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 11 11 13 14 15 16 16 19 . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . 21 . 21 . 21 . . . . . . 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 -. 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  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 . Another reason to study S-F systems is the possibility to achieve the absolute spin valve effect  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 . 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  it was suggested to use the proximity effect minigap  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 . This in turn requires that the F layer is made of a weak, diluted F alloy, to allow a significant supercurrent . 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 . 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 , unlike CuNi and many other Ni and Fe based alloys, which are prone to phase segregation . 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 . 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) . 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 . 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  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 . 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  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 . 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 . 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  and by neutron scattering experiments . 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 . 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  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  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 . 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 . 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  equations by averaging with respect to relative electron motion in the pair. The Eilenberger equations can be further simplified to Usadel  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  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 . 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 . 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 . 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  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 . 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 . 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)  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 . 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 . 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 . 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 T2K 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  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 , 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  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 . 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 . 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 . 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 ). 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  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). 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