We present local tunneling spectroscopy experiments in the superconducting and ferromagnetic phases of the reentrant superconductor ErRh$_4$B$_{4}$. The tunneling conductance curves jump from showing normal to superconducting features within a few mK close to the ferromagnetic transition temperature, with a clear hysteretic behavior. Within the ferromagnetic phase, we do not detect any superconducting correlations. Within the superconducting phase we find a peculiar V-shaped density of states at low energies, which is produced by the magnetically modulated phase that coexists with superconductivity just before ferromagnetism sets in.
High resolution measurements of the dynamic magnetic susceptibility are reported for ferromagnetic re-entrant superconductor, ErRh$_{4}$B$_{4}$. Detailed investigation of the coexisting regime reveals unusual temperature-asymmetric and magnetically anisotropic behavior. The superconducting phase appears via a series of discontinuous steps upon warming from the ferromagnetic normal phase, whereas the ferromagnetic phase develops via a gradual transition. A model based on local field inhomogeneity is proposed to explain the observations.
Tunnel-diode resonator technique was used to study crystals of ferromagnetic re-entrant superconductor, ErRh$_{4}$B$_{4}$. At the boundary between ferromagnetism (FM) and superconductivity (SC), dynamic magnetic susceptibility, $χ(T,H)$, exhibits highly asymmetric behavior upon warming and cooling as well as enhanced diamagnetism on the SC side. SC phase nucleates upon warming in a cascade of discontinuous jumps in magnetic susceptibility $χ(T,H)$, whereas FM phase develops gradually as reported in detail in \cite{prozorov2008}. Here we further investigate enhanced diamagnetism. We find that w…
We propose a realization of flux qubit based on the hybrid ferromagnetic-superconducting device where the flux bias is induced purely by vector potential of the vanishing magnetic field. We support our conclusions with theoretical analysis and self-consistent three-dimensional simulations for material specific parameters.
The superconductivity of graphite-sulfur composites is highly anisotropic and associated with the graphite planes. The superconducting state coexists with the ferromagnetism of pure graphite, and a continuous crossover from superconducting to ferromagnetic-like behavior could be achieved by increasing the magnetic field or the temperature. The angular dependence of the magnetic moment m(alpha) provides evidence for an interaction between the ferromagnetic and the superconducting order parameters.
The temperature-pressure phase diagram of ferromagnetic superconductor UCoGe includes four phase transitions. They are between the paramagnetic and the ferromagnetic states with the subsequent transition in the superconducting ferromagnetic state and between the normal and the superconducting states after which has to occur the transition to the superconducting ferromagnetic state. Here we have developed the Landau theory description of the phase diagram and established the specific ordering arising at each type of transition. The phase transitions to the ferromagnetic superconducting state ar…
A superconducting substrate is not able to shrink drastically domains in a ferromagnetic film, contrary to the prediction of Bulaevskii and Chudnovsky [Phys. Rev. B, 63, issue1 (2001)]. This is shown on the basis of the exact solution for the stripe domain structure.
In europium-based iron pnictides superconducting Fe-planes can be influenced by a Zeeman field originated from the neighboring Eu-planes. The field tends to induce spin-density waves with a ferromagnetic average which coexists with the superconducting order by forming complementary patterns of the superconducting and magnetic order parameters in a Fulde-Ferrell-Larkin-Ovchinnikov phase and a two-dimensional textured-superconducting phase. The hard gap around the Fermi energy disappears in these fragile inhomogeneous superconducting states, which features, instead, V-shaped spin-resolved local …
We find that the dependence on temperature and magnetic field of the electrical resistance of diffusive ferromagnetic nano-wires measured with superconducting electrodes changes drastically with the distance, $L$, between the ferromagnet/superconductor contacts, however is remarkably similar for the wires with the same $L$ ranging from 300 nm to 1000 nm, prepared under identical conditions. The result gives an evidence for the long-range superconductor-induced changes in transport properties of ferromagnetic nano-wires.
In the paper " Superconducting decay length in a ferromagnetic metal" by Gusakova, Kupriyanov and Golubov [Pis'ma v ZhETF 83, 487 (2006); cond-mat/0605137], the authors claim that they solved the linearized Eilenberger equation in the ferromagnetic region of an S/F heterostructure at arbitrary mean free path. In this comment we show that the solution suggested by the authors is not correct and explain details of the exact solution found by us in an earlier work several years ago (Phys. Rev. B 64, 134506, (2001).
