Nonequilibrium Spin Density Research Articles

Spin-anomalous-Hall unidirectional magnetoresistance in light-metal/ferromagnetic-metal bilayers

Nonreciprocal magnetotransport is one of the central topics in spintronics because of its importance for electrically probing magnetic information. Among numerous electrical probes used to read magnetic orders, unidirectional magnetoresistance (UMR), characterized by sign changes upon reversal of either current or magnetization, is currently a matter of great interest and has been identified in various spin–orbit-coupled bilayer systems composed of an (anti)ferromagnetic layer and a nonmagnetic layer with strong spin Hall effect. A recent theoretical work predicts that a spin-anomalous-Hall (SAH) UMR in those metallic conducting bilayers can originate from the spin-anomalous-Hall effect of the ferromagnetic layer and the structural inversion asymmetry. However, this type of UMR has not been reported experimentally. Here, we give the experimental evidence of spin-anomalous-Hall UMR in the light-metal/ferromagnetic-metal Cu/Co bilayers, where the emergence of net nonequilibrium spin density is attributed to the interfacial spin leakage asymmetry due to the spin memory loss effect at the Cu/Co interface and multiple spin reflections. We also show a highly tunable UMR in the Cu/Co/CuOx trilayer by varying the Cu thickness, which is due to the competition between the orbital Rashba effect in Co/CuOx and the spin-anomalous-Hall effect in Cu/Co. Our work widens the material choice for UMR device applications and provides an alternative approach to detect in-plane magnetization without an external spin polarizer.

Phase biasing of a Josephson junction using Rashba–Edelstein effect

A charge-current-induced shift in the spin-locked Fermi surface leads to a non-equilibrium spin density at a Rashba interface, commonly known as the Rashba–Edelstein effect. Since this is an intrinsically interfacial property, direct detection of the spin moment is difficult. Here we demonstrate that a planar Josephson Junction, realized by placing two closely spaced superconducting electrodes over a Rashba interface, allows for a direct detection of the spin moment as an additional phase in the junction. Asymmetric Fraunhofer patterns obtained for Nb-(Pt/Cu)-Nb nano-junctions, due to the locking of Rashba–Edelstein spin moment to the flux quantum in the junction, provide clear signatures of this effect. This simple experiment offers a fresh perspective on direct detection of spin polarization induced by various spin-orbit effects. In addition, this platform also offers a magnetic-field-controlled phase biasing mechanism in conjunction with the Rashba–Edelstein spin-orbit effect for superconducting quantum circuits.

Controllable valley magnetic response in phase-transformed tungsten diselenide

Achieving valley pseudospin with large polarization is crucial in the implementation of quantum information applications. Transition metal dichalcogenides (TMDC) with different phase structures provide an ideal platform for valley modulation. The valley splitting has been achieved in hybrid phase WSe2, while its valley polarization remains unstudied. Magnetic field controllable valley polarization is explored in WSe2 with coexistence of H and T phases by an all-optical route. A record high valley polarization of 58.3% is acquired with a 19.9% T phase concentration under a 4-T magnetic field and nonresonant excitation. The enhanced valley polarization is dependent on the phase component and shows various increasing slopes, owing to the synergy between the T phase WSe2 and the magnetic field. The magnetic field controlled local magnetic momentums are revealed as the mechanism for the large valley polarization in H / T-WSe2. This speculation is also verified by theoretical simulations of the nonequilibrium spin density. These results display a considerable valley magnetic response in phase-engineered TMDC and provide a large-scale scheme for valley polarization applications.

Twist angle controlled collinear Edelstein effect in van der Waals heterostructures

The generation of spatially homogeneous spin polarization by application of electric current is a fundamental manifestation of symmetry-breaking spin--orbit coupling (SOC) in solid-state systems, which underpins a wide range of spintronic applications. Here, we show theoretically that twisted van der Waals heterostructures with proximity-induced SOC are candidates par excellence to realize exotic spin-charge transport phenomena due to their highly tunable momentum-space spin textures. Specifically, we predict that graphene/group-VI dichalcogenide bilayers support room temperature spin--current responses that can be manipulated via twist-angle control. For critical twist angles, the non-equilibrium spin density is pinned parallel to the applied current. This effect is robust against twist-angle disorder, with graphene/$\text{WSe}_{2}$ possessing a critical angle (purely collinear response) of $\theta_{c} \simeq 14^{\circ}$. A simple electrical detection scheme to isolate the collinear Edelstein effect is proposed.

