Interfacial Spin-orbit Coupling Research Articles

Pd층의 두께 변화에 따른 [Co/Pd] 다층박막의 연엑스선 방사광 분광 연구

We have investigated the electronic structures of intermetallic multilayer (ML) films of [Co(2A)/Pd(xA)] (x: the thickness of the Pd sublayer; x = 1 A, 3 A, 5 A, 7 A, 9 A) by employing soft X-ray absorption spectroscopy (XAS) and soft X-ray magnetic circular dichroism (XMCD). Both Co 2p XAS and XMCD spectra are found to be similar to one another, as well as to those of Co metal, providing evidence for the metallic bonding of Co ions in [Co/Pd] ML films. By analyzing the measured Co 2p XMCD spectra, we have determined the orbital magnetic moments and the spin magnetic moments of Co ions in [Co(2A)/Pd(xA)] ML films. Based on this analysis, we have found that the orbital magnetic moments are enhanced greatly when x increases from 1 A to 3 A, and then do not change much for x ≥ 3 A. This finding suggests that the interface spin-orbit coupling plays an important role in determining the perpendicular magnetic anisotropy in [Co/Pd] ML films.

Enhancement of perpendicular magnetic anisotropy and anomalous hall effect in Co/Ni multilayers

The perpendicular magnetic anisotropy (PMA) and the anomalous Hall effect (AHE) in Co/Ni multilayer were optimized by manipulating its interface structure (inducing HfO2 capping layer and Pt insertion) and post-annealing treatment. A strong PMA can be obtained in Co/Ni multilayers with HfO2 capping layer even after annealing at 400°C. The heavy metal Hf may improve the interfacial spin-orbit coupling, which responsible for the enhanced PMA and high annealing stability. Moreover, the multilayer containing HfO2 capping layer also exhibited high saturation anomalous Hall resistivity through post-annealing, which is 0.85μΩcm after annealing at 375°C, 211% larger than in the sample at deposited state which is only 0.27μΩcm. The enhancement of AHE is mainly attributed to the interface scattering through post-annealing treatment.

Spin-current-driven thermoelectric generation based on interfacial spin-orbit coupling

The longitudinal spin Seebeck effect (SSE) in Bi2O3/Cu/yttrium-iron-garnet (YIG) devices has been investigated. When an out-of-plane temperature gradient is applied to the Bi2O3/Cu/YIG device, a spin current is generated across the Cu/YIG interface via the SSE and then converted into electric voltage due to the spin–orbit coupling at the Bi2O3/Cu interface. The sign of the SSE voltage in the Bi2O3/Cu/YIG devices is opposite to that induced by the conventional inverse spin Hall effect in Pt/YIG devices. The SSE voltage in the Bi2O3/Cu/YIG devices disappears in the absence of the Bi2O3 layer and its thermoelectric conversion efficiency is independent of the Cu thickness, indicating the important role of the Bi2O3/Cu interface. This result demonstrates that not only the bulk inverse spin Hall effect but also the spin–orbit coupling near the interface can be used for SSE-based thermoelectric generation.

Interfacial spin-orbit torque without bulk spin-orbit coupling

An electric current in the presence of spin-orbit coupling can generate a spin accumulation that exerts torques on a nearby magnetization. We demonstrate that, even in the absence of materials with strong bulk spin-orbit coupling, a torque can arise solely due to interfacial spin-orbit coupling, namely Rashba-Eldestein effects at metal/insulator interfaces. In magnetically soft NiFe sandwiched between a weak spin-orbit metal (Ti) and insulator (Al$_2$O$_3$), this torque appears as an effective field, which is significantly larger than the Oersted field and sensitive to insertion of an additional layer between NiFe and Al$_2$O$_3$. Our findings point to new routes for tuning spin-orbit torques by engineering interfacial electric dipoles.

Spin Circuit Model for 2D Channels with Spin-Orbit Coupling.

In this paper we present a general theory for an arbitrary 2D channel with “spin momentum locking” due to spin-orbit coupling. It is based on a semiclassical model that classifies all the channel electronic states into four groups based on the sign of the z-component of the spin (up (U), down (D)) and the sign of the x-component of the velocity (+, −). This could be viewed as an extension of the standard spin diffusion model which uses two separate electrochemical potentials for U and D states. Our model uses four: U+, D+, U−, and D−. We use this formulation to develop an equivalent spin circuit that is also benchmarked against a full non-equilibrium Green’s function (NEGF) model. The circuit representation can be used to interpret experiments and estimate important quantities of interest like the charge to spin conversion ratio or the maximum spin current that can be extracted. The model should be applicable to topological insulator surface states with parallel channels as well as to other layered structures with interfacial spin-orbit coupling.

