pt0.73Ni0.27
0,004
RH (:)
0,0020
cooling @ 0.1 T
heating @ -0.1 T
cooling @ -0.1 T
heating @ 0.1 T
0,0016
c)
0,0144
cooling @ 0.15 T
heating @ -0.15 T
d)
Pt0.60Ni0.40
Pt0.33Ni0.67
0,0128
0,003
0,016
0,008
heating @ -0.1 T
heating @ 0.1 T
0,0112
0
50
100
150
0
100
200
0,000
300
T (K)
Fig. 3.8. Temperature dependence of the measured Hall resistances, RH , for films with N i
concentrations of 13 (a), 27 (b), 40 (c) and 67 (d) at.% and for the different field orientations (±0.1 and ±0.15 T) perpendicular to the film. The Curie temperature corresponds
to the onset of large additional contribution to RH from anomalous Hall effect, which can
be either positive or negative and has strong temperature dependence.
where RH (H ± ) are the measured Hall resistances for positive and negative
field directions shown in Fig. 3.8. This way contribution from the longitudinal resistance (which is even with respect to the field direction) is canceled
out, and only the pure Hall contribution (odd with respect to field orientation) is left. The sample with 67 at.% of Ni is in ferromagnetic state at
temperature close to room temperature while the samples with 27 and 40
∗
at.% of Ni have the Curie temperature at T ∼ 50 K. The values of RH
/H of
−3
the films with 27, 40 and 67 at.% of Ni ranging between 4 · 10 and 3 · 10−2
depending on Ni concentration and, as it was mentioned before, have strong
∗
temperature dependence. The smaller value (∼ 10−3 at T = 4 K) of RH
/H
for the sample with 13 at.% of Ni is due to superparamagnetic contribution
to magnetization (as shown below). It originates from the permanent magnetic moments of some or all of the constituent atoms or small ferromagnetic
clusters. On applying a magnetic field, the average direction of the moments
is modified and an induced magnetization parallel to the field appears. This
magnetization is lower at higher temperatures, i.e. when the thermal agitation is larger. For the sample with 13 at.% of Ni, the superparamagnetism
appears at T ∼ 20 K and has weaker temperature dependence than contri-
49
3.2. MAGNETIC PROPERTIES OF PTNI THIN FILMS
R H /H (:/T)
0,03
Ni concentration:
13 %
27 %
40 %
67 %
*
0,02
0,01
0,00
0
50
100
150
200
250
T (K)
∗
Fig. 3.9. Field normalized Hall resistance, RH
, as a function of temperature for different
Ni concentrations. The data are obtained from the measured Hall resistance, RH , by
subtracting the linear term due to longitudinal resistance. The Curie temperatures of
the samples with 27, 40 and 67 at.% of Ni correspond to the onset of a large additional
contribution to RH due to anomalous Hall effect. The small contribution to RH for the
sample with 13 at.% of Ni at T ∼ 20 K is superparamagnetic contribution to magnetization
which appears in magnetic field at low temperatures.
RH (:)
-1,0
-0,5
0,0
40 %
0,376
0,5
1,0
Tž2K
0,414
0,411
0,374
13 %
0,372
-1,0
-0,5
0,0
0,5
1,0
0,408
0,405
H (T)
Fig. 3.10. Hall resistance as a function of the magnetic field at T ≈ 2K for the Ni
concentrations of 13 (black line, left axis) and 40 at.% (red line, right axis). The Hall
effect is anomalous with saturation at |H| > 0.4T for the film with 40 at.% of Ni and
remains normal for the film with 13 at.% of Ni.
50
CHAPTER 3. RESULTS AND DISCUSSION
bution from the anomalous Hall effect.
Fig. 3.10 shows the Hall resistance as a function of magnetic field at
T ≈ 2 K. It is seen that for the film with 40 at.% of Ni (red line, right axis),
the Hall effect is anomalous with saturation at |H| > 0.4T . On the other
hand, the Hall effect remains normal (i.e., linear in field) for the film with
13% of Ni (black line, left axis), implying that this film remains paramagnetic
even at 2 K.
Fig. 3.11 shows the Hall resistance as a function of magnetic filed for the
film with 40 at.% of Ni at different temperature ranges. The value of Hall
resistance is different upon sweeping of magnetic field over the full cycle. This
is true for all temperature ranges. In the cases of e) and f) this difference
can be explained by the difference in the temperature between starting and
ending points. However in all other cases there is no distinguishable difference
in temperature upon the sweeping of magnetic field over the full cycle. The
variation of temperature during magnetic field sweeping is shown in the inset
for all temperature ranges. In a) the temperature is different between starting
and ending points but becomes the same after some time while the Hall
resistance remains different. Saturation magnetic field is about the same for
all temperature ranges, except for T ∼50 K, and is |H| & 0.4T . The Hall
resistance becomes linear in field at T ∼50 K.
Magnetization goes to zero at the Curie temperature as the power law
M ≈ (T − TCurie )2 . To determinate the Curie temperature, the longitudinal part of the measured resistance, RH , was subtracted from Fig. 3.8 and
then remaining part was plotted as a function of (T − TCurie )2 . Fig. 3.12
shows the remaining resistance of the film with 27 at.% of Ni as a function
of (T − TCurie )2 for the different possible TCurie . Two contributions to the
remaining resistance can be seen. These contributions are, most likely, the
superparamagnetic and the ferromagnetic contributions. The superparamagnetic contribution starts at slightly higher temperature than the ferromagnetic. The ferromagnetic part of RH , before saturation, has the most linear
dependence on (T − TCurie )2 at TCurie = 54 K.
Fig. 3.13 shows RH , after subtracting the longitudinal resistance, versus
(T − TCurie )2 for the film with 40 at.% of Ni. By decreasing TCurie from 68 to
45 K, the ferromagnetic contribution changes its curvature from the negative
to positive being the most linear at T = 54 K. However, at the temperature
decreases, another contribution, above TCurie , appears as it can be seen from
the inset of Fig. 3.13. This contribution becomes more pronounced at lower
TCurie . At the temperature ∼ 62 K, the non ferromagnetic contribution
to RH is small enough and the dependence of ferromagnetic contribution
on (T − TCurie )2 is still very close to linear. However, neither TCurie = 54
K nor TCurie = 62 K is in agreement with Fig. 3.11 f) which shows the
linear dependence of the Hall resistance on the magnetic field at T = 50 K.
