We investigate spin-dependent quasiparticle and Cooper-pair transport through a central node interfaced with two superconductors and two ferromagnets. We demonstrate that voltage biasing of the ferromagnetic contacts induces superconducting triplet correlations on the node and reverses the supercurrent flowing between the two superconducting contacts. We further find that such triplet correlations can mediate a tunable spin current flow into the ferromagnetic contacts. Our key finding is that unequal spin-mixing conductances for the two interfaces with the ferromagnets result in equal-spin triplet correlations on the node, detectable via a net charge current between the two magnets. Our proposed device thus enables the generation, control, and detection of the typically elusive equal-spin triplet Cooper pairs.
The theory of the I-V characteristics in diffusive superconductor/weak ferromagnet/superconductor (SFS) junction is developed. We show that the exchange field $h$ of the ferromagnet manifests itself as an additional conductance peak at $eV \sim Δ+h$ in the phase-coherent regime, when the Thouless energy is of the order of superconducting order parameter. The excess current exhibits non-monotonous dependence on the exchange field and non-trivial temperature behavior, which is strongly influenced by the temperature dependence of the exchange field.
We investigate how domain structure of the ferromagnet in superconductor-ferromagnet heterostructures may change their transport properties. We calculate the distribution of current in the superconductor induced by magnetic field of Bloch domain walls, find the ``lower critical'' magnetization of the ferromagnet that provides vortices in the superconductor.
We present a theory of Andreev reflection in a ferromagnet/superconductor/ferromagnet double junction system. The spin polarized quasiparticles penetrate to the superconductor in the range of penetration depth from the interface by the Andreev reflection. When the thickness of the superconductor is comparable to or smaller than the penetration depth, the spin polarized quasiparticles pass through the superconductor and therefore the electric current depends on the relative orientation of magnetizations of the ferromagnets. The dependences of the magnetoresistance on the thickness of the superc…
We study the Josephson effect in a clean Superconductor-Ferromagnet-Superconductor junction for arbitrarily large spin polarizations. The Andreev reflection at a clean Ferromagnet-Superconductor interface is incomplete, and Andreev channels with a large incidence angle are progressively suppressed with increasing exchange energy. As a result, the critical current exhibits oscillations as a function of the exchange energy and of the length of the ferromagnet and has a temperature dependence which deviates from the one predicted by the quasiclassical theory.
We investigate the coupling between ferromagnet and superconducting phase dynamics in superconductor-ferromagnet-superconductor Josephson junction. The current-voltage characteristics of the junction demonstrate a pattern of subharmonic current steps which forms a devil's staircase structure. We show that a width of the steps becomes maximal at ferromagnetic resonance. Moreover, we demonstrate that the structure of the steps and their widths can be tuned by changing the frequency of the external magnetic field, ratio of Josephson to magnetic energy, Gilbert damping and the junction size.
We have measured the electrical transport of submicron ferromagnets (Ni) in contact with a mesoscopic superconductor (Al) for a range of interface resistances. In the geometry measured, the interface and the ferromagnet are measured separately. The ferromagnet itself shows no appreciable superconducting proximity effect, but the ferromagnet/superconductor interface exhibits strong temperature, field and current bias dependences. These effects are dependent on the local magnetic field distribution near the interface arising from the ferromagnet. We find that the temperature dependences may be f…
We realized point contact spectroscopy experiment on ferromagnet/superconductor bilayers. Differential conductance curves show several features that we explained within Bogoliubov-de Gennes formalism considering the presence of two interfaces in the normal-metal-tip/ferromagnet/superconductor device. We demonstrate that such configuration is suitable as local probe of the spin polarization and thickness of ferromagnetic layer, directly on bilayer areas. This is due to the high sensitivity of the Andreev surface states to the physical properties of the ferromagnetic interlayer.
We study theoretically the magnetic screening properties of thin, diffusive superconductor/ferromagnet bilayers subject to a perpendicular magnetic field. We find that the effective penetration depth characterizing the magnetic response oscillates with the thickness of the ferromagnetic layer on the scale of the ferromagnetic coherence length.
Ferromagnetic single electron transistors with Al islands and orthogonal ferromagnetic leads (Co) are fabricated using ebeam lithography followed by shadow evaporation techniques. I-V characteristics exhibit typical single electron tunneling effects. Transport measurements performed in external magnetic field show that, when the two ferromagnetic leads are in antiparallel configuration, spin imbalance leads to a suppression of superconductivity.
