Inverse Spin-Hall Effect and Spin Swapping in Spin-Split Superconductors.

When a spin-splitting field is introduced to a thin film superconductor, the spin currents polarized along the field couples to energy currents that can only decay via inelastic scattering. We study spin and energy injection into such a superconductor where spin-orbit impurity scattering yields inverse spin-Hall and spin-swapping currents. We show that the combined presence of a spin-splitting field, superconductivity, and inelastic scattering gives rise to a strong enhancement of the ordinary inverse spin-Hall effect, as well as unique inverse spin-Hall and spin-swapping signals orders of magnitude stronger than the ordinary inverse spin-Hall signal. These can be completely controlled by the orientation of the spin-splitting field, resulting in a long-range charge and spin accumulations detectable much further from the injector than in the normal state. While the enhanced inverse spin-Hall signals offer a major improvement in spin detection sensitivity, the unique spin-swap signals can be utilized for designing devices where both the spin and current directions are controlled and altered throughout the geometry.

dc Josephson Effect in Altermagnets.

The ability of magnetic materials to modify superconductors is an active research area for possible applications in thermoelectricity, quantum sensing, and spintronics. We consider the fundamental properties of the Josephson effect in a class of magnetic materials that recently have attracted much attention: altermagnets. We show that despite having no net magnetization and a band structure qualitatively different from ferromagnets and from conventional antiferromagnets without spin-split bands, altermagnets induce 0-π oscillations. The decay length and oscillation period of the Josephson coupling are qualitatively different from ferromagnetic junctions and depend on the crystallographic orientation of the altermagnet. The Josephson effect in altermagnets thus serves a dual purpose: it acts as a signature that distinguishes altermagnetism from ferromagnetism and conventional antiferromagnetism and offers a way to control the supercurrent via flow direction anisotropy.

Superconducting Proximity Effect and Long-Ranged Triplets in Dirty Metallic Antiferromagnets.

Antiferromagnets have no net spin splitting on the scale of the superconducting coherence length. Despite this, antiferromagnets have been observed to suppress superconductivity in a similar way as ferromagnets, a phenomenon that still lacks a clear understanding. We find that this effect can be explained by the role of impurities in antiferromagnets. Using quasiclassical Green's functions, we study the proximity effect and critical temperature in diffusive superconductor-metallic antiferromagnet bilayers. The nonmagnetic impurities acquire an effective magnetic component in the antiferromagnet. This not only reduces the critical temperature but also separates the superconducting correlations into short-ranged and long-ranged components, similar to ferromagnetic proximity systems.

Observation of Magnetic State Dependent Thermoelectricity in Superconducting Spin Valves.

Superconductor-ferromagnet tunnel junctions demonstrate giant thermoelectric effects that are being exploited to engineer ultrasensitive terahertz radiation detectors. Here, we experimentally observe the recently predicted complete magnetic control over thermoelectric effects in a superconducting spin valve, including the dependence of its sign on the magnetic state of the spin valve. The description of the experimental results is improved by the introduction of an interfacial domain wall in the spin filter layer interfacing the superconductor. Surprisingly, the application of high in-plane magnetic fields induces a double sign inversion of the thermoelectric effect, which exhibits large values even at applied fields twice the superconducting critical field.

Magnon Spin Current Induced by Triplet Cooper Pair Supercurrents.

At the interface between a ferromagnetic insulator and a superconductor there is a coupling between the spins of the two materials. We show that when a supercurrent carried by triplet Cooper pairs flows through the superconductor, the coupling induces a magnon spin current in the adjacent ferromagnetic insulator. The effect is dominated by Cooper pairs polarized in the same direction as the ferromagnetic insulator, so that charge and spin supercurrents produce similar results. Our findings demonstrate a way of converting Cooper pair supercurrents to magnon spin currents.

Controllable Enhancement of p-Wave Superconductivity via Magnetic Coupling to a Conventional Superconductor.

Unconventional superconductors are of high interest due to their rich physics, a topical example being topological edge states associated with p-wave superconductivity. A practical obstacle in studying such systems is the very low critical temperature T_{c} that is required to realize a p-wave superconducting phase in a material. We predict that the T_{c} of an intrinsic p-wave superconductor can be significantly enhanced by coupling to a conventional s-wave or d-wave superconductor with a higher critical temperature via an atomically thin ferromagnetic (F) layer. We show that this T_{c} boost is tunable via the direction of the magnetization in F. Moreover, we show that the enhancement in T_{c} can also be achieved using the Zeeman effect of an external magnetic field. Our findings provide a way to increase T_{c} in p-wave superconductors in a controllable way and make the exotic physics associated with such materials more easily accessible experimentally.

Controlling the Superconducting Transition by Rotation of an Inversion Symmetry-Breaking Axis.