Spin anomalous-Hall unidirectional magnetoresistance

We predict a spin anomalous-Hall unidirectional magnetoresistance (AH-UMR) in conducting bilayers composed of a ferromagnetic layer and a nonmagnetic layer, which does not rely on the spin Hall effect in the normal metal layer---in stark contrast to the well-studied unidirectional spin-Hall magnetoresistance---but instead arises from the spin anomalous Hall effect in the ferromagnetic layer. Physically, it is the charge-spin conversion induced by the spin anomalous Hall effect that conspires with the structural inversion asymmetry to generate a net nonequilibrium spin density in the ferromagnetic layer, which, in turn, modulates the resistance of the bilayer when the direction of the applied current or the magnetization is reversed. The dependencies of the spin AH-UMR effect on materials and geometric parameters are analyzed and compared with other nonlinear magnetoresistances. In particular, we show that, in magnetic bilayers where spin anomalous Hall and spin Hall effects are comparable, the overall UMR may undergo a sign change when the thickness of either layer is varied, suggesting a scheme to quantify the spin Hall or spin anomalous Hall angle via a nonlinear transport measurement.

Non-equilibrium spin polarization in magnetic two-dimensional electron gas with k-linear and k-cubed Dresselhaus spin–orbit interaction

The current-induced spin polarization (CISP) of charge carriers is one of the main mechanisms of spin-to-charge interconversion effects that can be used in new spintronics devices. Here, CISP is studied theoretically in symmetric quantum wells growing in [001] crystallographic direction, where both k -linear and k -cubed Dresselhaus spin–orbit interactions are present. The exchange interaction responsible for perpendicular to plane net magnetization is also taken into account. The main focus is on the influence of cubic Dresselhaus term on CISP and the interplay between spin–orbit interaction (SOI) and the exchange field. The analytical and numerical results are derived within the linear response theory and Matsubara Green’s function formalism. Apart from detailed numerical results, we also provide some analytical expressions that may be useful for interpretation of experimental results and for characterization of quantum wells with Dresselhaus SOI. Analytical expressions for the relevant Berry curvature are also derived, and it is shown that the Berry curvature in magnetic 2DEG with cubic Dresselhaus interaction oscillates in the k -space, while its averaged value is reduced. We also analyze the temperature behavior of CISP and calculate the low-temperature spin polarizability due to heat current. • The effects of the interplay of Dresselhaus spin–orbit interaction (SOI) (with both k -linear and k -cubed terms) and exchange interaction on the nonequilibrium current-induced spin polarization, have been analyzed. • The k -cubed term in Dresselhaus SOI leads to a decrease in nonequilibrium spin density with increasing chemical potential. • The cubic Dresselhaus SOI in magnetic 2DEG creates Berry curvature oscillations in the k -space and reduces the Berry curvature with increasing energy. • The out of plane magnetization leads to an additional component of spin polarization and also to anomalous Hall conductivity that is robust against impurities. • Thermally-induced spin-polarization is analyzed and is shown to be remarkable in a well-defined range of chemical potential.

Magnon- versus Electron-Mediated Spin-Transfer Torque Exerted by Spin Current across an Antiferromagnetic Insulator to Switch the Magnetization of an Adjacent Ferromagnetic Metal

The recent experiment [Y. Wang et al., Science 366, 1125 (2019)] on magnon-mediated spin-transfer torque (MSTT) was interpreted in terms of a picture where magnons are excited within an antiferromagnetic insulator (AFI), by applying nonequilibrium electronic spin density at one of its surfaces, so that their propagation across AFI deprived of conduction electrons eventually leads to reversal of magnetization of a ferromagnetic metal (FM) attached to the opposite surface of AFI. We employ a recently developed time-dependent nonequilibrium Green functions combined with the Landau-Lifshitz-Gilbert equation (TDNEGF+LLG) formalism to evolve conduction electrons quantum-mechanically while they interact via self-consistent back-action with localized magnetic moments described classically by atomistic spin dynamics solving a system of LLG equations. Upon injection of square current pulse as the initial condition, TDNEGF+LLG simulations of FM-polarizer/AFI/FM-analyzer junctions show that reversal of localized magnetic moments within FM-analyzer is less efficient, in the sense of requiring larger pulse height and its longer duration, than conventional electron-mediated STT (ESTT) driving magnetization switching in standard FM-polarizer/normal-metal/FM-analyzer spin valve. Since both electronic, generated by spin pumping from AFI, and magnonic, generated by direct transmission from AFI, spin currents are injected into the FM-analyzer, its localized magnetic moments will experience combined MSTT and ESTT. Nevertheless, by artificially turning off ESTT we demonstrate that MSTT plays a dominant role whose understanding, therefore, paves the way for all-magnon-driven magnetization switching devices with no electronic parts.