We study a diffusive superconductor--ferromagnet--superconductor (SFS) junction with in-plane ferromagnetic domains. Close to the superconducting transition temperature, we describe the proximity effect in the junction with the linearized Usadel equations. We find that properties of such a junction depend on the size of the domains relative to the magnetic coherence length. In the case of large domains, the junction exhibits transitions to the $π$ state, similarly to a single-domain SFS junction. In the case of small domains, the magnetization effectively averages out, and the junction is alwa…
Results of theoretical study of spin-polarized tunneling in ferromagnet/superconductor junctions are presented. Spin and charge currents are calculated as a function of applied voltage and spin polarization in a ferromagnet. The model takes into account the splitting of different spin subbands in a ferromagnet and impurity scattering in the contact. The excess resistance of an FS contact due to the charge-imbalance in a superconductor is calculated for the first time. The results have implications for spin-coupled magnetoresistance in ferromagnet/superconductor contacts and for measuring spin …
We propose the phase dynamics induced by spin waves in a superconductor/ferromagnet/superconductor (SC/FM/SC) Josephson junction. The resistively shunted junction (RSJ) model, which describes the dynamics of superconducting phase difference, is extended to include the spin wave excitation by ferromagnetic resonance (FMR) using the gauge invariant phase difference between two s-wave superconductors. The current-voltage characteristics show step structures when the magnetization in FM is driven by tuning the microwave frequency to FMR in the SC/FM/SC junction. The result presents a new route to …
We show that at zero temperature the supercurrent through the superconductor - ferromagnetic metal - superconductor junctions does not decay exponentially with the thickness $L$ of the junction. At large $L$ it has a random sample-specific sign which can change with a change in temperature. In the case of mesoscopic junctions the phase of the order parameter in the ground state is a random sample-specific quantity. In the case of junctions of large area the ground state phase difference is $\pm π/2$.
We study subgap transport in a ferromagnet-superconductor junction at low temperature due to Andreev reflection. The mismatch of spin polarized current in the ferromagnet and spinless current in the superconductor results in an additional contact resistance which can be reduced by magnon emission in the ferromagnet. Using the s-f model and focusing on half-metallic ferromagnets, we calculate the corresponding nonlinear contribution to the current which is asymmetric with respect to the sign of the bias voltage and is related to the density of states of magnons in the ferromagnet.
We show that quantum spin fluctuations in inhomogeneous ferromagnets drastically affect the Andreev reflection of electrons and holes at a ferromagnet-superconductor interface. As a result a strong long-range proximity effect appears, associated with electron-hole spin triplet correlations and persisting on a lenght scale typical for non-magnetic materials, but anomalously large for ferromagnets.
We consider a bi-layer consisting of a $d-$wave layerd superconductor and diffusive ferromagnet with a domain wall (DW). The $c-$axis in the superconductor and DW in the ferromagnet are assumed to be perpendicular to the interface. We demonstrate that in such a heterostructure the inhomogeneous exchange field enhances the proximity effect. It is shown that, whereas in the absence of the exchange field the $d-$wave condensate decays in the normal metal on the mean free path $l$, the superconductivity penetrates the ferromagnet along the DW over much larger distances. This happens because the pr…
We theoretically study the spin-dependent transport in a ferromagnet/superconductor/ferro-magnet double barrier tunnel junction. The spin-polarized tunneling currents give rise to spin imbalance in the superconductor. The resulting nonequilibrium spin density suppresses the superconductivity with increase of the tunneling currents. We focus on the effect of asymmetry in the double tunnel junction, where the barrier height of the tunnel junction and the spin-polarization of the ferromagnets are different, on spin injection, and discuss how the superconductivity is suppressed in the asymmetric j…
The Josephson current through a long s-wave superconductor/weak ferromagnet/s-wave superconductor weak link is studied theoretically in the regime of nonequilibrium spin-dependent occupation of electron states in the ferromagnetic intelayer. While under the considered nonequilibrium condition the standard supercurrent, carried by the singlet part of current-carrying density of states, is not modified, the additional supercurrent flowing via the triplet part of the current-carrying density of states appears. Depending on voltage, controlling the particular form of spin-dependent nonequilibrium …
We study Superconductor-Ferromagnet-Superconductor (Nb-Cu0.47 Ni0.53-Nb) Josephson junctions with spatial variations in the barrier thickness. Critical current vs. magnetic flux diffraction patterns indicate that the critical current density changes sign along the width of the junctions, creating interfaces between 0 and pi junction regions around which spontaneous currents can circulate. Shapiro steps observed at half-integer Josephson voltages can be explained by the phase-locking of the spontaneous circulating currents to the applied rf modulation.