We study the perpendicular transport characteristics of small superconductor/ferromagnetic insulator/superconductor (YBa$_2$Cu$_3$O$_{7-x}$/LaMnO$_{3+δ}$/YBa$_2$Cu$_3$O$_{7-x}$) tunnel junctions. At a large bias voltage $V\sim 1$ V we observe a step-like onset of excess current that occurs below the superconducting transition temperature $T<T_c$ and is easily suppressed by a magnetic field. The phenomenon is attributed to a novel type of the superconducting proximity effect of non-equilibrium electrons injected into the conduction band of the ferromagnetic insulator via a Fowler-Nordheim tunne…
We investigated the pinning of flux lines in a superconducting film by a regular array of magnetic antidots. The sample consists of a Co/Pt multilayer with perpendicular magnetic anisotropy in which a regular pattern of submicron holes is introduced and which is covered by a type-II superconducting Pb film. The resulting ferromagnetic/superconducting heterostructure shows a pronounced asymmetric magnetization curve with respect to the field polarity. This asymmetry clearly demonstrates that the magnetic contribution dominates the pinning potential imposed by the magnetic antidots on the superc…
The screening currents induced in a superconducting film by a magnetic annulus whose magnetization is perpendicular to the superconductor are calculated. We show that close to the superconductor transition temperature $T_c$ particular values of the magnetization and radii of the annulus make the creation of superconducting vortices energy favorable. We also show that the magnetic annulus offers an alternative tool for vortex pinning in the superconductor. Statistical mechanical properties of this system are discussed.
The complex-field approach is developed to derive analytical expressions of the magnetic field distributions around superconducting strips on ferromagnetic substrates (SC/FM strips). We consider the ferromagnetic substrates as ideal soft magnets with an infinite magnetic permeability, neglecting the ferromagnetic hysteresis. On the basis of the critical state model for a superconducting strip, the ac susceptibility $χ_1'+iχ_1''$ of a SC/FM strip exposed to a perpendicular ac magnetic field is theoretically investigated, and the results are compared with those for superconducting strips on nonm…
We investigate the current induced magnetization dynamics and magnetization switching in an unconventional p-wave superconductor sandwiched between two misaligned ferromagnetic layers by numerically solving Landau-Lifshitz-Gilbert equation modified with current induced Slonczewski's spin torque term. A modified form of Ginzburg-Landau free energy functional has been used for this purpose. We demonstrated the possibility of current induced magnetization switching in the spin-triplet ferromagnetic superconducting hybrid structures with strong easy axis anisotropy and the condition for magnetizat…
The description of the proximity effect in superconducting/ferromagnetic heterostructures requires to use spin-dependent boundary conditions. Such boundary conditions must take into account the spin dependence of the phase shifts acquired by electrons upon scattering on the boundaries of ferromagnets. The present article shows that this property can strongly affect the critical temperature and the energy dependence of the density of states of diffusive heterostructures. These effects should allow a better caracterisation of diffusive superconductor/ferromagnet interfaces.
Strong pinning of superconducting flux quanta by a square array of 1 $μ$m-sized ferromagnetic dots in a magnetic-vortex state was visualized by low-temperature magnetic force microscopy (LT-MFM). A direct correlation of the superconducting flux lines with the positions of the dots was derived. The force that the MFM tip exerts on the individual vortex in the depinning process was used to estimate the spatial modulation of the pinning potential. It was found, that the superconducting vortices which are preferably located on top of the Py dots experience about 15 times stronger pinning forces as…
In order to explore the possibility of tuning superconducting and ferromagnetic transitions by Cu doping (for Ru) in GdSr2RuCu2O8, we have carried out synthesis and characterization of GdSr2Ru{1-x}Cu{2+x)O8 (x = 0, 0.05, 0.1, 0.2) and studied their physical properties. Coexistence of superconductivity and ferromagnetism is observed in all the Cu doped samples studied here. The zero field susceptibility data suggests formation of a spontaneous vortex phase. Cu doping decreases the ferromagnetic Curie temperature, whereas the superconducting transition temperature increases until an optimal conc…
The theoretical description of the thermodynamic properties of ferromagnetic/superconductor/ferromagnetic (F/S/F) systems of nanoscopic scale is proposed. Their superconducting characteristics strongly depend on the mutual orientation of the ferromagnetic layers. In addition, depending on the transparency of S/F interfaces, the superconducting critical temperature can exhibit four different types of dependences on the thickness of the F-layer. The obtained results permit to give some practical recommendations for the spin-valve effect experimental observation. In this spin-valve sandwich, we a…
We have measured and modeled, using three different approaches, the tunneling current in a Nb/NbxOy/Ni planar tunnel junction. The experimental data could be fitted and the correct current polarization could be extracted using a simple quasiclassical model, even in the absence of an applied magnetic field. We also discuss the microscopic structure of the barrier.
