Controlling the proximity in a Co/Nb multilayer: the properties of electronic transport

We present both a theoretical and experimental investigation of the proximity effect in a stack-like superconductor/ferromagnet (S/F) superlattice, where ferromagnetic layers with different thicknesses and coercive fields are made of Co. Calculations based on Usadel equations allow us to find conditions at which switching from the


Introduction
Multilayer superconductor/ferromagnet (S/F) heterostructures can be used for construction of tunable cryolelctronic element, such as switches, Josephson junctions, inductances et cetera [1][2][3][4][5][6][7][8]. Below we present theoretical and experimental investigations of an S/F "stranded wire" with a controllable proximity effect. The wire is composed of ferromagnetic (F) layers separated by thin superconducting layers (s), in which the superconducting order parameter is supported due to the proximity to a thick superconducting S-bank. Switching from the antiparallel (AP) to the parallel (P) alignment of neighboring F1 and F2 layers leads to a significant enhancement of the effective exchange field in such an artificial ferromagnet. Previously, properties of [Co (1.5 nm) / Nb (8 nm) / Co (2.5 nm) / Nb (8 nm)]6 multilayer structures for cryogenic memory applications were studied using neutron scattering and magnetometry techniques [9]. In particular, parameter regions where the aforementioned switching between the P and AP orientations of the F1 and F2 layers is possible, was found experimentally.
In this work we perform theoretical and experimental analysis of electronic properties of Nb/Co multilayers with different F1 and F2 thicknesses and several stacking periods. It is demonstrated that magnetization switching result in modulations of superconductivity in the superlattice with a corresponding change in kinetic inductances of superconducting parts of the wire core, due to the inverse proximity effect. We argue that this effect facilitates new possibilities for development of tunable superconducting electronic components. For example, the considered "stranded wire" can be readily applied in a synaptic connection for a superconducting artificial neural networks (ANN) where information is represented in a "current domain" [10][11][12][13][14][15][16][17][18][19][20][21].
The paper is organized as follows. In the next Section we highlight the manifestation of the proximity effect in hybrid S/F structures, the most interesting for the applications discussed, present the model and methods of theoretical research, and formulate obtained results. In the Section "Experimental Results" we analyze the transport measurements of the manufactured samples. At the end, we discuss possible applications of the results for implementations of superconducting synapses and give a conclusion.

Model and theoretical results
Contrary to traditional semiconductor basic elements (transistors), the tunable kinetic inductors (TKI) as well as nonlinear elements (Josephson junctions) are not fabricated in a substrate. That allows benefiting from 3D topology, which is especially important for deep ANNs. The F1/s/F2/s super-lattice, in which the thick S-bank acts as the source of induced superconductivity, is the simplest "model" of the 3D structure. Let us consider the applications, which are possible due to control over the order parameter in thin s-layers in such a structure. The simplest cell for the current flow control using the TKI is a splitter. The input current, iin, induced in the input inductance, lin, splits toward the two TKI elements. ). The synapse modulates the "weight" of an arriving signal, which corresponds to the input current. The transfer function of such a current transformer can be described as follows: where iin and iout stands for the normalized input/output current respectively, Δl = l1 -l2; Σl = l1 + l2; l1, l2 are the values of normalized inductance for two TKIs, lp is the stray geometric inductance of a splitter branch. For the functioning of the device, it is critically important to find conditions when the kinetic inductance changes significantly due to the controlled proximity effect in the S/F structure.
To test the concept of the magnetically tunable kinetic inductor we calculated the superconducting order parameter in S/[F1/s/F2/s]n superlattices presented in Figure 1.
We study proximity effect and electronic transport in the multilayer hybrid structures in the frame of Usadel equations [22] (2) with Kupriyanov-Lukichev boundary conditions [23,24] , at the SF interfaces. Here Gp,q and Φp,q are normal and anomalous Green's functions, ω=πT(2n+1) is Matsubara frequency. = ω+iH, where H is the exchange energy in F-layer, p and qindexes, which denotes the materials, ξpthe coherence length, γBpq=RBA/ρpξpinterface parameter, where RBAthe resistance per square of the interface and ρpresistivity of material from the p-side of boundary.
Note that the boundary conditions at the SF interface are written from the both sides, that leads to two independent parameters γBSF and γBFS. Their ratio γ= ρSξS/ ρFξF is suitable parameter for understanding the properties of the system, since it depends only from material properties.
In our calculations we put the origin of the x axis at free interface of the bulk S electrode with the thickness LS=10ξS and have considered its proximity effect with artificial ferromagnetic material (AFM) consisting of the alternating thin superconducting (LS =1 ξS) and ferromagnetic layers with exchange energy H=10TC.
In AFM every odd F layer has thickness LF1=0.15 ξS, while every even ferromagnetic layer has thickness LF2=0.1ξS. We assume that the diffusive coherence length of S and F material are the same, but relative resistivities can differ. Numerical solution of the boundary problem (2)-(3) provides the required spatial distribution of pair potential Δ(x) as well as anomalous Φ(x) and normal G(x) Green function for a given temperature.
We have found that behavior of the system significantly depends on the relative resistivities and coherence lengths of the chosen material. In the case γ=1, when ferromagnetic metal and superconductor have the same resistivity and diffusion coefficient, the pair potential in the whole structure evenly grows with decrease of the temperature (See Figure 2a). The main source of the superconductivity is the bulk S layer, while the thin s-layers just slightly support the pairing amplitude coming from the source. Figure   T=0.6TC (c).
However, the properties of proximity effect are completely different if the resistivity of superconductor is significantly smaller than ferromagnetic one (γ=0.1). In this case, thin s-layer are protected from superconductivity suppression due to inverse proximity effect and the sF-multylayer acts as additional source of superconductivity.
However, the effective critical temperature of that magnetic superconductor is significantly smaller than in the bulk S material. This property of the system is