Andreev reflection is a smart tool to investigate the spin polarisation P of the current through point contacts between a superconductor and a ferromagnet. We compare different models to extract P from experimental data and investigate the dependence of P on different contact parameters.
We theoretically study the tunnel magnetoresistance(TMR) of ferromagnet / superconductor / ferromagnet single-electron tunneling transistors with a special attention to the parity effect. It is shown that in the plateau region, there is no spin accumulation in the island even at finite bias voltage. However, the information of the injected spin is carried by the excess electron and thus the TMR exists. The spin relaxation rate of the excess electron can be estimated from the TMR. We also show that the TMR increases with decreasing the size of the superconducting island.
We investigate charge pumping in ferromagnet/triplet superconductor junctions where the magnetization of the ferromagnet is inhomogeneous and dynamical. It is shown that charge current is pumped due to the coupling of the localized spin with triplet vector spin chirality, vector spin chirality formed by the triplet vector of Cooper pairing. Physical mechanism of the charge pumping is also discussed.
We report on the experimental observation of nonlocal spin-dependent thermoelectric effects in superconductor-ferromagnet multiterminal structures. Our samples consist of a thin superconducting aluminum wire with several ferromagnetic tunnel junctions attached to it. When a thermal excitation is applied to one of the junctions in the presence of a Zeeman splitting of the density of states of the superconductor, a thermoelectric current is observed in remote junctions at distances exceeding $10~\mathrm{μm}$. The results can be explained by recent theories of coupled spin and heat transport in h…
We develop a quasi-classical theory for the superconducting proximity effect in a ballistic ferromagnetic layer in contact with a d-wave superconductor. In agreement with recent experiments we find that the density of states oscillate around the normal state value with varying the thickness of the ferromagnetic layer. We show that the phase, the amplitude, and the period of these oscillations depend on the orientation of the superconductor. This effect reveals spatial oscillations and anisotropy of the induced superconducting correlations in the ferromagnet.
Experimental and theoretical study of superconductor (S) -- ferromagnet (F) -- superconductor junctions showed that in certain range of parameters (e.g., the length of the ferromagnet $d_F$, the exchange field, $E_{\rm ex}$) the ground state of a SFS junction corresponds to superconducting phase difference $π$ or 0. The phase diagram of a SFS junction with the respect to $π$ and 0 states is investigated in this letter in $E_{\rm ex}, d_{F}, T$ space. It is shown that the phase diagram is very sensitive to the geometry of the system, in particular, to the amount of disorder.
A promising scheme for electron microrefrigeration based on ferromagnet-superconductor contacts is presented. In this setup, cooling power densities up to 600 nW/$μ$m$^2$ can be achieved leading to electronic temperature reductions largely exceeding those obtained with existing superconductor-normal metal tunnel contacts. Half-metallic CrO$_2$/Al bilayers are indicated as ideal candidates for the implementation of the device.
The Andreev reflection of narrow ferromagnet/superconductor point contacts is theoretically studied. We show that the conductance quantization depends on whether the contact region is superconducting or ferromagnetic as well as on the strength of the exchange field in the ferromagnet. The Andreev reflection of the ferromagnetic contact is more suppressed than that of the superconducting contact. We also show that the conductance-voltage curve has a bump at zero bias-voltage if there is no interfacial-scattering. On the contrary, the conductance-voltage curve shows a dip if the system has an in…
A theory of crossed Andreev reflection in structures consisting of a superconductor with two ferromagnetic leads is presented. The electric current due to the crossed Andreev reflection strongly depends on the relative orientation of the magnetization of two ferromagnetic leads. It is shown that the dependence of the electric current and the magnetoresistance on the distance between two ferromagnetic leads is understood by considering the interference between the wave functions in ferromagnets. The current and the magnetoresistance are calculated as functions of the exchange field and the heig…
We present an overview of the contributions made by Konstantin B. Efetov and the authors to the field of triplet odd-frequency superconductivity in hybrid ferromagnet-superconductor structures and the repercussions they had on experimental and theoretical research. Konstantin B. Efetov passed away in August 2021. We hope the present short review gives a faithful testimony of an important part of his scientific legacy.