Superconductivity and ferromagnetism are antagonistic forms of order, and rarely coexist. Many interesting new phenomena occur, however, in hybrid superconducting/ferromagnetic systems. For example, a Josephson junction containing a ferromagnetic material can exhibit an intrinsic phase shift of pi in its ground state for certain thicknesses of the material. Such "pi-junctions" were first realized experimentally in 2001, and have been proposed as circuit elements for both high-speed classical superconducting computing and for quantum computing. Here we demonstrate experimentally that the phase …
Coupling a conventional s-wave superconductor to a ferromagnet allows, via the proximity effect, to generate superconducting triplet correlations. This feature can be employed to achieve a superconducting triplet spin-valve effect in superconductor-ferromagnet (SF) hybrid structures, for example by switching the magnetizations of the ferromagnets between parallel and antiparallel configurations in F1SF2 and SF1F2 trilayers, or in SF bilayers with both Rashba and Dresselhaus SOC. It was recently reported that geometric curvature can control the generation of long ranged triplets. We use this pr…
We present a theoretical investigation of anisotropic superconducting spin transport at a magnetic interface between a p-wave superconductor and a ferromagnetic insulator. Our formulation describes the ferromagnetic resonance modulations due to spin current generation depending on spin-triplet Cooper pair, including the frequency shift and enhanced Gilbert damping, in a unified manner. We find that the Cooper pair symmetry is detectable from the qualitative behavior of the ferromagnetic resonance modulation. Our theory paves the way toward anisotropic superconducting spintronics.
The space-group approach to the wavefunction of a Cooper pair is extended to Shubnikov groups of type III and applied to newly discovered nearly ferromagnetic superconductor UTe2. A nonunitary triplet SOP (superconducting order parameter), manifested experimentally, was obtained for Shubnikov group m'm'm . The nodal structure of triplet nonunitary SOP is investigated and it was shown that in the case of Shubnikov III symmetry nodal structure of ESP (equal spin pairing) state is in some cases unstable, i.e. changes when a complex phase winding is added. The irreducible corepresentations of a Co…
We examined the proximity effect in granular films made of Pb, a superconductor, and Ni, a ferromagnet, with various compositions. Slow decay of the critical temperature as a function of the relative volume concentration of Ni per sample was demonstrated by our measurements, followed by a saturation of T$_c$. Using an approximate theoretical description of our granular system in terms of a layered one, we show that our data can only be reasonably fitted by a multilayer model. This indicates the importance of the interplay between different ferromagnetic grains; when non-collinearly magnetized …
We consider how superconducting correlations influence spin-transfer torques in ferromagnetic superconductors. It is demonstrated that there is a novel torque arising from particle-hole interference that depends on the U(1) phase associated with the superconducting order parameter. We also show that there is an equilibrium exchange torque between two ferromagnetic superconductors in contact via a normal metal mediated by Andreev states. The latter equilibrium magnetic torque is also sensitive to spin-resolved phase differences in the superconducting order parameters as well as to an externally…
We investigate numerically the local density of states (LDOS) in the vicinity of a vortex core in a ferromagnetic superconductor. Specifically, we investigate how the LDOS is affected by the relative weight of the spin bands in terms of the superconducting pairing, and we also examine the effect of different pairing symmetries for the superconducting order parameter. Our findings are directly related to scanning tunneling microscopy measurements and may thus be highly useful to clarify details of the superconducting pairing in recently discovered ferromagnetic superconductors.