Therefore, the significant superparamagnetic effect in the films at T > TCurie
complicates the exact determination of TCurie . Assuming that all the Hall
51
3.2. MAGNETIC PROPERTIES OF PTNI THIN FILMS
0,0
0,4
0,8
-0,8 -0,4
1,62
0,004
0,0
5,2
-1
a)
0
1
H (T)
-1
b)
1
T (K)
10,2
-1
0
20,22
0,004
20,19
d)
c)
0,000
-0,004
T (K)
10,3
0,004
0
H (T)
T=5.22-5.32 K
T=1.57-1.63 K
RH (:)
0,004
5,3
-0,004
0,000
0,8
1,60
1,58
0,000
0,4
T (K)
T (K)
-0,8 -0,4
1
-1
H (T)
0
H (T)
1
0,000
T=20.17-20.23 K
-0,004
-0,004
0,004
-1,4
-0,7
0,7
1,4
50,2
30,18
30,16
30,14
0,000
0,0
T (K)
T (K)
T=10.22-10.30 K
-1
0
50,1
1
H (T)
e)
0,004
-1
0
H (T) 1
0,000
f)
-0,004
-0,004
T=30.14-30.19 K
-0,8 -0,4
0,0
T=50.12-50.20 K
0,4
0,8
-0,8 -0,4
0,0
0,4
0,8
H (T)
Fig. 3.11. Hall resistance as a function of the magnetic filed for the film with 40 at.%
of Ni at different temperature ranges. The insets show the temperature variation during
the sweep of magnetic field for each temperature range. The value of Hall resistance is
different upon the sweeping of magnetic field over the full cycle. Saturation magnetic field
is |H| & 0.4 T for all cases except for T ∼50 K when the Hall resistance becomes linear
in field. The difference in Hall resistances between different field directions decreases with
temperature.
52
CHAPTER 3. RESULTS AND DISCUSSION
0,6 a) TC=33 K
TC=48 K TC=54 K
RH (m:)
TC=60 K
0,4
27 at.% of Ni
0,2
0,0
0
1500
3000
2
(T-TCurie ) (K)
Fig. 3.12. Hall resistance after subtracting the longitudinal part as a function of (T −
TCurie )2 for the Ni concentration of 27 at.%. The dependence is plotted for possible TCurie
of 33, 48, 54 and 60 K. There are two contributions to the remaining resistance. These
contributions are, most likely, the superparamagnetic and ferromagnetic contributions.
b)
40 at.% of Ni
TC=45 K
TC=54 K
TC=62 K
TC=68 K
RH (m:)
1,6
2
0
0,8
0,0
(T-TCurie ) (K)
150
300
RH (m:)
0,3
0,0
0
1500
2
3000
(T-TCurie ) (K)
Fig. 3.13. Hall resistance after subtracting the longitudinal part as a function of (T −
TCurie )2 for the Ni concentration of 40 at.%. The dependence is plotted for the possible
TCurie 45, 54, 62 and 68 K. The ferromagnetic part of RH , before saturation, has the most
linear dependence on (T − TCurie )2 at TCurie = 54 K. At TCurie = 62 K the dependence
is still quite linear but non ferromagnetic contribution is much less than for TCurie = 54
K as it can be seen from the inset.
53
3.2. MAGNETIC PROPERTIES OF PTNI THIN FILMS
signal at T > 50 K for the 40 at.% film is due to superparamagnetism I
∗
introduced the corresponding threshold level in the RH
/H plot in Fig. 3.9. I
∗
determined the TCurie as the temperature at which RH /H is larger than the
superparamagnetic threshold, as indicated by arrows in Fig. 3.9.
To characterize the strength of ferromagnetism of the PtNi thin films,
the left axis of Fig. 3.14 shows the normalized anomalous Hall resistance,
∗
RH
/H, taken from Fig. 3.9 at T =4.2 K (squares), for all measured films,
as a function of Ni concentration. The right axis of Fig. 3.14 shows the
estimated Curie temperatures of the films with 27, 40 and 67 at.% of Ni (open
circles) as a function of Ni concentration. As expected, both increase with
Ni concentration. The Curie temperature increases in a nonlinear manner
with increasing Ni concentration.
T=4.2K
300
R H /H (: / T)
0,03
0,02
200
*
TCurie (K)
0,01
0,00
0
100
10
20
30
40
50
60
0
70
Ni concentration (at.%)
∗
Fig. 3.14. Normalized Hall resistance, RH
/H, (full squares, left axis) taken from Fig. 3.9
at 4.2 K for the films with 13, 27, 40 and 67 at.% of Ni. The Curie temperature of the
films with 27, 40 and 67 at.% of Ni (open circles, right axis) determined from Fig. 3.8.
From above discussion the following conclusions can be made: The thin
films with 27, 40 and 67 at.% of Ni are, most likely, in the ferromagnetic
state at the low temperatures. The way how to determine TCurie remains
unclear especially for the film with low Ni concentration. The thin film with
13% of Ni remains in the paramagnetic or spin glass state down to T ≈2 K.
The Ni concentration of 27 at.% is smaller than the critical ferromagnetic
concentration experimentally observed for both disordered (40 at.% of Ni)
and ordered (50 at.% of Ni) PtNi bulk alloys (see section 1.3.4). In [17] was
calculated that the critical Ni concentration is 25 at.% for ordered PtNi alloy
which is very close to the result presented in this work. This is somewhat
surprising since the described here alloys are expected to be in the disordered
state in which, according to [17], zero temperature ferromagnetism appears
54
CHAPTER 3. RESULTS AND DISCUSSION
at 40 at.% of Ni. Also the Curie temperatures are higher than previously
reported for bulk alloys. It was reported in [42] that TCurie =161 K for disordered Pt0.40 Ni0.60 alloy in compare to TCurie =263 K reported in this work
for the thin film with 67 at.% of Ni.
The possibility to detect the Hall voltage in the thin films with applied
magnetic field perpendicular to the film plane indicates that, indeed, the
magnetic moment of PtNi thin films lies in the direction perpendicular to
the plane, at least in high magnetic fields [41].
3.3
Characterization of S-F-S Josephson junctions
Fig. 3.15 shows a resistive transition of the Nb-Pt0.40 Ni0.60 (20 nm)-Nb junction. Above Tc ∼ 9 K, the resistance ∼ 6Ω is predominantly the resistance
of the Nb bridge (See Fig. 2.11). From Fig. 3.15 one can see, that the
resistance of the bridge first drops abruptly at ∼ 8.8 K and then at ∼ 8.6 K.
These temperatures represent Tc of upper and lower Nb layers respectively.
The difference between Tc is because of the different structure of two Nb
7
100
50
R (:)
5
4
Ic (P A)
6
0
2
4
T (K)
3
6
Tc of upper and
lower Nb layers
2
Pt0.40Ni0.60
1
0
4
6
T (K)
8
10
12
Fig. 3.15. Temperature dependence of the normal state resistance for the Nb-Pt0.40 Ni0.60 Nb Josephson junction. The resistance (above T ∼ 9 K) ∼ 6Ω is the resistance of the Nb
bridge. The two transition temperatures at ∼ 8.8 and ∼ 8.6 K correspond to Tc of upper
and lower Nb layers. The inset shows the dependence of junction Ic on the temperature
for the same Josephson junction.
layers due to the substrate effect on the lower Nb layer and, to some extent,
due to different thicknesses of Nb layers and correspondingly the different
over all proximity effect of the Pt0.40 Ni0.60 interlayer. The resistive transition
of the junction itself is impossible to see on the main panel of Fig. 3.15.