Experimental results
The next important step was to search for evidence of a significant changes in the pair potential in thin s-layers in [Co (1.5 nm) / Nb (8 nm) / Co (2.5 nm) / Nb (8 nm)]3 AFM. For these superlattices the possibility of switching between P and AP cases using magnetic fields with a strength of about 30 Oersteds has already been demonstrated [9]. The samples were prepared using magnetron sputtering system Leybold Herraeus Z-400 during single deposition cycle without depressurization the chamber. Only three targets were used for structure preparation: niobium (99.95% purity) as a superconducting Cooper pair generator and interlayer separator between two neighboring films of ferromagnetic layers grown using cobalt (99.95% purity); the pure silicon target (99.999%) was used to create a passivating layer to prevent structure oxidation. In details the deposition technology is described in [27].
The structure for transport measurements was etched in pure argon atmosphere (Ar + milling) in a CRYO RIE Alba Nova machine (Stockholm University). The pattern design allows to perform a four point type measurement of six segments of the sample in one cooling cycle (see Figure 4): the pair of contacts was applied for setting current and the pair of micro-wiresfor an induced potential difference testing. All low-temperature measurements during this work were done using cryogen-free magnet system with a flowing gas insert. The Figure 4 represents the principle scheme of measurement, this "centipede"-like sample design permits to measure electrical resistance of different "belly" (synapselike) segments simply by alternating arms. The sample was cooled down to 10K in zero field cooling mode and no current was applied. Critical temperature measurements were started at 10 K by sweeping the temperature (R(T) measurements), and external 1μА current was used in AC mode with frequency 127Hz. The temperature change rate was chosen to provide minimal gradient for two casesdownward and upward sweep direction, and resulting shapes of curves totally resembled each other but slightly shifted by 0.05 K.
In this article we present only the results of three segments measurement because the rest demonstrated the similar behavior to either one of showed here. At the beginning the resistivity as function of temperature was measured without applied external magnetic field for all "belly" segments immediately after cooling down the sample. In Figure 5a we  The observed variation of step-like R(T) dependence may also be due to the specific sample geometry with different orientation of electrodes, horizontal or vertical in Figure 4(a). Due to the shape anisotropy, the "body" of the "centipede" is magnetized in longitudinal direction, while the arms are perpendicular to the field. Such geometry provides different magnetic structure and effective exchange field for different parts of the structure. It seems, that critical temperature of the arms is lower, than in the body, providing the injection of normal current into it, with conversion process inside it. It provides the finite voltage, measured on middle segments. At the same time, decrease of the temperature leads to transition of thin s-layers into superconducting state, which occurs step-by-step according to Figure 3 providing jumps on R(T) dependence.
This model is supported by results of our measurements: the resistance-temperature dependencies with current transport along RT-and TV-paths in Figure 5(b) are almost the same. It means, that the source of the voltage is in the T-electrode, which is the source of normal quasiparticles. At the same time, connection between N and R electrodes provides the jumps at significantly smaller temperatures, which probably correspond to magnetic configuration in the N electrode.

Discussion and Conclusion
We continued theoretical and experimental research of Co/Nb multilayer, since neutron reflectometry and SQUID-magnetometry have proven that effective exchange energy can be controlled here by applying relatively weak magnetic fields.
This time we focused on the "life" of superconductivity (pair potential) in thin s-layers in a changing "magnetic environment".
Theoretical studies in the present article have shown that it is possible to change "magnetically" the kinetic inductance of superconducting layers, and even transfer thin layers to a normal state at a fixed temperature.
Experimental studies have shown that transition of thin s-layers to the normal state in the considered multilayer structure is possible; the temperature of this transition depends on the magnetic environment.
Summarizing the entire above one can conclude that the electronic transport properties found in multilayer structure S/[F1/s/F2/s]n can be used to create different switching electronic elements, including synapses. Let's discuss this new type of application in more detail.
The creation of artificial neural networks is one of the current trends in the development of superconductor electronics [10][11][12][13][14][15]. Such an artificial neural network contains layers of elements that nonlinearly transform the incoming signal (neurons) connected by linear tunable connections (synapses). The number of synapses in neural networks that are interesting for applications is more than 10 6 . Energy dissipation at such interconnects is a serious problem, that explains the abovementioned interest in energy-efficient superconducting solutions in this research field. In