We investigate transverse charge and spin dc supercurrents in a ferromagnet coupled to a superconductor where the ferromagnet has inhomogeneous magnetic structure. These transverse supercurrents arise from non-trivial structure of the magnetization. The magnetic structure manifested in the transverse charge supercurrent is essentially different from that discussed in the context of anomalous Hall effect, reflecting the disspationless nature of supercurrent. Possible candidates of magnetic structure to verify our prediction are also discussed.
Motivated by recent experiments searching for Majorana zero modes in tripartite semiconductor nanowires with epitaxial superconductor and ferromagnetic-insulator layers, we explore the emergence of topological superconductivity in such devices for paradigmatic arrangements of the three constituents. Accounting for the competition between magnetism and superconductivity, we treat superconductivity self consistently and describe the electronic properties, including the superconducting and ferromagnetic proximity effects, within a direct wave-function approach. We conclude that the most viable me…
Contacting a bilayer ferromagnet with a singlet even-frequency superconductor allows for the realization of an effective triplet odd-frequency superconductor. In this work, we investigate the Josephson effect between superconductors with different symmetries (e.g. odd- versus even-frequency). In particular, we study the supercurrent flowing between two triplet odd-frequency superconducting leads through a weak singlet even-frequency superconductor. We show that the peculiar temperature dependence of the critical current below the superconducting transition of the weak superconductor is a signa…
We study the electronic density of states in a mesoscopic superconductor near a transparent interface with a ferromagnetic metal. In our tunnel spectroscopy experiment, a substantial density of states is observed at sub-gap energies close to a ferromagnet. We compare our data with detailed calculations based on the Usadel equation, where the effect of the ferromagnet is treated as an effective boundary condition. We achieve an excellent agreement with theory when non-ideal quality of the interface is taken into account.
We theoretically investigate an opportunity to implement a source of highly spin-polarized ac current on the basis of superconductor/weak ferromagnet/superconductor (SFS) voltage-biased junction in the regime of essential proximity effect and calculate the current flowing through the probe electrode tunnel coupled to the ferromagnetic interlayer region. It is shown that while the polarization of the dc current component is generally small in case of weak exchange field of the ferromagnet, there is an ac component of the current in the system. This ac current is highly spin-polarized and entire…
The stationnary Josephson effect in a clean Superconductor-Ferromagnet-Superconductor junction is revisited for arbitrarily large spin polarizations. The quasiclassical calculation of the supercurrent assumes that the Andreev reflection is complete for all channels. However, De Jong and Beenakker have shown that the Andreev reflection at a clean FS interface is incomplete, due to the exchange interaction in the ferromagnet. Taking into account this incomplete Andreev reflection, we investigate the quasiparticle spectrum, the Josephson current and the $0-π$ transition in a ballistic single chan…
We propose a new process of magnon-assisted Andreev reflection at a ferromagnetic metal - superconductor interface, which consists of the simultaneous injection of a Cooper pair from the superconductor and the emission of a magnon inside the ferromagnet. At low temperature this process represents an additional channel for sub-gap transport across an FS interface, which lifts restrictions on the current resulting from the necessity to match spin-polarized current in the ferromagnet with spin-less current in the superconductor. For a junction between a superconductor and a ferromagnet with an ar…
We analyze the Josephson current in a junction consisting of two superconductors (S) and a ferromagnetic layer (F) for arbitrary impurity concentration. In addition to non-magnetic impurities, we consider also magnetic ones and spin-orbit scattering. In the limit of weak proximity effect we solve the linearized Eilenberger equation and derive an analytical expression for the Josephson critical current valid in a broad range of parameters. This expression enables us to obtain not only known results in the dirty and clean limits but also in a intermediate region of the impurity concentration, wh…
We study spin-dependent electronic transport across ferromagnet/superconductor ballistic junctions modeled using tight-binding Hamiltonians with s, p and d orbitals and material-specific parameters. We show that by accurately modeling the band structure of the bulk materials, one can reproduce the measured differential conductance of Cu/Pb nanocontacts. In contrast the differential conductance of Co/Pb contacts can only be reproduced if an enhanced magnetic moment is present at the interface.