Hybrid magnetoresistance in Pt-based multilayers: Effect originated from strong interfacial spin-orbit coupling.

The hybrid magnetoresistance (MR) behaviors in Pt/Co90Fe10/Pt, Mn1.5Ga/Pt and Mn1.5Ga/Pt/Co90Fe10/Pt multilayers have been investigated. Both planer Hall effect (PHE) and angle-dependent MR in Pt/Co90Fe10/Pt revealed the combination of spin Hall MR (SMR) and normal anisotropic MR (AMR), indicating the large contribution of strong spin-orbit coupling (SOC) at the interfaces. When Pt contacted with perpendicular magnetic anisotropy (PMA) metal Mn1.5Ga, the strong interfacial SOC modified the effective anomalous Hall effect. The MR in Mn1.5Ga/Pt/Co90Fe10/Pt is not a simple combination of SMR and AMR, but ascribed to the complicated domain wall scattering and strong interfacial SOC when Pt is sandwiched by the in-plane magnetized Co90Fe10 and the PMA Mn1.5Ga.

Effect of interfacial spin–orbit coupling on spin-dependent tunnelling

We investigate the incident angle-dependent spin polarisation transport in a ballistic nonmagnetic nanojunction with interfacial spin–orbit (SO) coupling by means of the mode-matching approach. In the absence of interfacial SO coupling, for both delta function and square-shaped barriers, the probabilities of transmission for spin up and spin down are the same and are even functions of the injection angle. On the other hand, in the presence of interfacial SO coupling, the transmission probabilities for spin up and spin down are different and are asymmetric with respect to the direction of the normal incidence. Moreover, we study the total transmission properties and analyse the spin polarisation properties of these systems. In particular, for the case of interface with SO coupling, we find that the spin polarisation oscillates with respect to the incident angle. This characteristic offers an efficient way to achieve the spin injection device without using ferromagnets.

Tunneling Anomalous and Spin Hall Effects.

We predict, theoretically, the existence of the anomalous Hall effect when a tunneling current flows through a tunnel junction in which only one of the electrodes is magnetic. The interfacial spin-orbit coupling present in the barrier region induces a spin-dependent momentum filtering in the directions perpendicular to the tunneling current, resulting in a skew tunneling even in the absence of impurities. This produces an anomalous Hall conductance and spin Hall currents in the nonmagnetic electrode when a bias voltage is applied across the tunneling heterojunction. If the barrier is composed of a noncentrosymmetric material, the anomalous Hall conductance and spin Hall currents become anisotropic with respect to both the magnetization and crystallographic directions, allowing us to separate this interfacial phenomenon from the bulk anomalous and spin Hall contributions. The proposed effect should be useful for proving and quantifying the interfacial spin-orbit fields in metallic and metal-semiconductor systems.

Out-of-plane spin-orientation dependent magnetotransport properties in the anisotropic helimagnetCr1/3NbS2

Understanding the role of spin-orbit coupling (SOC) has been crucial to controlling magnetic anisotropy in magnetic multilayer films. It has been shown that electronic structure can be altered via interface SOC by varying the superlattice structure, resulting in spontaneous magnetization perpendicular or parallel to the plane. In lieu of magnetic thin films, we study the similarly anisotropic helimagnet Cr$_{1/3}$NbS$_2$, where the spin polarization direction, controlled by the applied magnetic field, can modify the electronic structure. As a result, the direction of spin polarization can modulate the density of states, and in turn affect the in-plane electrical conductivity. In Cr$_{1/3}$NbS$_2$, we found an enhancement of in-plane conductivity when the spin polarization is out-of-plane, as compared to in-plane spin polarization. This is consistent with the increase of density of states near the Fermi energy at the same spin configuration, found from first principles calculations. We also observe unusual field dependence of the Hall signal in the same temperature range. This is unlikely to originate from the non-collinear spin texture, but rather further indicates strong dependence of electronic structure on spin orientation relative to the plane.