3.3. CHARACTERIZATION OF S-F-S JOSEPHSON JUNCTIONS
55
The critical temperature of the junction with 60 % of Ni (the temperature
at which critical current became measurable) is defined from the dependence
of the junction critical current on the temperature (inset of Fig. 3.15) to
∼ 5 K. The Tc of the junction depends on the Ni concentration and becomes
close to 8 K for the junctions with zero Ni concentration.
The most basic measurement one can perform on a Josephson junction is
a current-voltage characterization. Fig 3.16 shows I-V curves of two junctions
with 0 at.% (full squares) and 40 at.% (open circles) of Ni in the absence of
external magnetic field and at the base temperature of 3.2 K. The thickness
of PtNi interlayer is 30 nm in both cases. The I-V characteristics of measured
0,4
2
Pt1.00Ni0.00 (17088 nm )
2
Pt0.60Ni0.40 (225640 nm )
I (mA)
0,2
H=0 T
T=3.2 K
0,0
-0,2
-0,4
-0,2
0,0
V (mV)
0,2
Fig. 3.16. I-V characteristics of the Josephson junctions with 0 at.% (full squares) and 40
at.% (open circles) of Ni in the absence of external magnetic field and at temperature of
3.2 K. The barrier thickness is 30 nm in both cases. The values of Rn are 0.6 Ω and 0.4
Ω for the junctions with 0 at.% and 40 at.% of Ni respectively.
junctions are well described by RCSJ model (see section 1.2.3). The normal
state resistances (Rn ) are 0.6 Ω and 0.4 Ω for the junctions with 0 at.% and 40
at.% of Ni respectively. The value of Rn provides the value of resistivity for
PtNi alloys which is ranging from ∼ 25µΩcm for pure Pt to several hundreds
µΩcm for the junctions with high Ni concentration. The appendix shows the
resistivity and some other characteristics of all measured junctions.
The I-V characteristics of the junctions with pure Pt and low Ni concentrations exhibit a hysteresis at low temperatures and low external magnetic
fields. So that the retrapping current (Ir ) at which the junction switch from
the resistive to the superconducting state is smaller than the critical current (Ic ). Fig 3.17 shows I-V curves for the Nb-Pt1.00 Ni0.00 -Nb Jospehson
junction at the magnetic fields of 0, 0.024 and 0.048 T. The hysteresis (the
difference between critical and retrapping currents) decreases with increasing
the temperature and vanishes at ∼ 4.5 K for the Nb-Pt1.00 Ni0.00 -Nb junction
56
CHAPTER 3. RESULTS AND DISCUSSION
0,28
2
Pt1.00Ni0.00 (17088 nm )
T=3.2 K
4
0,20
0T
0.024 T
0.048 T
0,16
0,00
I (mA)
I (mA)
0,24
T (K)
6
Ic
Ir
0,2
0,1
0,04
0,08
V (mV)
0,12
Fig. 3.17. I-V characteristics of the Nb-Pt1.00 Ni0.00 -Nb Josephson junction at the magnetic
fields of 0 (full squares), 0.024 (open triangles) and 0.048 (full circles) T. The hysteresis
disappears at 0.048 T. The inset shows the dependence of the Ic and Ir on the temperature
at zero magnetic field for the same Jospehson junction. The hysteresis disappears at
T ∼ 4.5 K.
as it is shown in the inset of Fig 3.17. The appearance of hysteresis can
not be explained within the RCSJ model. According to the RCSJ model,
the hysteresis is related to damping and appears
√in underdamped Josephson
junctions with quality factor at zero bias Q0 = β > 0.84. This requires the
capacitance (C) for Nb-Pt1.00 Ni0.00 -Nb junction to be equal ∼ 4pF . The overlap capacitance of the Nb-Pt1.00 Ni0.00 -Nb junction is small, approximately a
few femtofarads, due to small area of the junction (∼ 0.015µm2 ). The stray
capacitance was estimated to be of the same order of magnitude. Therefore,
the total C of this junction is insufficient for observing hysteresis within the
RCSJ model. Another origin for hysteresis can be self-heating phenomenon
[40]. Within the self-heating scenario, the retrapping current simply represents Ic at the elevated temperature due to power dissipation at the resistive
branch of the I-V curve. One way to check the origin of hysteresis is to study
the power dissipation dependence of Ir . It turns out, that the self-heating
scenario as well can not fully explain the presence of hysteresis in this junction. In general, the hysteresis in I-V curves is quite common phenomenon in
S-N-S type of Josephson junctions and can be attributed to non-equilibrium
phenomena or frequency dependent damping. More details about the origin
of hysteresis in the Nb-Pt1.00 Ni0.00 -Nb junction can be found in the appended
paper A.
Right panel of Fig. 3.18 shows the dependence of Ic on the in-plane
magnetic field, H|| , (Fraunofer pattern) for the junction with size of 1140×230
3.3. CHARACTERIZATION OF S-F-S JOSEPHSON JUNCTIONS
57
nm2 , Ni concentrations of 54 at.% and barrier layer thickness of 20 nm. The
field was applied across the longer (1140 nm) size. In general, the field can
be applied in either x-direction or y-direction, as it is shown in the left panel
of Fig 3.18, depending on the chip orientation on the sample holder. The
experimentally measured Ic (H|| ) curve is in a very good agreement with a
calculated field dependence of Ic (solid line in the right panel of Fig 3.18).
From the right panel of Fig 3.18 the magnetic thickness of the Nb-Pt0.46 Ni0.54 Φ0
≈ 214 nm, where ∆H ≈ 8.5 mT
Nb junction can be estimated d magn = L∆H
is the periodicity of the Fraunhofer pattern. Using the equations (1.8) and
2
Pt0.46Ni0.54
1
(1140230 nm )
T=1.8K
IC (mA)
2
0
-1
-2
-0,06
-0,03
0,00
H (T)
0,03
0,06
Fig. 3.18. (Left) Schematic of the magnetic field experiment. (Right) Dependence of
the Nb-Pt0.46 Ni0.54 -Nb Josephson junction critical current (Ic ) on in-plane magnetic field
across the side of the length of 1140 nm. The solid line represents calculated Ic (H|| ) using
expression (1.17) and experimental value of d magn .
(1.16) one can find λJ ≈ 392 nm and λ ≈ 118 nm. λ has the same order of
magnitude for different junctions while λJ is different for different junctions
depending on the Ni concentration and thickness of the junction barrier layer.
This is because λJ inversely proportional to the square root of critical current
density (see equation (1.8)). The values of λJ ranging between hundreds of
nm to several µm.