We provide a derivation of a spin Skyrmion number classification for two-dimensional topological superconductors constructed from ferromagnetic and Rashba spin-orbit coupled semiconductor-superconductor heterostructures. We show that in the non-trivial topological phase, characterized by a non-zero Chern number, there is always a topological spin texture in the occupied bands represented by a Skyrmion number. The Skyrmion number has the advantage of being both physically intuitive and directly measurable using spin-sensitive band structure imaging techniques. In addition, we show that the Skyr…
We report on the experimental observation of thermoelectric currents in superconductor-ferromagnet tunnel junctions in high magnetic fields. The thermoelectric signals are due to a spin-dependent lifting of particle-hole symmetry, and are found to be in excellent agreement with recent theoretical predictions. The maximum Seebeck coefficient inferred from the data is about $-100~\mathrm{μV/K}$, much larger than commonly found in metallic structures. Our results directly prove the coupling of spin and heat transport in high-field superconductors.
We report on large thermoelectric effects in superconductor-ferromagnet tunnel junctions in proximity contact with the ferromagnetic insulator europium sulfide. The combination of a spin-splitting field and spin-polarized tunnel conductance in these systems breaks the electron-hole symmetry and leads to spin-dependent thermoelectric currents. We show that the exchange splitting induced by the europium sulfide boosts the thermoelectric effect in small applied fields and can therefore eliminate the need to apply large magnetic fields, which might otherwise impede applications in thermometry or c…
We study the ground state properties of a superconductor - ferromagnet - insulator trilayer on the basis of a Hubbard Model featuring exchange splitting in the ferromagnet and electron - electron attraction in the superconductor. We solve the spin - polarized Hartree - Fock - Gorkov equations together with the Maxwell's equation (Ampere's law) fully self-consistently. For certain values of the exchange splitting we find that a spontaneous spin polarized current is generated in the ground state and is intimately related to Andreev bound states at the Fermi level. Moreover, the polarization of t…
We have measured the evolution of the tunneling density of states (DOS) in superconductor/ferromagnet (S/F) bilayers with increasing F-layer thickness, where F in our experiment is the strong ferromagnet Ni. As a function of increasing Ni thickness, we detect multiple oscillations in the DOS at the Fermi energy from differential conductance measurements. The features in the DOS associated with the proximity effect change from normal to inverted twice as the Ni thickness increases from 1 to 5 nm.
We have previously shown that a ferromagnet-superconductor heterostructure may possess a spontaneous current circulation parallel to the interface. This current is caused by Andreev bound states in the thin ferromagnetic layer, and can be fully spin-polarized. Here we investigate the total energy of the system in cases where the current either does or does not flow. We show that the current is a true quantum ground state effect, and examine the effect of the current on the different contributions to the total energy.
Superconductor/ferromagnet bilayers are known to exhibit nontrivial dependence of the critical temperature T_c on the thickness d_f of the ferromagnetic layer. We develop a general method for investigation of T_c as a function of the bilayer's parameters. It is shown that interference of quasiparticles makes T_c(d_f) a nonmonotonic function. The results are in good agreement with experiment. Our method also applies to multilayered structures.
We examine the appearance of a spontaneous bulk spin current in a triplet superconductor in contact with a metallic ferromagnet. The spin current results from the spin-flip of Cooper pairs upon reflection from the interface with the ferromagnet, and is shown to display strong similarities to the spontaneous charge current in a Josephson junction. We express the spin current in terms of the Andreev reflection coefficients, which are derived by the construction of the quasiclassical scattering wavefunctions. The dependence of the spin current upon a number of parameters is investigated, in parti…
We present a description of spin-polarized transport in mesoscopic ferromagnet-superconductor (F/S) systems, where the transport is diffusive, and the interfaces are transparent. It is shown that the spin reversal associated with Andreev reflection generates an excess spin density close to the F/S interface, which leads to a spin contact resistance. Expressions for the contact resistance are given for two terminal and four terminal geometries. In the latter the sign depends on the relative magnetization of the ferromagnetic electrodes.
We investigated experimentally the transport properties of a superconducting cross-shaped aluminium microbridge fabricated on top of ferromagnetic BaFe12O19 single crystal. It was demonstrated that a one-dimensional domain structure in the ferromagnetic substrate can induce the formation of superconducting channels above magnetic domains. This leads to a giant anisotropy of resistivity of the superconducting bridge, caused by the appearance of continuous paths of supercurrents flowing along domain walls.
We study the transport properties of nanoscale superconducting (S) devices in which two superconducting electrodes are bridged by two parallel ferromagnetic (F) wires, forming an SFFS junction with a separation between the two wires less than the superconducting coherence length. This allows crossed Andreev reflection to take place. We find that the resistance as a function of temperature exhibits behavior reminiscent of the re-entrant effect and, at low temperatures and excitation energies below the superconducting gap, the resistance corresponding to antiparallel alignment of the magnetizati…
We develop a theory which describes hybrid structures consisting out of superconducting and ferromagnetic parts. We give two examples for applications. First, we consider a hybrid structure containing a strong ferromagnet in the ballistic limit. Second, we study for a weak ferromagnet the influence of a domain wall on the superconducting proximity effect. In both cases we account quantitatively for the mixing between singlet and triplet correlations.