We report thermal expansion measurements on a single crystal of the superconducting ferromagnet UCoGe for magnetic fields applied along the main orthorhombic axes. The thermal expansion cell was mounted on a piezo-electric rotator in order to fine-tune the magnetic field angle. The superconducting and magnetic phase diagram has been determined. With our bulk technique we confirm the $S$-shape of the upper-critical field, $B_{c2}$, for $B \parallel b$ and reinforcement of superconductivity above 6 T. At the same time the Curie point shifts towards lower temperatures on increasing the field alon…
A strong mutual influence of superconductors (S) and ferromagnetic (F) conductors in hybrid F/S (Ni/Al) nanostructures is observed. The magnitude of a proximity-induced conductance on the F-side is more than two orders larger than that predicted by theory. Re-entrance of the superconductors to the normal state reciprocated by changes on the F-side has been found in low applied magnetic fields with new peaks in the differential resistance as an effect of the saturation magnetisation. An analysis has been developed providing a base for a numerical description of the system. PACS numbers: 74.50.+…
The appearance of magnetization during the application of mechanical stress and the creation of elastic deformation during the application of a magnetic field are two fundamental properties of piezomagnetic materials. The symmetry of superconducting ferromagnets UGe_2, URhGe, UCoGe allows piezomagnetism. In addition to conventional piezomagnetic properties occurring in both normal and superconducting states, superconducting state of these piezomagnets has its own specificity. Unlike conventional superconductors, in uranium ferromagnets, the critical transition temperature to the superconductin…
Spin transport currents and the spin-transfer torques in voltage-biased superconducting-ferromagnetic nanopillars (SFNFS point contacts) are computed. We develop and implement an algorithm based on the Ricatti formulation of the quasiclassical theory of superconductivity to solve the time-dependent boundary conditions for the nonequilibrium Green's functions for spin transport through the ferromagnetic interfaces. A signature of the nonequilibrium torque is a component perpendicular to the plane spanned by the two ferromagnetic moments. The perpendicular component is absent in normal-metal-fer…
We have measured the tunnelling current in Nb/Nb$_x$O$_y$/Ni planar tunnel junctions at different temperatures. The junctions are in the intermediate transparency regime. We have extracted the current polarization of the metal/ferromagnet junction without applying a magnetic field. We have used a simple theoretical model, that provides consistent fitting parameters for the whole range of temperatures analyzed. We have also been able to gain insight into the microscopic structure of the oxide barriers of our junctions.%
We have calculated the temperature dependence of the conductance variation ($δS(T)$) of mesoscopic superconductor normal metal(S/N) structures, in the diffusive regime, analysing both weak and strong proximity effects. We show that in the case of a weak proximity effect there are two peaks in the dependence of $δS(T)$ on temperature. One of them (known from previous studies) corresponds to a temperature $T_1$ of order of the Thouless energy ($ε_{Th}$), and another, newly predicted maximum, occurs at a temperature $T_2$ where the energy gap in the superconductor $Δ(T_2)$ is of order $ε_{Th}$. I…
We report a comparative analysis and theoretical description of the superconducting properties of two spin-valve-valve structures containing the Heusler alloy Co$_2$Cr$_{1-x}$Fe$_x$Al$_{y}$ as one of two ferromagnetic (F1 or F2) layers of the F1/F2/S structure, where S stands for the superconducting Pb layer. In our experiments we used the Heusler alloy layer in two roles: as a weak ferromagnet on the place of the F2 layer and as a half-metal on the place of the F1 layer. In the first case, we obtained a large ordinary superconducting spin-valve effect $ΔT_c$ assisted by the triplet supercondu…
We study the interplay of the ferromagnetic (FM) state and the p-wave superconducting (SC) state observed in several materials such as UCoGe and URhGe in a totally nonperturbative manner. To this end, we introduce a lattice Ginzburg-Landau model that is a genuine generalization of the phenomenological Ginzburg-Landau theory proposed previously in the continuum and also a counterpart of the lattice gauge-Higgs model for the s-wave SC transition, and study it numerically by Monte-Carlo simulations. The obtained phase diagram has qualitatively the same structure as that of UCoGe in the region whe…
The interaction between a superconducting vortex in a type II superconducting film (SC) and a ferromagnet (FM) with out-of-plane magnetization is investigated theoretically within the London approximation. The dependence of the interaction energy on the FM-vortex distance, film thickness and different geometries of the magnetic structures: disk, annulus(ring), square and triangle are calculated. Analytic expressions and vectorplots of the current induced in the SC due to the presence of the FM are presented. For a FM disk with a cavity, we show that different local minima for the vortex positi…
On the basis of Usadel equations we investigate superconductor/ferromagnet/superconductor (S/F/S) hybrid systems which consist of superconducting nanostructures (spheres, rods) embedded in ferromagnetic metal. The oscillations of the critical current of the S/F/S Josephson junctions with the thickness of ferromagnetic spacer between superconducting electrodes are studied. We demonstrate that the $π$ state can be realized in such structures despite of a dispersion of the distances between different parts of the electrodes. The transitions between 0 and $π$ states at some thickness of ferromagne…