Fig. 3.19 shows the Fraunhofer patterns for the junctions with 13, 20,
27 and 40 at.% of Ni. In order to compare the different junctions with
different properties and geometries, the critical current density is plotted as
a function of the total magnetic flux through the junction plane normalized
by the magnetic flux quanta. The critical current density vanishes when the
total magnetic flux is equal to an integer number of Φ0 (see section 1.2.4).
Fig. 3.20 characterizes another junction with highest measured Ni concentration of 67 at.%. The size of the junction is 120 × 350 nm2 which is
too small to detect any Ic . Instead, the resistance, R, was measured with
the software-based lock-in amplifier (see section 2.2.2). The applied bias current was 2.26 · 10−5 A and R was measured at the maximum bias current.
R modulation shows the same behavior as Ic (H|| ) modulation. The maxi-
58
CHAPTER 3. RESULTS AND DISCUSSION
8
13 %
20 %
27 %
40 %
2
4
JC (10 A/cm )
6
5
T~3 K
2
0
-3
-2
-1
0
)/)0
1
2
3
Fig. 3.19. Jc as a function of Φ/Φ0 for the junctions with 13, 20, 27 and 40 at.% of Ni.
Jc vanishes when the total magnetic flux is equal to an integer number of Φ0 . The good
quality of the Fraunhofer patterns can serves as evidence for uniformity of the junctions
properties and monodomain structure of the ferromagnetic layer.
R (:)
0,27
Pt0.33Ni0.67
2
(120350 nm )
T=1.8 K
0,24
0,21
-0,08
-0,04
0,00
0,04
0,08
H (T)
Fig. 3.20. Rn as a function of in-plane magnetic field for the Josephson junction with 67
at.% of Ni. Rn was measured due to very small Ic of the junctions with this concentration
of Ni. The maximum Rn corresponds to an integer number of Φ0 through the junction
plane.
3.3. CHARACTERIZATION OF S-F-S JOSEPHSON JUNCTIONS
59
PtNi
0,4
IC (mA)
mum R, when there is no contribution to the resistance from supercurrent,
corresponds to an integer number of Φ0 through the junction plane.
There is no visible distortions or asymmetry of the Fraunhofer patterns
and R(H|| ) modulation. This can serves as evidence for uniformity of the
junctions’ properties and monodomain structure of the ferromagnetic layer
in these nano-scale junctions.
During this work it turned out that the undercutting of the Nb layer can
be a problem, since some current can flow not through the junction barrier
as it is schematically shown in the inset of Fig. 3.21. As it was mentioned
Josephson current
0,5
Nb
0,0
Nb
IC (mA)
0,3
excess current
Pt0.87Ni0.13
-0,5
2
0,2
0,1
(180218 nm )
T~3 K
-0,1
before additional cut
after additional cut
after additional cut
and anodization
0,0
V (mV)
0,1
0,0
-0,2
0,0
H (T)
0,2
Fig. 3.21. Dependence of the Nb-Pt0.87 Ni0.13 -Nb Josephson junction critical current (Ic )
on in-plane magnetic field. The curve, shown by open stars, indicates that there is an
excess current of ∼ 0.1 mA which flow not through the junction barrier. The additional cut
removes the remaining Nb material in the lower Nb electrode resulting in the improvement
of Ic (H) modulation (full squares). The anodization further improves the Ic (H) (open
circles). The inset shows the schematic of the junction side view where the arrows indicate
the Josephson supercurrent and excess current through the remaining Nb material in the
lower electrode. The inset shows I-V curve for the same junction before and after additional
cut at zero magnetic field.
in section 2.1.3, one should overmill in to the Nb layer for some depth in
order to eliminate the appearance of excess current. Still, sometime it was
difficult to determine with a good accuracy the depth of overmilling due to
the several reasons:
• the junction width is not well known during the fabrication process;
• sometime it is difficult to recognize the barrier layer;
• the drift of the sample, during the milling, results in change of the
position of ion beam for side cut.
60
CHAPTER 3. RESULTS AND DISCUSSION
The dependence of Ic of the undercut Nb-Pt0.87 Ni0.13 -Nb junction on in-plane
magnetic field is shown by open stars in Fig. 3.21. From Fig 3.21 the value
of excess current can be estimated to about 0.1 mA which can be also verified from the I-V curve at zero magnetic field shown in the inset of Fig 3.21.
This current does not flow through the junction barrier and hence does not
obey the equation (1.17). To eliminate the problem of the excess current, the
junction was extra milled from the side with larger overmill into the upper
Nb layer. The full squares in Fig 3.21 shows Ic (H|| ) of the same junction
but after additional cut. The value of Ic at H=0 T is decreased by ∼ 0.1
mA, which corresponds to the value of excess current, and the Fraunhofer
modulation appears. The anodization further improves the Fraunhofer pattern indicating that there were some remaining short circuits after additional
cut. The Ic (H|| ) after anodization is shown in Fig 3.21 by open circles. The
increase of ∆H after anodization from ∼ 0.081 to ∼ 0.085 T corresponds to
decreasing in size of the junction side, across which field was applied, from
180 to 172 nm. This effective size corresponds to the total size minus the
depth of the anodized oxide layer.
0,18
before anodization
after anodization
Pt0.80Ni0.20
2
(319117 nm )
across long side
T~3.2 K
IC (mA)
0,12
0,06
0,00
-0,08
-0,04
0,00
H (T)
0,04
0,08
Fig. 3.22. Critical current of the junction with 20 at.% of Ni as a function of in-plane
magnetic filed before (full squares) and after (open circles) anodization. The field was
applied across the long (319 nm) side. From the difference in the periodicity of Ic (H|| )
before and after anodization, the depth of anodization was estimated to ∼ 30 nm.
Fig. 3.22 shows Ic (H|| ) for another junction with 20 at.% of Ni before and
after anodization at T ∼ 3.2 K. The initial size of the junction was 319× 117
nm. From the periodicity of the Fraunhofer pattern the depth of anodization
can be estimated to ∼ 30 nm.
Fig. 3.23 shows Jc√
, plotted in the semi-logarithmic scale, as a function
of T (left panel) and T (right panel) for the junctions with different Ni
concentrations. From Fig 3.23 it is seen that the critical current density has
3.3. CHARACTERIZATION OF S-F-S JOSEPHSON JUNCTIONS
7
7
10
6
10
5
10
10
6
10
5
JC (A)
JC (A)
10
4
10
3
10
2
10
1
10
61
1
2
4
10
Ni concentration:
0%
20 %
54 % (low IC)
54 % (high IC)
60 % (low IC)
60 % (high IC)
3
10
2
10
1
3
4
5
T (K)
6
7
10
8
Ni concentration:
0%
20 %
54 % (low IC)
54 % (high IC)
60 % (low IC)
60 % (high IC)
1,5
2,0
1/2
2,5
sqrt(T) (K)
Fig. 3.23. Dependence of the critical current densities on the temperature (left panel) and
the square root of temperature (right panel) in the semi-logarithmic scale
√ for the junctions
with 0, 20, 54 and 60 at.% of Ni. Jc has strong dependence on T and T . Jc (T ) becomes
exponential for 54 and 60 at.% of Ni.