We investigate transport properties of a trilayer made of a d-wave superconductor connected to two ferromagnetic electrodes. Using Keldysh formalism we show that crossed Andreev reflection and elastic cotunneling exist also with d-wave superconductors. Their properties are controlled by the existence of zero energy states due to the anisotropy of the d-wave pair potential.
Superconductor-ferromagnet-superconductor Josephson junctions are known to exist in the $0$ and $π$ states with the transitions between them controlled by the temperature and ferromagnetic interlayer thickness. We demonstrate that these transitions can be controlled also by the external magnetic field directed perpendicular to the layers. By varying the ratio of diffusion coefficients in superconducting and ferromagnetic layers, these field-controlled transitions can be made detectable for arbitrary large value of the exchange energy in the ferromagnet. We also show that the $0$-$π$ transition…
We predict a novel type of Josephson effect to occur in triplet superconductor - ferromagnet - triplet superconductor Josephson junctions. We show that the Josephson current, I_J, exhibits a rich dependence on the relative orientation between the ferromagnetic moment and the d-vectors of the superconductors. This dependence can be used to build several types of Josephson current switches. Moreover, we predict an unconventional temperature dependence of I_J in which I_J changes sign with increasing temperature
We analyze the proximity effect of superconductor/ferromagnet nanostructures and point out that the scattering of quasiparticle of spin-triplet pairs by local magnetic moments leads to large resistance peak slightly below the superconducting transition temperature of the superconductor. Both the temperature and the magnitude of the resistance peak decrease with increasing magnetic field, which agree quite well with the experimental results reported in [Nature Phys. 6, 389 (2010)].
We demonstrate that in multilayered superconductor-ferromagnet structures a non-collinear alignment of the magnetizations of different ferromagnetic layers generates a triplet superconducting condensate which is odd in frequency. This triplet condensate coexists in the superconductors with the conventional singlet one but decays very slowly in the ferromagnet, which should lead to a large Josephson effect between the superconductors separated by the ferromagnet. Depending on the mutual direction of the ferromagnetic moments the Josephson coupling can be both of 0 and $π$ type.
We study a magnetic proximity effect at superconductor (S) - ferromagnet (F) interface. It is shown that due to an exchange of electrons between the F and S metals ferromagnetic correlations extend into the superconductor, being dependent on interface parameters. We show that ferromagnetic exchange field pair breaking effect leads to a formation of subgap bands in the S layer local density of states, that accommodate only one spin-polarized quasiparticles. Equilibrium magnetization leakage into the S layer as function of SF interface quality and a value of ferromagnetic interaction have also b…
We consider some properties of odd frequency triplet superconducting condensates. In order to describe fluctuations we construct a supermatrix sigma-model for the superconductor/ferromagnet or superconductor/normal-metal structures. We show that an odd frequency triplet superconductor, when in isolation or coupled to a normal metal, generally displays behaviour comparable to a superconductor with the usual singlet pairings. However, for spin dependent systems such as the superconductor/ferromagnet the two types of superconductor have quite different behaviour. We discuss this difference by con…
We propose a novel platform for the creation and manipulation of Majorana zero modes consisting of a ferromagnetic metallic wire placed between conventional superconductors which are in proximity to ferromagnetic insulators. Our device relies on the interplay of applied supercurrents and exchange fields emerging from the ferromagnetic insulators. We assert that the proposed superconductor/ferromagnet heterostructures exhibit enhanced controllability, since topological superconductivity can be tuned apart from gate voltages applied on the ferromagnetic wire, also by manipulating the applied sup…
We study a possibility of a non-homogeneous magnetic order (cryptoferromagnetic state) in heterostructures consisting of a bulk superconductor and a ferromagnetic thin layer that can be due to the influence of the superconductor. The exchange field in the ferromagnet may be strong and exceed the inverse mean free time. A new approach based on solving the Eilenberger equations in the ferromagnet and the Usadel equations in the superconductor is developed. We derive a phase diagram between the cryptoferromagnetic and ferromagnetic states and discuss the possibility of an experimental observation…