We consider a hybrid structure where a material with Rashba-like spin-orbit coupling is proximity coupled to a conventional superconductor. We find that the superconducting critical temperature T_{c} can be tuned by rotating the vector n characterizing the axis of broken inversion symmetry. This is explained by a leakage of s-wave singlet Cooper pairs out of the superconducting region, and by conversion of s-wave singlets into other types of correlations, among these s-wave odd-frequency pairs robust to impurity scattering. These results demonstrate a conceptually different way of tuning T_{c} compared to the previously studied variation of T_{c} in magnetic hybrids.

Prediction of a Paramagnetic Meissner Effect in Voltage-Biased Superconductor-Normal-Metal Bilayers.

Conventional superconductors respond to external magnetic fields by generating diamagnetic screening currents. However, theoretical work has shown that one can engineer systems where the screening current is paramagnetic, causing them to attract magnetic flux-a prediction that has recently been experimentally verified. In contrast to previous studies, we show that this effect can be realized in simple superconductor-normal-metal structures with no special properties, using only a simple voltage bias to drive the system out of equilibrium. This is of fundamental interest, since it opens up a new avenue of research, and at the same time highlights how one can realize paramagnetic Meissner effects without having odd-frequency states at the Fermi level. Moreover, a voltage-tunable electromagnetic response in such a simple system may be interesting for future device design.

Current Control of Magnetism in Two-Dimensional Fe_{3}GeTe_{2}.

The recent discovery of magnetism in two-dimensional van der Waals systems opens the door to discovering exciting physics. We investigate how a current can control the ferromagnetic properties of such materials. Using symmetry arguments, we identify a recently realized system in which the current-induced spin torque is particularly simple and powerful. In Fe_{3}GeTe_{2}, a single parameter determines the strength of the spin-orbit torque for a uniform magnetization. The spin-orbit torque acts as an effective out-of-equilibrium free energy. The contribution of the spin-orbit torque to the effective free energy introduces new in-plane magnetic anisotropies to the system. Therefore, we can tune the system from an easy-axis ferromagnet via an easy-plane ferromagnet to another easy-axis ferromagnet with increasing current density. This finding enables unprecedented control and provides the possibility to study the Berezinskiǐ-Kosterlitz-Thouless phase transition in the 2D XY model and its associated critical exponents.

Field-Free Nucleation of Antivortices and Giant Vortices in Nonsuperconducting Materials.

Giant vortices with higher phase winding than 2π are usually energetically unfavorable, but geometric symmetry constraints on a superconductor in a magnetic field are known to stabilize such objects. Here, we show via microscopic calculations that giant vortices can appear in intrinsically nonsuperconducting materials, even without any applied magnetic field. The enabling mechanism is the proximity effect to a host superconductor where a current flows, and we also demonstrate that antivortices can appear in this setup. Our results open the possibility to study electrically controllable topological defects in unusual environments, which do not have to be exposed to magnetic fields or intrinsically superconducting, but instead display other types of order.

Anisotropic Paramagnetic Meissner Effect by Spin-Orbit Coupling.

Conventional s-wave superconductors repel an external magnetic field. However, a recent experiment [A. Di Bernardo et al., Phys. Rev. X 5, 041021 (2015)] has tailored the electromagnetic response of superconducting correlations via adjacent magnetic materials. We consider another route of altering the Meissner effect where spin-orbit interactions induce an anisotropic Meissner response that changes sign depending on the field orientation. The tunable electromagnetic response opens new paths in the utilization of hybrid systems comprising magnets and superconductors.

Extreme enhancement of superconductivity in epitaxial aluminum near the monolayer limit.

BCS theory has been widely successful at describing elemental bulk superconductors. Yet, as the length scales of such superconductors approach the atomic limit, dimensionality as well as the environment of the superconductor can lead to drastically different and unpredictable superconducting behavior. Here, we report a threefold enhancement of the superconducting critical temperature and gap size in ultrathin epitaxial Al films on Si(111), when approaching the 2D limit, based on high-resolution scanning tunneling microscopy/spectroscopy (STM/STS) measurements. Using spatially resolved spectroscopy, we characterize the vortex structure in the presence of a strong Zeeman field and find evidence of a paramagnetic Meissner effect originating from odd-frequency pairing contributions. These results illustrate two notable influences of reduced dimensionality on a BCS superconductor and present a platform to study BCS superconductivity in large magnetic fields.

Non-Fraunhofer interference pattern in inhomogeneous ferromagnetic Josephson junctions.

Generic conditions are established for producing a non-Fraunhofer response of the critical supercurrent subject to an external magnetic field in ferromagnetic Josephson junctions. Employing the quasiclassical Keldysh-Usadel method, we demonstrate theoretically that an inhomogeneity in the magnitude of the energy scales in the system, including Thouless energy, exchange field and temperature gradient normal to the transport direction, influences drastically the standard Fraunhofer pattern. The exotic non-Fraunhofer response, similar to that observed in recent experiments, is described in terms of an intricate interplay between multiple "0-π" states and is related to the appearance of proximity vortices.