We study diffusive magnetic Josephson junctions with four superconducting terminals in the weak proximity limit where the leads are arranged in cross form. Employing the linearized Keldysh-Usadel technique, the anomalous Green's function and Josephson current are analytically obtained based on a quasiclassical theory using the Fourier series method. The derived results may be reduced to non-magnetic junctions by setting the exchange field equal to zero. We find that increments of the magnetic barrier thickness may cause a reversal of the supercurrent direction flowing into some of the leads, w…
University of Science and Technology Beijing（北京科技大学）；North China Electric Power University（华北电力大学）；Chinese Academy of Sciences（中国科学院）；Anhui University（安徽大学）；Center for High Pressure Science and Technology Advanced Research（高压科学前沿中心）；Beijing Normal University（北京师范大学）
We study the shift of the the superconducting transition temperature $T_c$ in ferromagnetic-superconducting bi-layers and in a superconducting film supplied a square array of ferromagnetic dots. We find that the transition temperature in these two cases change presumably in opposite direction and that its change is not too small. We extend these results to multilayer structures. We predict that rather small external magnetic field $\sim 10$ Oe can change the transition temperature of the bilayer by 10% .
The theoretical description and the survey of physical properties of superconducting states in the uranium ferromagnetic materials are presented. On the basis of microscopic theory is shown that the coupling between the electrons in these ferromagnetic metals by means of magnetization fluctuations gives rise the triplet pairing superconducting state and the general form of the order parameter dictated by the symmetry is established. The theory allows to explain some specific observations including peculiar phenomenon of reentrant superconductivity in URhGe in magnetic field perpendicular to th…
We study theoretically the spectral and transport properties of a superconducting wire with a magnetic defect. We start by modelling the system as a one dimensional magnetic Josephson junction and derive the equation determining the full subgap spectrum in terms of the normal-state transfer matrix for arbitrary length and exchange field of the magnetic region. We demonstrate that the quantum phase transition predicted for a short-range magnetic impurity, and associated with a change of the total spin of the system, also occurs in junctions of finite length. Specifically, we find that the total…
We calculate the current phase relation of a planar Josephson junction with a ferromagnetic weak link located on top of a thin normal metal film. Following experimental observations we assume transparent superconductor-ferromagnet interfaces. This provides the best interlayer coupling and a low suppression of the superconducting correlations penetrating from the superconducting electrodes into the ferromagnetic layer. We show that this Josephson junction is a promising candidate for an experimental ϕ junction realization.
Heterostructures of superconducting and ferromagnetic materials are of fundamental interest because of the mutual interaction of antagonistic kinds of ordering at the S-F interface. Normally, the superconducting transition temperature Tc should be strongly suppressed at the S-F interface owing to the penetration of Cooper pairs into the ferromagnetic side. Nevertheless, constructive interactions between S and F orders have been suggested to occur via the modification of ferromagnetic order by the superconducting state. This may induce an inhomogeneous magnetic state, often called a cryptoferro…
The current distribution and the AC loss in a composite superconducting tape containing a layer from magnetic material is calculated and compared with experiments, showing a very good agreement. The situations of an alternating uniform applied field or a transport current are studied. The newly developed numerical model is an approximation to the critical state model, adapted for the applicability to commercial finite elements codes that solve the vector potential. Substantial feature of this procedure is that it can be carried out in the case when the critical current density in superconducto…
The discovery of materials that simultaneously host different phases of matter has often initially confounded, but ultimately enhanced, our basic understanding of the coexisting types of order. The associated intellectual challenges, together with the promise of greater versatility for potential applications, have made such systems a focus of modern materials science. In particular, great efforts have recently been devoted to making semiconductors ferromagnetic and metallic ferromagnets superconducting. Here we report the unprecedented observation of a heavily donor-doped ferromagnetic semicon…
A theory of tunneling conductance in ferromagnetic metal/insulator/triplet - supercondcutor junctions is presented for unitary and non-unitary spin triplet pairing states which are promising candidates for the superconducting paring symmetry of Sr2RuO4. As the magnitude of the exchange interaction in the ferromagnetic metal is increased, the conductance for the unitary pairing state below the energy gap is reduced in contrast to the case for the non-unitary pairing state.