6
5
4
Ni concentration:
54 % (low Ic)
54 % (high Ic)
60 % (low Ic)
60 % (high Ic)
6
coherent length (nm)
coherent length (nm)
strong temperature dependence. Jc (T ) becomes exponential for high Ni concentrations. Such the temperature dependence is typical for S-N-S proximity
coupled junctions, in which the thickness of the normal metal exceeds the
coherence length ξN [43]. In this case, the temperature dependence of Jc is
determined by the temperature dependence of the coherence length in the
barrier. If so, ξF , for the junctions with strong ferromagnetic barrier, should
also has strong temperature
√ dependence. Fig 3.24 shows ξF as a function
of 1/T (left panel) and 1/ T (right panel) calculated from Jc (T ) using the
expression for temperature dependence of Jc in S-N-S junctions
t/2
Jc (T ) ∝ Jc (0) exp −
.
(3.1)
ξF (T )
√
ξF has linear dependence on 1/ T typical fore ”dirty” normal metals (see
3
2
5
4
Ni concentration:
54 % (low Ic)
54 % (high Ic)
60 % (low Ic)
60 % (high Ic)
3
2
1
1
0,1
0,2
0,3
0,4
1/T (1/K)
0,5
0,6
0,3
0,4
0,5
0,6
1/sqrt(T) (1/K)
1/2
0,7
0,8
√
Fig. 3.24. 1/T (left panel) and 1/ T (right panel) dependence of the coherence lengths in
the ferromagnet barrier for 54 and 60 at.% of Ni. The coherent length is calculated from
the expression (3.1).
62
CHAPTER 3. RESULTS AND DISCUSSION
the expression (1.4)). Such strong temperature dependence is somewhat
surprising since ξF is expected to have a negligible temperature dependence
in strong ferromagnets, at least in the ”dirty” case (see the expression (1.19)
or (26b) in [44]).
Fig. 3.25 summarizes the study of various Nb-Pt1−x Nix -Nb Josephson
junctions with different Ni concentrations. It shows critical current density
at T = 3.1 − 3.2 K as a function of Ni concentration. Jc decreases with
36
8
5
5
15
12
9
6
3
0
13 %
2
T~3 K
18
JC (10 A/cm )
2
12
Jc (10 A/cm )
33
4
20 %
27 %
20
25
10
20
30
30
d (nm)
d=20 nm
d=20 nm
d=25 nm
d=23.75 nm
d=30 nm
40
50
60
70
Ni concentration (at.%)
Fig. 3.25. Jc of the Nb-Pt1−x Nix -Nb Josephson junctions for all measured Ni concentrations. The non-monotonous behavior of Jc can be due to switching into the π state
as a function of Ni concentration. The inset shows Jc as a function of Pt1−x Nix barrier
thickness.
increasing Ni concentration from 0 to 40 %. For larger Ni content (54 and 60
% of Ni) the maximum Jc becomes larger, before it becomes unmeasurably
small in the case of 67% Ni. Such a non-monotonous behavior can be due to
switching into the π state [6] as function of Ni concentration. At the same
time, S-F-S junctions with similar geometry on the same chip with 54 and 60
at.% Ni concentration could exhibit a large spread in Jc , as marked in Fig.
3.25. The inset of Fig. 3.25 shows dependence of Jc on the barrier thickness
for the Ni concentrations of 13, 20 and 27 at.%. Jc monotonically decreases
with increasing of thickness in all cases.
Fig. 3.26 shows Ic (H|| ) modulations for the junctions with low and high
Jc and Ni concentration of 54 (left panel) and 60 (right panel) at.%. H||
was applied across the long side for all junctions. The modulation of Ic
can be clearly distinguished in all cases. The junctions with the same Ni
concentrations have similar periods of modulation, which is in agrement with
the junction cross sections, but very different Ic .
Interestingly, the junctions with high Jc (shown in Fig. 3.25 by circles
with cross inside) had spontaneous jump from low to the present value of Jc .
63
3.3. CHARACTERIZATION OF S-F-S JOSEPHSON JUNCTIONS
0,8
800225 nm
2
1140230 nm
1050420 nm
Pt0.46Ni0.54
T=1.8 K
2
0,06
1,2
0,05
0,04
0,2
0,0
-0,2
0,0
0,2
H (T)
0,03
2
Pt0.40Ni0.60
T=1.8 K
IC (mA)
IC (mA)
0,6
0,4
2
1200300 nm
0,8
0,12
0,08
0,4
0,04
0,00
0,02
0,04
H (T)
Fig. 3.26. (Left) Ic (H|| ) modulations for the junctions with low (full squares) and high
(full circles) Jc and Ni concentration of 54 at.%. (Right) Ic (H|| ) modulations for the
junctions with low (open squares) and high (full circles) Jc and Ni concentration of 60
at.%. The modulation of Ic can be clearly distinguished in all cases and the periods of
modulation is in agreement with the junction cross sections. All this confirms the quality
of the junctions. H|| was applied across the long side for all junctions.
0,30
Pt1.00Ni0.00
2
(207104 nm )
across long side
T=1.8 K
IC (mA)
0,24
0,18
0,12
0,06
0,1
0,2
0,3
H (T)
Fig. 3.27. Ic (H|| ) modulations of the junction with 0 at.% of Ni. Sweeping down (full
squares), up (open circles) and down (open triangles) at T =1.8 K. The magnetic field was
applied across the junction side of 207 nm. Each jump corresponds to the entrance or
exit of a vortex into the upper or lower superconducting electrode. The vortex enters at
different field than exits. This leads to the metastability when changing sweeping direction
of magnetic field.
Jc before the jump had value similar to Jc of the corresponding junction with
the same (54 or 60 at.%) Ni concentrations but low Jc shown by open circles
in Fig. 3.25. The jump in Jc was accompanied by the jump in resistivity. The
resistivity increased about tree times to 262 and 342 µΩcm for the junctions
64
CHAPTER 3. RESULTS AND DISCUSSION
with 54 and 60 at.% of Ni respectively.