Spin transfer torque in Mn3Ga -based ferrimagnetic tunnel junctions from first principles

We report on first-principles calculations of spin-transfer torque (STT) in epitaxial magnetic tunnel junctions (MTJs) based on ferrimagnetic tetragonal Mn$_3$Ga electrodes, both as analyzer in an Fe/MgO stack, and also in an analogous stack with a second Mn$_3$Ga electrode (instead of Fe) as polarizer. Solving the ballistic transport problem (NEGF + DFT) for the nonequilibrium spin density in a scattering region extended to over 7.6 nm into the Mn$_3$Ga electrode, we find long-range spatial oscillations of the STT decaying on a length scale of a few tens of angstroms, both in the linear response regime and for finite bias. The oscillatory behavior of the STT in Mn$_3$Ga is robust against variations in the stack geometry and the applied bias voltage, which may affect the phase and the amplitude of the spatial oscillation, but the wave number is only responsive to variations in the longitudinal lattice constant of Mn$_3$Ga (for fixed in-plane geometry) without being commensurate with the lattice. Our interpretation of the long-range STT oscillations is based on the bulk electronic structure of Mn$_3$Ga, taking also into account the spin-filtering properties of the MgO barrier. Comparison to a fully Mn$_3$Ga-based stack shows similar STT oscillations, but a significant enhancement of both the TMR effect at the Fermi level and the STT at the interface, due to resonant tunneling for the mirror-symmetric junction with thinner barrier (three monoatomic layers). From the calculated energy dependence of the spin-polarized transmissions at 0 V, we anticipate asymmetric or symmetric TMR as a function of the applied bias voltage for the Fe-based and the all-Mn$_3$Ga stacks, respectively, which also both exhibit a sign change below 1 V. In the latter (symmetric) case we expect a TMR peak at zero, which is larger for the thinner barriers because of a spin-polarized resonant tunneling contribution.

Switchable Enhanced Spin Photocurrent in Rashba and Cubic Dresselhaus Ferroelectric Semiconductors

Generating and controlling spin current (SC) are of central interest in spin physics and applications. To date, the spin-orbit interaction (SOI) is an established pathway to generate SC through the spin-charge current conversion. We predict an efficient spin-light conversion via the Rashba and higher-order cubic Dresselhaus SOIs in ferroelectrics. Different from the known Edelstein effect, where SC is created by the nonequilibrium spin density, our predicted spin-polarized current is from direct interactions between light and unique spin textures generated by SOI in ferroelectrics. Using first-principles simulations, we demonstrate these concepts by calculating the DC spin photocurrent in a prototypical Rashba ferroelectric, α-GeTe. The photoinduced SC is about 2 orders of magnitude larger than the charge photocurrent. More importantly, we can conveniently switch the direction of SC by an applied electric field via inverting the spin textures. These predictions give hope to generating and controlling light-driven SC via a nonvolatile electric field.

Harnessing Orbital-to-Spin Conversion of Interfacial Orbital Currents for Efficient Spin-Orbit Torques.

Current-induced spin-orbit torques (SOTs) allow for the efficient electrical manipulation of magnetism in spintronic devices. Engineering the SOT efficiency is a key goal that is pursued by maximizing the active interfacial spin accumulation or modulating the nonequilibrium spin density that builds up through the spin Hall and inverse spin galvanic effects. Regardless of the origin, the fundamental requirement for the generation of the current-induced torques is a net spin accumulation. We report on the large enhancement of the SOT efficiency in thulium iron garnet (TmIG)/Pt by capping with a CuO_{x} layer. Considering the weak spin-orbit coupling (SOC) of CuO_{x}, these surprising findings likely result from an orbital current generated at the interface between CuO_{x} and Pt, which is injected into the Pt layer and converted into a spin current by strong SOC. The converted spin current decays across the Pt layer and exerts a "nonlocal" torque on TmIG. This additional torque leads to a maximum colossal enhancement of the SOT efficiency of a factor 16 for 1.5nm of Pt at room temperature, thus opening a path to increase torques while at the same time offering insights into the underlying physics of orbital transport, which has so far been elusive.