Experimental demonstration of the coexistence of spin Hall and Rashba effects inβ−tantalum/ferromagnetbilayers

We have measured the spin torques of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{tantalum}/\mathrm{C}{\mathrm{o}}_{20}\mathrm{F}{\mathrm{e}}_{60}{\mathrm{B}}_{20}$ bilayers versus Ta thickness at room temperature using a ferromagnetic resonance (FMR) technique. A significant fieldlike spin torque originating from Ta was identified, which is constant and independent of Ta thickness. Because of this constant torque, the spin Hall coefficient ${\ensuremath{\theta}}_{\mathrm{SH}}$ needs to be calculated from the ratio of the symmetric component of the FMR signal to the slope of the antisymmetric component with Ta thickness, from which a value of $\ensuremath{-}0.11\ifmmode\pm\else\textpm\fi{}0.01$ was determined. The saturation magnetization of the CoFeB layers for samples deposited with Ta was found to be smaller than that of a single CoFeB layer, with values of $1.84\ifmmode\pm\else\textpm\fi{}0.01$ and $1.92\ifmmode\pm\else\textpm\fi{}0.01$ T, respectively. The origin of the fieldlike torque is ascribed to an interface spin-orbit coupling, or Rashba effect, due to the strength and constancy of the torque with Ta thickness. From fitting measured data to a semiclassical diffusion model that includes interface spin-orbit coupling, we have determined the spin diffusion length for \ensuremath{\beta}-tantalum to be 2.5 nm.

Current-induced spin polarization at the surface of metallic films: A theorem and anab initiocalculation

The broken inversion symmetry at the surface of a metallic film (or, more generally, at the interface between a metallic film and a different metallic or insulating material) greatly amplifies the influence of the spin-orbit interaction on the surface properties. The best known manifestation of this effect is the momentum-dependent splitting of the surface state energies (Rashba effect). Here we show that the same interaction also generates a spin-polarization of the bulk states when an electric current is driven through the bulk of the film. For a semi-infinite jellium model, which is representative of metals with a closed Fermi surface, we prove as a theorem that, regardless of the shape of the confinement potential, the induced surface spin density at each surface is given by ${\bf S} =-\gamma \hbar {\bf \hat z}\times {\bf j}$, where ${\bf j}$ is the particle current density in the bulk, ${\bf \hat z}$ the unit vector normal to the surface, and $\gamma=\frac{\hbar}{4mc^2}$ contains only fundamental constants. For a general metallic solid $\gamma$ becomes a material-specific parameter that controls the strength of the interfacial spin-orbit coupling. Our theorem, combined with an {\it ab initio} calculation of the spin polarization of the current-carrying film, enables a determination of $\gamma$, which should be useful in modeling the spin-dependent scattering of quasiparticles at the interface.

Intrinsic magnetoresistance in metal films on ferromagnetic insulators

We predict a magnetoresistance induced by the interfacial Rashba spin-orbit coupling in normal metal/ferromagnetic insulator bilayers. It depends on the angle between current and magnetization directions as found for the ``spin Hall magnetoresistance'' mechanism, i.e., the combined action of spin Hall and inverse spin Hall effects. By the identical phenomenology it is not obvious whether the magnetoresistance reported by Nakayama et al. [Phys. Rev. Lett. 110, 206601 (2013)] is a bulk metal or interface effect. The interfacial Rashba-induced magnetoresistance may be distinguished from the bulk metal spin Hall magnetoresistance by its dependence on the metal film thickness.

Spin Hall and Edelstein effects in metallic films: From two to three dimensions

A normal metallic film sandwiched between two insulators may have strong spin-orbit coupling near the metal-insulator interfaces, even if spin-orbit coupling is negligible in the bulk of the film. In this paper, we study two technologically important and deeply interconnected effects that arise from interfacial spin-orbit coupling in metallic films. The first is the spin Hall effect, whereby a charge current in the plane of the film is partially converted into an orthogonal spin current in the same plane. The second is the Edelstein effect, in which a charge current produces an in-plane, transverse spin polarization. At variance with strictly two-dimensional Rashba systems, we find that the spin Hall conductivity has a finite value even if spin-orbit interaction with impurities is neglected and ``vertex corrections'' are properly taken into account. Even more remarkably, such a finite value becomes ``universal'' in a certain configuration. This is a direct consequence of the spatial dependence of spin-orbit coupling on the third dimension, perpendicular to the plane of the film. The nonvanishing spin Hall conductivity has a profound influence on the Edelstein effect, which we show to consist of two terms, the first with the standard form valid in a strictly two-dimensional Rashba system, and a second arising from the presence of the third dimension. Whereas the standard term is proportional to the momentum relaxation time, the new one scales with the spin relaxation time. Our results, although derived in a specific model, should be valid rather generally, whenever a spatially dependent Rashba spin-orbit coupling is present and the electron motion is not strictly two dimensional.

Angular dependence of anisotropic magnetoresistance in magnetic systems

Anisotropic magnetoresistance (AMR), whose physical origin is attributed to the combination of spin dependent scattering and spin orbital coupling (SOC), usually displays simple angular dependence for polycrystalline ferromagnetic metals. By including generic spin dependent scattering and spin Hall (SH) terms in the Ohm's law, we explicitly show that various magneto-transport phenomena such as anomalous Hall (AH), SH, planar Hall (PH) and AMR could be quantitatively related for bulk polycrystalline ferromagnetic metals. We also discuss how AMR angular dependence is affected by the presence of interfacial SOC in magnetic layered structure.