Fig. 3.27 shows the Fraunhofer modulations of the junction with 0 at.%
of Ni for the different sweeping directions of magnetic field. Each jump on
the Fraunhofer pattern corresponds to the entrance or exit of a vortex into
the upper or lower superconducting electrode (see Fig. 2.10). Each vortex
0,3
0,15
Pt0.46Ni0.54
0,10
(1140230 nm )
across long side
T=1.83 K
2
0,2
IC (mA)
IC (mA)
H=57 mT
0,05
2,1
2,2
2,3
Ib (mA)
0,1
Ib = 0.5 mA
Ib = 2.2 mA
0,042
0,048
0,054
0,060
H (T)
Fig. 3.28. Main panel shows Ic (H|| ) modulations of the junction with 54 at.% of Ni for
bias currents of 0.5 mA (full squares) and 2.2 mA (open circles) at T =1.83 K. The field
was applied across the junction side of 1140 nm. At H|| ≈ 57 mT, the jump between
two vortex states occurs for Ib = 2.2 mA. The system switches to another vortex state at
H|| ≈ 58 mT. For Ib = 0.5 mA, system remains in the same vortex state over the whole
field range. Inset shows Ic vs Ib for the same Josephson junction at T =1.83 K and at
constant H|| ≈ 57 mT. By changing the bias current from ∼2.1 to ∼2.3 mA the system
can be brought between two vortex states with the difference in Ic between these vortex
states ∼0.09 mA.
carries one flux quanta and can enter into a superconductor at some threshold
field which is called lower critical field and is a characteristic of the particular
material. The vortex state then coexist with superconducting state up to the
so-called upper critical filed. At this field the normal cores of the vortices are
overlap with each other leading to destroying of the superconducting state.
When the vortex configuration in the superconducting electrode changes,
the local field in the junction also changes leading to the jump of Ic in the
Fraunhofer pattern as it is shown in Fig. 3.27.
By changing the applied magnetic field, the force needed for vortex to enter or exit can be tuned. In mesoscopic junction, the vortex enters at a higher
field than it exits causing metastability upon changing the field sweeping direction. The system can be also switched between different vortex states by
changing the bias current through the junction as it is shown in the inset of
Fig. 3.28 for the junction with 54 at.% of Ni. By changing the bias current
from ∼2.1 to ∼2.3 mA at constant magnetic field the system can be switched
3.3. CHARACTERIZATION OF S-F-S JOSEPHSON JUNCTIONS
65
between two consecutive vortex states back and force. The difference in Ic
between these vortex states is ∼0.09 mA. A mesoscopic superconductor can
thus act as a memory cell in which the junction is used both for reading and
writing information. The information is represented by the vortex. Moreover, since the vortex has the quantized nature (it can not slowly disappear
with time), such memory can be considered as non-volatile.
The main panel of Fig. 3.28 shows the Ic (H|| ) modulations for the same
junction as in the inset and for different bias currents. The field was applied
across the long side of the junction and swept from negative to positive
direction for both bias currents. At the field ∼57 mT, the jump between
two vortex states occurs for Ib = 2.2 mA which is in agreement with the
case shown in the inset of Fig. 3.28. By increasing the field further, the
system switches to another vortex state at H|| ≈ 58 mT. For Ib = 0.5 mA,
the system remains in the same state over the whole field range shown in Fig.
3.28. From the comparison between Fig. 3.27 and Fig. 3.28 it is seen that
the vortex state is less metastable for field direction across the shorter side
of the junction. More details about the field and current induced switching
between vortex states can be found in the appended paper C.
66
CHAPTER 3. RESULTS AND DISCUSSION
Chapter 4
Summary
During this work, the FIB workstation was used to fabricate nano-scale S-FS Nb-Pt1−x Nix -Nb Josephson junctions with the concentration of Ni ranging
between 0 and 67 at.%. The FIB allows to fabricate the Josephson junctions
with sizes down to 70 × 80 nm2 . The barrier layer of the studied junctions
ranges between 20 and 30 nm. The small size of the junction allows to
use conventional measurement technique due to sufficiently high junction
resistance (Rn & 0.1Ω) and facilitated mono-domain structure of F layer.
To study chemical composition of deposited Pt1−x Nix thin films, the EDS
technique was used. To eliminate possible errors during EDS characterization, caused by the secondary fluorescence and the errors in the quantitative
analysis, the results were analyzed depending on electron beam energy and
electron beam incident angle. To completely eliminate the possible effect of
the substrate material the EDS characterization was also performed on the
free standing Pt0.67 Ni0.33 flakes.
Various complications for EDS on thin films were discussed. It was found
that the conventional quantitative correction for bulk specimen analysis can
not be applied to the thin film when using intermediate electron beam energies. The XPP correction procedure, which was used during this work, seems
to work properly for the electron beam energies of 15 and 30 keV. Thus, it is
advisable to use high electron beam energies for chemical analyze of a thin
films.
To characterize the ferromagnetic properties of Pt1−x Nix thin films, the
Hall effect in the films with the Ni concentrations of 13, 27, 40 and 67 at.%
and with the thicknesses ranging between 50 and 100 nm was studied. The
magnetic filed was applied perpendicular to the thin film and Hall voltage
was measured in transverse direction at constant current bias in longitudinal
direction. It was found that the thin films with 27, 40 and 67 at.% of Ni are
in the ferromagnetic state while the thin film with 13 at.% of Ni remains in
paramagnetic or spin glass state down to T ≈2 K.
The Ni concentration of 27 at.% is smaller than the critical ferromagnetic
concentration experimentally observed for both disordered (40 at.% of Ni)
68
CHAPTER 4. SUMMARY
and ordered (50 at.% of Ni) PtNi bulk alloys but consistent with calculated
critical Ni concentration for ordered PtNi alloy. Also the Curie temperatures
are higher than previously reported for bulk alloys.
The I-V characteristics of measured junctions are well described by RCSJ
model. The measured Fraunhofer patterns, of different Josephson junctions
with different Ni concentrations of barrier layer, serve as evidence for uniformity of the junction properties and monodomain structure of the ferromagnetic layer.
The critical current density of the measured junctions has strong temperature dependence and becomes exponentially dependent on temperature for
high Ni concentrations. The non-monotonous dependence of critical current
density can be attributed to switching from the conventional 0 state into the
π state as a function of the Ni concentration.
By changing the junction bias current at constant magnetic field the
vortices can be manipulated. In this way the system can be switched between
two consecutive vortex states. A mesoscopic superconductor can thus act as
a non-volatile memory cell in which the junction is used both for reading and
writing information.
Chapter 5
Conclusions
In conclusion, Pt1−x Nix thin films were fabricated using the deposition target consisted from the separate Pt and Ni elements. This allows easy way
to control the concentration of Ni in the alloy. The systematic analysis of
both chemical composition, and ferromagnetic properties of the Pt1−x Nix
thin films was performed with the Ni concentrations ranging between 0 and
67 at.%.
3D FIB sculpturing was used to fabricate nano-scale S-F-S Nb-Pt1−x Nix Nb Josephson junctions with the sizes down to ∼ 70 × 80 nm2 . With the
FIB it is possible to make the junctions even with the smaller size. The
Nb-Pt1−x Nix -Nb Josephson junctions with different Ni concentrations and
sizes were studied. The fabricated junctions are characterized by the good
uniformity of the junction properties and the monodomain structure of the
ferromagnetic layer. Therefore, such junctions may be promising for hybrid
S-F spin-valve devices, which require small, mono-domain ferromagnetic barrier.