Spin-orbit-proximitized ferromagnetic metal by monolayer transition metal dichalcogenide: Atlas of spectral functions, spin textures, and spin-orbit torques in Co/MoSe2, Co/WSe2 , and Co/TaSe2 heterostructures

The bilayer heterostructures composed of an ultrathin ferromagnetic metal (FM) and a material hosting strong spin-orbit (SO) coupling are principal resource for SO torque and spin-to-charge conversion nonequilibrium effects in spintronics. We demonstrate how hybridization of wavefunctions of Co layer and a monolayer of transition metal dichalcogenides (TMDs)---such as semiconducting MoSe$_2$ and WSe$_2$ or metallic TaSe$_2$---can lead to dramatic transmutation of electronic and spin structure of Co within some distance away from its interface with TMD, when compared to the bulk of Co or its surface in contact with vacuum. This is due to proximity induced SO splitting of Co bands encoded in the spectral functions and spin textures on its monolayers, which we obtain using noncollinear density functional theory (ncDFT) combined with equilibrium Green function (GF) calculations. In fact, SO splitting is present due to structural inversion asymmetry of the bilayer even if SO coupling within TMD monolayer is artificially switched off in ncDFT calculations, but switching it on makes the effects associated with proximity SO coupling within Co layer about five times larger. Injecting spin-unpolarized charge current through SO-proximitized monolayers of Co generates nonequilibrium spin density over them, so that its cross product with the magnetization of Co determines SO torque. The SO torque computed via first-principles quantum transport methodology, which combines ncDFT with nonequilibrium GF calculations, can be used as the screening parameter to identify optimal combination of materials and their interfaces for applications in spintronics. In particular, we identify heterostructure two-monolayer-Co/monolayer-WSe$_2$ as the most optimal.

Scattering-induced and highly tunable by gate damping-like spin-orbit torque in graphene doubly proximitized by two-dimensional magnet Cr2Ge2Te6 and monolayer WS2

The authors design in silico a graphene-based van der Waals heterostructure where purely two-dimensional electronic transport generates nonequilibrium spin density in all spatial directions, due to scattering of impurities or potential barriers.

Control of Spin-Orbit Torques by Interface Engineering in Topological Insulator Heterostructures.

(Bi1-xSbx)2Te3 topological insulators (TIs) are gathering increasing attention owing to their large charge-to-spin conversion efficiency and the ensuing spin-orbit torques (SOTs) that can be used to manipulate the magnetization of a ferromagnet (FM). The origin of the torques, however, remains elusive, while the implications of hybridized states and the strong material intermixing at the TI/FM interface are essentially unexplored. By combining interface chemical analysis and spin-transfer ferromagnetic resonance (ST-FMR) measurements, we demonstrate that intermixing plays a critical role in the generation of SOTs. By inserting a suitable normal metal spacer, material intermixing is reduced and the TI properties at the interface are largely improved, resulting in strong variations in the nature of the SOTs. A dramatic enhancement of a field-like torque, opposing and surpassing the Oersted-field torque, is observed, which can be attributed to the non-equilibrium spin density in Rashba-split surface bands and to the suppression of spin memory loss. These phenomena can play a relevant role at other interfaces, such as those comprising transition metal dichalcogenides.

Spin current polarization and electrical conductivity in metal helimagnets

The peculiarities of spin and charge kinetics in helical magnetic metals that are due to forces acting on the magnetic moment of conduction electrons in inhomogeneous magnetic field have been considered. Analyzing the equations of motion for non-equilibrium spin density shows that an electric field directed along the axis of the helix produces conduction-electron spin polarization along this direction. Under the same conditions, the directions of polarization of the spin current and polarization of the locally equilibrium spin density are collinear. The specific structure of the effective exchange field acting on the conduction electrons in helical magnets causes two additional spin relaxation mechanisms to emerge. In addition to the mechanism of spin-lattice relaxation, “diffusion” and “precession” mechanisms of spin relaxation exist in conductive helical magnets. The diffusion mechanism is analogous to the Dyakonov-Perel spin relaxation mechanism. The key point is that the inhomogeneities of a magnetic field initiate a coupling between the spin and charge systems. It has been shown that, in a helical metal, the electrical conductivity decreases due to the action of the non-uniform exchange magnetic field.

Electrically-driven Domain Wall Motion in Quantum Anomalous Hall States

We theoretically study domain wall motion induced by an electric field in the quantum anomalous Hall states on a two-dimensional Kagome lattice with ferromagnetic order and spin-orbit coupling. We show that an electric charge is accumulated near the domain wall which indicates that the electric field drives both the accumulated charge and the domain wall with small energy dissipation. Using the linear response theory we compute the non-equilibrium spin density which exerts a non-adiabatic spin transfer torque on textures of the local magnetization. This torque emerges even when the bulk is insulating and does not require the longitudinal electric current. Finally, we estimate the velocity of domain wall motion in this system, which is faster than that in conventional metals.