Current-induced torques and interfacial spin-orbit coupling

In bilayer systems consisting of an ultrathin ferromagnetic layer adjacent to a metal with strong spin-orbit coupling, an applied in-plane current induces torques on the magnetization. The torques that arise from spin-orbit coupling are of particular interest. Here, we calculate the current-induced torque in a Pt-Co bilayer to help determine the underlying mechanism using first principles methods. We focus exclusively on the analogue to the Rashba torque, and do not consider the spin Hall effect. The details of the torque depend strongly on the layer thicknesses and the interface structure, providing an explanation for the wide variation in results found by different groups. The torque depends on the magnetization direction in a way similar to that found for a simple Rashba model. Artificially turning off the exchange spin splitting and separately the spin-orbit coupling potential in the Pt shows that the primary source of the "field-like" torque is a proximate spin-orbit effect on the Co layer induced by the strong spin-orbit coupling in the Pt.

Chirality from Interfacial Spin-Orbit Coupling Effects in Magnetic Bilayers

As nanomagnetic devices scale to smaller sizes, spin-orbit coupling due to the broken structural inversion symmetry at interfaces becomes increasingly important. Here, we study interfacial spin-orbit coupling effects in magnetic bilayers using a simple Rashba model. The spin-orbit coupling introduces chirality into the behavior of the electrons and through them into the energetics of the magnetization. In the derived form of the magnetization dynamics, all of the contributions that are linear in the spin-orbit coupling follow from this chirality, considerably simplifying the analysis. For these systems, an important consequence is a correlation between the Dzyaloshinskii-Moriya interaction and the spin-orbit torque. We use this correlation to analyze recent experiments.

Influence of spin–orbit coupling on differential conductance of normal metal/ferromagnetic p wave superconductor junctions

The extended Blonder–Tinkham–Klapwijk model is applied to studying tunneling conductance in normal metal/ferromagnetic p wave superconductor junctions. It is found that the spin–orbit scattering at the interfaces significantly affects the tunneling conductance. The interface spin–orbit coupling (SOC) suppresses the split conductance peaks in the N/ferromagnetic px wave superconductor junction and enhances the zero-bias conductance dip (ZBCD) of py wave superconductor junction. The SOC gives rise to the asymmetry of the conductance spectrum in the ferromagnetic px+py wave superconductor junctions.

Current induced torques and interfacial spin-orbit coupling: Semiclassical modeling

In bilayer nanowires consisting of a ferromagnetic layer and a non-magnetic layer with strong spin-orbit coupling, currents create torques on the magnetization beyond those found in simple ferromagnetic nanowires. The resulting magnetic dynamics appear to require torques that can be separated into two terms, damping-like and field-like. The damping-like torque is typically derived from models describing the bulk spin Hall effect and the spin transfer torque, and the field-like torque is typically derived from a Rashba model describing interfacial spin-orbit coupling. We derive a model based on the Boltzmann equation that unifies these approaches. We also consider an approximation to the Boltzmann equation, the drift-diffusion model, that qualitatively reproduces the behavior, but quantitatively fails to reproduce the results. We show that the Boltzmann equation with physically reasonable parameters can match the torques for any particular sample, but in some cases, it fails to describe the experimentally observed thickness dependences.

Odd-frequency spin-triplet pairing states in half-metal/d-wave superconductor junctions

Based on the extended Blonder–Tinkham–Klapwijk formalism, differential conductance spectrum of d-wave superconductor/half-metal junctions is investigated as a function of the interfacial spin–orbit coupling (SOC). It shows that the SOC modifies the interfacial spin-flip scattering, enabling spin-singlet and spin-triplet pairing conversion with the aid of equal-spin-band Andreev reflection. A zero-bias conductance peak has been found, which is closely related to the zero energy Andreev bound state of equal-spin pairing correlation induced by the broken electron-hole symmetry of model Hamiltonian and gives strong evidences for the odd-frequency spin-triplet pairing states.

Spin-Hall conductivity and electric polarization in metallic thin films

We predict theoretically that, when a normal metallic thin film (without bulk spin-orbit coupling, such as Cu or Al) is sandwiched by two insulators, two prominent effects arise due to the interfacial spin-orbit coupling: a giant spin-Hall conductivity due to the surface scattering and a transverse electric polarization due to the spin-dependent phase shift in the spinor wave functions.