70
CHAPTER 5. CONCLUSIONS
Chapter 6
Appendix
Ni (at.%)
0
13
T (K)
2.5
3.2
3.2
3.2
3.2
1.65
3.2
1.8
2.76
2.7
2.7
2.8
2.8
2.8
3.0
3.0
2.9
3.0
2.9
3.0
2.9
3.0
3.2
3.1
3.1
3.1
3.2
3.2
3.2
3.2
size (nm)
90×180
106×106
170×88
117×88
95×70
207×104
207×104
274×113
110×100
140×120
90×120
134×237
111×214
222×226
209×213
175×228
158×211
192×235
161×204
351×85
308×128
330×139
310×119
372×130
349×107
340×122
308×90
d (nm)
30
30
30
30
23.75
23.75
23.75
30
30
30
28.75
28.75
28.75
28.75
23.75
23.75
23.75
23.75
23.75
23.75
20
20
20
20
20
20
20
20
20
Ic (mA)
0.16
0.2
0.26
0.156
0.057
1.4
0.762
1.7
0.028
0.065
0.006
0.24
0.18
0.3
0.22
0.46
0.41
0.36
0.3
0.51
0.37
0.18
0.035
0.43
0.57
0.456
0.61
0.47
0.51
0.34
A
Jc (105 cm
2)
9.87
17.86
17.33
15.15
8.64
65.1
35.4
54.8
2.54
3.87
0.55
7.6
7.6
7.79
7.79
9.17
9.17
9.02
9.02
11.3
11.3
6.04
10.9
12.4
12.4
12.6
12.6
12.29
12.29
Rn (Ω)
ρ (µΩcm)
0.71
0.5
0.78
26.51
25.00
26.78
0.34
0.34
0.22
30.78
30.78
28.72
0.21
28.12
0.146
30.84
0.187
31.42
0.133
25.26
0.133
30.52
0.125
30.25
0.138
28.63
72
CHAPTER 6. APPENDIX
Ni (at.%)
20
27
40
54
60
T (K)
2.9
2.9
3.1
3.08
3.1
3.2
3.1
3.3
3.0
3.0
3.0
3.0
3.0
3.1
3.1
3.1
3.1
3.2
3.2
3.2
3.2
3.2
3.2
3.08
3.08
3.2
3.2
3.0
3.0
3.0
2.8
2.18
2.19
2.97
3.17
1.8
2.2
3.0
3.2
1.8
2.2
3.0
3.2
1.8
1.8
2.2
3.0
3.2
1.8
2.2
size (nm)
144×197
144×229
319×106
266×128
319×117
280×95
287×106
277×128
170×106
287×106
319×64
266×181
193×266
167×266
140×256
210×120
210×170
212×90
210×190
202×140
175×180
158×149
175×123
175×140
255×96
300×165
280×180
260×110
640×225
630×230
770×320
770×320
770×320
800×225
800×225
800×225
800×225
1140×230
1140×230
1140×230
1140×230
1140×380
1200×300
1200×300
1200×300
1200×300
1050×420
1050×420
d (nm)
20
20
30
30
30
30
30
30
25
25
25
25
25
25
30
30
30
20
20
20
20
20
20
25
25
20
20
30
30
30
30
25
25
25
25
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
Ic (mA)
0.23
0.3
0.12
0.024
0.13
0.043
0.18
0.129
0.12
0.155
0.08
0.125
0.08
0.25
0.104
0.095
0.073
0.1015
0.157
0.072
0.179
0.120
0.137
0.0615
0.074
0.13
0.136
0.14
0.0075
0.0183
0.11
0.16
2.07
0.73
0.52
0.063
0.048
0.028
0.025
2.1
1.6
0.8
0.67
0.092
3.49
2.87
1.48
1.17
0.136
0.1
A
Jc (105 cm
2)
8.13
9.12
3.55
3.55
3.82
3.82
4.83
4.83
3.95
4.37
4.44
4.11
3.92
5.2
2.03
2.14
2.04
4.03
4.4
3.77
4.49
4.24
4.35
2.62
3.44
5.31
5.55
2.83
0.149
0.64
0.76
1.1
8.4
2.96
2.11
0.35
0.267
0.156
0.139
8.0
6.1
3.05
2.55
0.21
9.69
7.98
4.12
3.26
0.308
0.227
Rn (Ω)
ρ (µΩcm)
0.237
26.70
0.228
25.84
0.181
22.50
0.302
0.248
0.462
0.307
0.390
36.72
35.22
33.26
37.33
31.82
0.203
0.218
0.278
0.415
0.293
0.53
0.245
0.36
0.335
0.375
0.33
0.3
0.32
2.0
1.03
2.2
0.3
0.05
0.22
0.22
0.22
0.05
0.05
0.05
0.05
0.12
0.12
0.12
0.12
0.022
0.09
0.09
0.09
0.09
0.025
0.025
34.71
32.26
33.17
52.29
52.30
50.61
48.88
50.94
52.76
35.25
28.38
36.75
39.20
330.00
173.04
209.73
144.00
29.00
216.83
216.83
216.83
45.00
45.00
45.00
45.00
157.32
157.32
157.32
157.32
47.65
162.00
162.00
162.00
162.00
55.10
55.10
73
Ni (at.%)
60
67
T (K)
3.0
3.2
2.0
2.0
2.0
2.0
2.0
size (nm)
1050×420
1050×420
190×350
120×350
182×290
180×410
160×490
d (nm)
20
20
20
20
20
20
20
Ic (mA)
0.062
0.058
A
Jc (105 cm
2)
0.141
0.131
Rn (Ω)
0.025
0.025
0.16
0.25
0.20
0.16
0.135
ρ (µΩcm)
55.10
55.10
53.20
52.50
52.78
59.00
52.9
Those junctions, which are described by the bold type, were anodized
prior the measurements (see section 2.1.4). Each anodized junction in the
table follows the same junction characterized before anodization. The depth
of anodization was estimated by assuming that the critical current density
remains the same for a junction before and after anodization. Then by measuring the critical current after anodization, and taking into account the
value of critical current density before anodization, the effective area of the
junction was estimated.
References
[1] Bascom S. Deaver, Jr. and William M. Fairbank, Phys. Rev. Lett. 7, 43
(1961)
[2] R. Doll and M. Näbauer, Phys. Rev. Lett. 7, 51 (1961)
[3] B. D. Josephson, Phys. Lett. 1, 251 (1962)
[4] P. W. Anderson and J. M. Rowell, Phys. Rev. Lett. 10, 230 (1963)
[5] L. Bulaevskii, V. Kuzii, A. Sobyanin, JETP Lett. 25, 7 (1977)
[6] V.V. Ryazanov, V.A. Oboznov, A.Yu. Rusanov, A.V. Veretennikov,
A.A. Golubov, and J. Aarts, Phys. Rev. Lett. 86, 2427 (2001)
[7] T. Kontos, M. Aprili, J. Lesueur, F. Genet, B. Stephanidis, and R.