Since the discovery of the long-range superconducting proximity effect, the interaction between spin-triplet Cooper pairs and magnetic structures such as domain walls and vortices has been the subject of intense theoretical discussions, while the relevant experiments remain scarce. We have developed nanostructured Josephson junctions with highly controllable spin texture, based on a disk-shaped Nb/Co bilayer. Here, the vortex magnetization of Co and the Cooper pairs of Nb conspire to induce long-range triplet (LRT) superconductivity in the ferromagnet. Surprisingly, the LRT correlations emerge…
We present a theoretical study of the quasiparticle and subgap conductance of generic $X/I_{sf}/S_{M}$ junction with a spin-filter barrier $I_{sf}$, where $X$ is either a normal $N$ or a ferromagnetic metal $F$ and $S_{M}$ is a superconductor with a built-in exchange field. Our study is based on the tunneling Hamiltonian and the Green's function technique. First, we focus on the quasiparticle transport, both above and below the superconducting critical temperature. We obtain a general expression for the tunneling conductance which are valid for arbitrary values of the exchange field and arbitr…
We study the thermodynamic properties of a dirty ferromagnetic S$\mid$F$\mid$S Josephson junction with s-wave superconducting leads in the low-temperature regime. We employ a full numerical solution with a set of realistic parameters and boundary conditions, considering both a uniform and non-uniform exchange field in the form of a Bloch domain wall ferromagnetic layer. The influence of spin-active interfaces is incorporated via a microscopic approach. We mainly focus on how the electronic specific heat and density of states (DOS) of such a system is affected by the \textit{proximity effect}, …
We consider a Josephson junction consisting of superconductor/ferromagnetic insulator (S/FI) bilayers as electrodes which proximizes a nearby 2D electron gas. By starting from a generic Josephson hybrid planar setup we present an exhaustive analysis of the the interplay between the superconducting and magnetic proximity effects and the conditions under which the structure undergoes transitions to a non-trivial topological phase. We address the 2D bound state problem using a general transfer matrix approach that reduces the problem to an effective 1D Hamiltonian. This allows for straightforward…
We analyze superconducting correlations in the one-dimensional Kondo lattice models with Ising anisotropy under transverse magnetic fields, using the density matrix renormalization group. For the spin-1/2 local spin model, the Ising anisotropy is introduced by the ferromagnetic Ising interaction between the local spins, while for the spin-1 model, it is taken by the single-ion anisotropy. The magnetic properties under the transverse fields for the spin-1/2 model are very similar to those for the spin-1 model [K. Suzuki and K. Hattori, J. Phys. Soc. Jpn. 88, 024707 (2019).]. For the superconduc…
We report experiments in which one dimensional (1D) and two dimensional (2D) arrays of YBa2Cu3O7-x-Nb pi-rings are cooled through the superconducting transition temperature of the Nb in various magnetic fields. These pi-rings have degenerate ground states with either clockwise or counter-clockwise spontaneous circulating supercurrents. The final flux state of each ring in the arrays was determined using scanning SQUID microscopy. In the 1D arrays, fabricated as a single junction with facets alternating between alignment parallel to a [100] axis of the YBCO and rotated 90 degrees to that axis, …
The symmetry of the superconducting states arising directly from ferromagnetic states in the crystals with cubic and orthorombic symmetries is described. The symmetry nodes in the quasiparticle spectra of such the states are pointed out if they exist. The superconducting phase transition in the ferromagnet is accompanied by the formation of superconducting domain structure consisting of complex conjugate states imposed on the ferromagnet domain structure with the opposite direction of the magnetization in the adjacent domains. The interplay between stimulation of a nonunitary superconducting s…