Spin-transfer and exchange torques in ferromagnetic superconductors.

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 applied phase difference.

Spin current in generic hybrid structures due to interfacial spin-orbit scattering.

We demonstrate a general principle that hybrid structures of any sort inevitably will give rise to a pure spin current flowing parallel to the interface region when a charge current is injected. This stems from the broken mirror symmetry near the interface which gives rise to spin-orbit coupling that deflects incoming electrons in a spin-discriminating fashion. We establish a general analytical condition for the appearance of this effect, and calculate the transverse spin current explicitly using two different models. In addition, we investigate how the process of Andreev reflection influences this phenomenon in the scenario where one of the materials is superconducting.

Self-consistent solution for the magnetic exchange interaction mediated by a superconductor.

We theoretically determine the magnetic exchange interaction between two ferromagnets coupled by a superconductor using a tight-binding lattice model. The main purpose of this study is to determine how the self-consistently determined superconducting state influences the exchange interaction and the preferred ground-state of the system, including the role of impurity scattering. We find that the superconducting state eliminates RKKY-like oscillations for a sufficiently large superconducting gap, making the anti-parallel orientation the ground state of the system. Interestingly, the superconducting gap is larger in the parallel configuration than in the anti-parallel configuration, giving a larger superconducting condensation energy, even when the preferred ground state is anti-parallel. We also show that increasing the impurity concentration in the superconductor causes the exchange interaction to decrease, likely due to an increasing localization of the mediating quasiparticles in the superconductor.

Superconductivity assisted change of the perpendicular magnetic anisotropy in V/MgO/Fe junctions.

Controlling the perpendicular magnetic anisotropy (PMA) in thin films has received considerable attention in recent years due to its technological importance. PMA based devices usually involve heavy-metal (oxide)/ferromagnetic-metal bilayers, where, thanks to interfacial spin-orbit coupling (SOC), the in-plane (IP) stability of the magnetisation is broken. Here we show that in V/MgO/Fe(001) epitaxial junctions with competing in-plane and out-of-plane (OOP) magnetic anisotropies, the SOC mediated interaction between a ferromagnet (FM) and a superconductor (SC) enhances the effective PMA below the superconducting transition. This produces a partial magnetisation reorientation without any applied field for all but the largest junctions, where the IP anisotropy is more robust; for the smallest junctions there is a reduction of the field required to induce a complete OOP transition ([Formula: see text]) due to the stronger competition between the IP and OOP anisotropies. Our results suggest that the degree of effective PMA could be controlled by the junction lateral size in the presence of superconductivity and an applied electric field. We also discuss how the [Formula: see text] field could be affected by the interaction between magnetic stray fields and superconducting vortices. Our experimental findings, supported by numerical modelling of the ferromagnet-superconductor interaction, open pathways to active control of magnetic anisotropy in the emerging dissipation-free superconducting spin electronics.

Unconventional superconductivity on a topological insulator.

We study proximity-induced superconductivity on the surface of a topological insulator (TI), focusing on unconventional pairing. We find that the excitation spectrum becomes gapless for any spin-triplet pairing, such that both subgap bound states and Andreev reflection is strongly suppressed. For spin-singlet pairing, the zero-energy surface state in the d(xy)-wave case becomes a Majorana fermion, in contrast with the situation realized in the topologically trivial high-T(c) cuprates. We also study the influence of a Zeeman field on the surface states. Both the magnitude and direction of this field are shown to strongly influence the transport properties, in contrast with the case without TI. We predict an experimental signature of the Majorana states via conductance spectroscopy.

Controlling spin supercurrents via nonequilibrium spin injection.

We propose a mechanism whereby spin supercurrents can be manipulated in superconductor/ferromagnet proximity systems via nonequilibrium spin injection. We find that if a spin supercurrent exists in equilibrium, a nonequilibrium spin accumulation will exert a torque on the spins transported by this current. This interaction causes a new spin supercurrent contribution to manifest out of equilibrium, which is proportional to and polarized perpendicularly to both the injected spins and the equilibrium spin current. This is interesting for several reasons: as a fundamental physical effect; due to possible applications as a way to control spin supercurrents; and timeliness in light of recent experiments on spin injection in proximitized superconductors.

Author Correction: Induced unconventional superconductivity on the surface states of Bi2Te3 topological insulator.

The original version of this Article omitted the following from the Acknowledgements:"This work was partly supported by the Research Council of Norway through its Centres of Excellence funding scheme, project number 262633, QuSpin."This has now been corrected in both the PDF and HTML versions of the article.