Boursier, Phys. Rev. Lett. 89, 137007 (2002)
[8] R.S. Keizer, S.T.B. Goennenwein, T.M. Klapwijk, G. Miao, G. Xiao,
and A. Gupta, Nature (London) 439, 825 (2006)
[9] T. Yokoyama, Y. Tanaka, and A.A. Golubov, Phys. Rev. B 75, 134510
(2007)
[10] F.S. Berget, A.F. Volkov, and K.B. Efetov, Phys. Rev. Lett. 86, 4096
(2001)
[11] G. Blatter, V.B. Geshkenbein, and L.B. Ioffe, Phys. Rev. B 63, 174511
(2001); E. Terzioglu and M.R. Beasley, IEEE Trans. Appl. Supercond.
8, 48 (1998); A.V. Ustinov and V.K. Kaplunenko, J. Appl. Phys. 94,
5405 (2003)
[12] Daniel Huertas-Hernando, Yu. V. Nazarov, and W. Belzig, Phys. Rev.
Lett. 88, 047003 (2002)
[13] P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sowers,
Phys. Rev. Lett. 57, 2442 (1986); M. N. Baibich , J. M. Broto, A. Fert,
F. Nguyen Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich,
and J. Chazelas, Phys. Rev. Lett. 61, 2472 (1988)
75
76
REFERENCES
[14] W.L. McMillan, Phys. Rev. 175, 537 (1968)
[15] M.J.Besnus and A.Herr, Phys. Lett. A 39, 83 (1972)
[16] J.Beille, D.Bloch and M.J.Besnus, J. Phys. F 4, 1275 (1974)
[17] Uday Kumar, P.K. Mukhopadhyay, Biplab Sanyal, Olle Eriksson, Per
Nordblad, Durga Paudyal, Kartick Tarafder and Abhijit Mookerjee,
Phys. Rev. B 74, 064401 (2006)
[18] A. A. Golubov, M. Yu. Kupriyanov and E. Il’ichev, Rev. Mod. Phys.
76, 411 (2004)
[19] A. Buzdin and I. Baladié, Phys. Rev. B 67, 184519 (2003)
[20] A. F. Andreev, Sov. Phys. JETP 19, 1228 (1964)
[21] V.V. Schmidt ”The Physics of Superconductors: Introduction to Fundamentals and Applications”, Springer-Verlag (1997)
[22] V.M. Krasnov and D. Winkler, Phys. Rev. B 56, 9106 (1997)
[23] É.du Trémolet de Lacheisserie, D. Gignoux, M. Schlenker ”Magnetism:
Fundamentals, Materials and Applications”, Springer (2005)
[24] C A F Vaz, J A C Bland and G Lauhoff, Rep. Prog. Phys. 71, 056501
(2008)
[25] R.E. Parra and J.W. Cable, Phys. Rev. B 21, 5494 (1980)
[26] C.E. Dahmani, M.C. Cadeville, J.M. Sanchez, and J.L. Morán-López,
Phys. Rev. Lett. 55, 1208 (1985)
[27] E.A. Demler, G.B. Arnold and M.R. Beasley, Phys. Rev. B 55, 15174
(1997)
[28] G. Eilenberger, Z. Phys. 214, 195 (1968)
[29] L. Usadel, Phys. Rev. Lett. 25, 507 (1970)
[30] A.I. Buzdin, L. N. Bulaevskii, and S. V. Panyukov, JETP Lett. 35, 178
(1982)
[31] A.I. Buzdin, and M. Y. Kuprianov, JETP Lett. 53, 321 (1991)
[32] The deposition and pattering of the samples were made in the clean
room at the Department of Microtechnology and Nanoscience, Chalmers
University of Technology
[33] C. Bell, G. Burnell, D-J. Kang, R.H. Hadfield, M.J. Kappers, and M.G.
Blamire, Nanotechnology 14, 630 (2003)
REFERENCES
77
[34] D. Nakada, K.K. Berggren, E. Macedo, V. Liberman, T.P. Orlando,
IEEE Transactions on Applied Superconductivity 13, 111 (2003)
[35] The EDS measurements were carried out at Electron Microscopy Center,
Department of Physical, Inorganic and Structural Chemistry, Arrhenius
Laboratory, Stockholm University
[36] T.M. Phung et al., X-Ray Spectrom. 37, 608 (2008)
[37] M. Takakura, H. Takahashi and T. Okumura, JEOL News 33, 15 (1998)
[38] Jean-Louis Pouchou and Francoise Pichoir ”Quantitative analysis of homogeneous or stratified microvolumes applying the model PAP”, pages
31-75 of Electron Probe Quantitation edited by K.F.J. Heinrich and
Date E. Newbury, Plenum (1991)
[39] G.F. Bastin and H.J.M. Heijligers, X-Ray Spectrom. 29, 212 (2000)
[40] G. Burnell, E.J. Tarte, D.-J. Kang, R.H.Hadfield, M.G. Blamire, Physica
C 241, 241 (2002)
[41] I.S. Veshchunov, V.A. Oboznov, A.N. Rossolenko, A.S. Prokofiev, L.Ya.
Vinnikov, A.Yu. Rusanov, and D.V. Matveev, Pis’ma Zh. Eksp. Teor.
Fiz. 88, 873 (2008)
[42] Uday Kumar, K.G. Padmalekha, P.K. Mukhopadhyay, Durga Paudyal,
Abhijit Mookerjee, Journal of Magnetism and Magnetic Materials 292,
234 (2005)
[43] V.M. Krasnov, Physica C 252, 319 (1995)
[44] A.S. Vasenko, A.A. Golubov, M.Yu. Kupriyanov and M. Weides, Phys.
Rev. B 77 134507 (2008)
Paper A
V. M. Krasnov, T. Golod, T. Bauch and P. Delsing, Anticorrelation between temperature and fluctuations of the switching current in moderately damped Josephson junctions, Phys. Rev. B
76 224517 (2007)
Author’s contribution: My part of this work consists of fabrication and assistance in characterization of one of the studied
samples.
Paper B
T. Golod, H. Frederiksen and V. M. Krasnov, Nb-PtNi-Nb Josephson junctions made by 3D FIB nano-sculpturing, J. Phys.: Conf.
Ser. 150 052062 (2009)
Author’s contribution: My contribution to this work is the
samples fabrication and characterization. This paper is also written by me.
Paper C
A. Rydh, T. Golod and V. M. Krasnov, Field- and current controlled switching between vortex states in a mesoscopic superconductor, J. Phys.: Conf. Ser. 153 012027 (2009)
Author’s contribution: My contribution to this work is the
sample fabrication and assistance in the measurements.
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