Nonequilibrium spin density and spin-orbit torque in a three-dimensional topological insulator/antiferromagnet heterostructure

We study the behavior of non-equilibrium spin density and spin-orbit torque in a topological insulator - antiferromagnet heterostructure. Unlike ferromagnetic heterostructures where Dirac cone is gapped due to time-reversal symmetry breaking, here the Dirac cone is preserved. We demonstrate the existence of a staggered spin density corresponding to a damping like torque, which is quite robust against the scalar impurity, when the transport energy is in the topological insulator surface energy regime. We show the contribution to the non-equilibrium spin density due to both surface and bulk topological insulator bands. Finally, we show that the torques in topological insulator-antiferromagnet heterostructure exhibit an angular dependence that is consistent with the standard spin-orbit torque obtained in Rashba system with some additional nonlinear effects arising from the interfacial coupling.

Spin-orbit torque in a thin film of the topological insulator Bi2Se3: Crossover from the ballistic to diffusive regime

The spin-orbit torque provides an efficient method for switching the direction of a magnetization by using an electric field. Owing to the spin-orbit coupling, when an electric field is applied, a nonequilibrium spin density is generated, which exerts a torque on the local magnetization. Here, we investigate the spin-orbit torque in a thin film of topological insulator based upon a Boltzmann equation, with proper boundary conditions, which is applicable from the ballistic regime to the diffusive regime. It is shown that due to the spin-momentum interlocking of the electron surface states, the magnitude of the field-like torque is simply in linear proportion to the longitudinal electrical current. For a fixed electric field, the spin-orbit torque is proportional to the sample length in the ballistic limit, and saturates to a constant in the diffusive limit. The dependence of the torque on the magnetization direction and exchange coupling strength is also studied. Our theory may offer useful guidance for experimental investigations of the spin-orbit torque in finite-size systems.

Giant spin-orbit torque and spin current generation in carriers at oxide interfaces

Interfacing polar insulating oxides may result in the formation of interface-confined, high density carriers with a number of emergent properties. A local coupling of carriers to a helimagnetic oxide layer is shown to lead to an effective spin-orbit interaction with a band splitting determined by the local s-d exchange interaction. As a result a bias-induced, non-equilibrium long-lived spin density normal to the spiral plane is predicted. We find that the spin accumulation is strongly enhanced when only one of the two bands is at the Fermi level and the chemical potential is close to the band edge. As a consequence we predict a large spin-transfer torque and spin current emission that can be utilized for oxide-based spintronic applications.

Spin-torque generation in topological insulator based heterostructures

Heterostructures utilizing topological insulators exhibit a remarkable spin-torque efficiency. However, the exact origin of the strong torque, in particular whether it stems from the spin-momentum locking of the topological surface states or rather from spin-Hall physics of the topological-insulator bulk remains unclear. Here, we explore a mechanism of spin-torque generation purely based on the topological surface states. We consider topological-insulator-based bilayers involving ferromagnetic metal (TI/FM) and magnetically doped topological insulators (TI/mdTI), respectively. By ascribing the key theoretical differences between the two setups to location and number of active surface states, we describe both setups within the same framework of spin diffusion of the non-equilibrium spin density of the topological surface states. For the TI/FM bilayer, we find large spin-torque efficiencies of roughly equal magnitude for both in-plane and out-of-plane spin torques. For the TI/mdTI bilayer, we elucidate the dominance of the spin-transfer-like torque. However, we cannot explain the orders of magnitude enhancement reported. Nevertheless, our model gives an intuitive picture of spin-torque generation in topological-insulator-based bilayers and provides theoretical constraints on spin-torque generation due to topological surface states.

Diffusive Spin Dynamics in Ferromagnetic Thin Films with a Rashba Interaction

In a ferromagnetic metal layer, the coupled charge and spin diffusion equations are obtained in the presence of both Rashba spin-orbit interaction and magnetism. The misalignment between the magnetization and the nonequilibrium spin density induced by the Rashba field gives rise to Rashba spin torque acting on the ferromagnetic order parameter. In a general form, we find that the Rashba torque consists of both in-plane and out-of-plane components, i.e., T=T(perpendicular)y^×m^+T(parallel)m^×(y^×m^). Numerical simulations on a two-dimensional nanowire consider the impact of diffusion on the Rashba torque and reveal a large enhancement to the ratio T(parallel)/T(perpendicular) for thin wires. Our theory provides an explanation for the mechanism driving the magnetization switching in a single ferromagnet as observed in the recent experiments.