Spin-galvanic Effect Research Articles

Theory of current-induced spin polarization in an electron gas

We derive the Bloch equations for the spin dynamics of a two-dimensional electron gas in the presence of spin-orbit coupling. For the latter we consider both the intrinsic mechanisms of structure inversion asymmetry (Rashba) and bulk inversion asymmetry (Dresselhaus), and the extrinsic ones arising from the scattering from impurities. The derivation is based on the SU(2) gauge-field formulation of the Rashba-Dresselhaus spin-orbit coupling. Our main result is the identification of a new spin-generation torque arising from the Elliot-Yafet process, which opposes a similar term arising from the Dyakonov-Perel process. The new spin-generation torque contributes to the current-induced spin polarization (CISP) -- also known as the Edelstein or inverse spin-galvanic effect. As a result, the behavior of the CISP turns out to be more complex than one would surmise from consideration of the internal Rashba-Dresselhaus fields alone. In particular, the symmetry of the current-induced spin polarization does not necessarily coincide with that of the internal Rashba-Dresselhaus field, and an out-of-plane component of the CISP is generally predicted, as observed in recent experiments. We also discuss the extension to the three-dimensional electron gas, which may be relevant for the interpretation of experiments in thin films.

Inverse Spin Galvanic Effect in the Presence of Impurity Spin-Orbit Scattering: A Diagrammatic Approach

Spin-charge interconversion is currently the focus of intensive experimental and theoretical research both for its intrinsic interest and for its potential exploitation in the realization of new spintronic functionalities. Spin-orbit coupling is one of the key microscopic mechanisms to couple charge currents and spin polarizations. The Rashba spin-orbit coupling in a two-dimensional electron gas has been shown to give rise to the inverse spin galvanic effect, i.e., the generation of a non-equilibrium spin polarization by a charge current. Whereas the Rashba model may be applied to the interpretation of experimental results in many cases, in general, in a given real physical system, spin-orbit coupling also occurs due to other mechanisms such as Dresselhaus bulk inversion asymmetry and scattering from impurities. In this work, we consider the inverse spin galvanic effect in the presence of Rashba, Dresselhaus and impurity spin-orbit scattering. We find that the size and form of the inverse spin galvanic effect is greatly modified by the presence of the various sources of spin-orbit coupling. Indeed, spin-orbit coupling affects the spin relaxation time by adding the Elliott–Yafet mechanism to the Dyakonov–Perel, and, furthermore, it changes the non-equilibrium value of the current-induced spin polarization by introducing a new spin generation torque. We use a diagrammatic Kubo formula approach to evaluate the spin polarization-charge current response function. We finally comment about the relevance of our results for the interpretation of experimental results.

Electrical Spin Orientation, Spin-Galvanic, and Spin-Hall Effects in Disordered Two-Dimensional Systems.

In disordered systems, the hopping conductivity regime is usually realized at low temperatures where spin-related phenomena differ strongly from the cases of delocalized carriers. We develop the unified microscopic theory of current-induced spin orientation, spin-galvanic, and spin-Hall effects for the two-dimensional hopping regime. We show that the corresponding susceptibilities are proportional to each other and determined by the interplay between the drift and the diffusion spin currents. Estimations are made for realistic semiconductor heterostructures using the percolation theory. We show that the electrical spin polarization in the hopping regime increases exponentially with the increase of the concentration of localization sites and may reach a few percent at the crossover from the hopping to the diffusion conductivity regime.

Spin-charge coupled dynamics driven by a time-dependent magnetization

The spin-charge coupled dynamics in a thin, magnetized metallic system are investigated. The effective driving force acting on the charge carriers is generated by a dynamical magnetic texture, which can be induced, e.g., by a magnetic material in contact with a normal-metal system. We consider a general inversion-asymmetric substrate/normal-metal/magnet structure, which, by specifying the precise nature of each layer, can mimick various experimentally employed setups. Inversion symmetry breaking gives rise to an effective Rashba spin-orbit interaction. We derive general spin-charge kinetic equations which show that such spin-orbit interaction, together with anisotropic Elliott-Yafet spin relaxation, yields significant corrections to the magnetization-induced dynamics. In particular, we present a consistent treatment of the spin density and spin current contributions to the equations of motion, inter alia identifying a novel term in the effective force which appears due to a spin current polarized parallel to the magnetization. This "inverse spin filter" contribution depends markedly on the parameter which describes the anisotropy in spin relaxation. To further highlight the physical meaning of the different contributions, the spin pumping configuration of typical experimental setups is analyzed in detail. In the two-dimensional limit the build-up of a DC voltage is dominated by the spin galvanic (inverse Edelstein) effect. A measuring scheme that could isolate this contribution is discussed.

Supercurrent generation by spin injection in ans-wave superconductor–Rashba metal bilayer

The spin-galvanic (inverse Edelstein) and inverse spin-Hall effects are calculated for a hybrid system that combines thin superconductor and Rashba-metal layers. These effects are produced by a nonequilibrium spin polarization which is injected into the normal metal layer. This polarization gives rise to an electric potential that relaxes within some characteristic length, which is determined by Andreev reflection. Within this length the dissipative electric current of quasiparticles in the normal layer converts into the supercurrent. This process involves only subgap states and at low temperature the inelastic electron-phonon interactions are not important. It is discussed how such a hybrid system can be integrated into a SQUID where it produces an effect similar to a magnetic flux.

Spin galvanic effect at the conducting SrTiO3 surfaces

The (001) surface of SrTiO3 were transformed from insulating to conducting after Ar+ irradiation, producing a quasi two-dimensional electron gas (2DEG). This conducting surface layer can introduce Rashba spin orbital coupling due to the broken inversion symmetry normal to the plane. The spin splitting of such a surface has recently been demonstrated by magneto-resistance and angular resolved photoemission spectra measurements. Here, we present experiments evidencing a large spin-charge conversion at the conducting surface. We use spin pumping to inject a spin current from NiFe film into the surface, and measure the resulting charge current. The results indicate that the Rashba effect at the surface can be used for efficient charge-spin conversion. The conversion efficiency measured by the ratio of the spin flow density to the charge flow density is about 0.23 nm. This value is on the same order as the interfaces in metallic multilayers and 2DEG of LaAlO3/SrTiO3. In this point of view, the conducting SrTiO3 surface provides another solution for oxide spintronics.

Robust spin-orbit torque and spin-galvanic effect at the Fe/GaAs (001) interface at room temperature.

Interfacial spin-orbit torques (SOTs) enable the manipulation of the magnetization through in-plane charge currents, which has drawn increasing attention for spintronic applications. The search for material systems providing efficient SOTs, has been focused on polycrystalline ferromagnetic metal/non-magnetic metal bilayers. In these systems, currents flowing in the non-magnetic layer generate—due to strong spin–orbit interaction—spin currents via the spin Hall effect and induce a torque at the interface to the ferromagnet. Here we report the observation of robust SOT occuring at a single crystalline Fe/GaAs (001) interface at room temperature. We find that the magnitude of the interfacial SOT, caused by the reduced symmetry at the interface, is comparably strong as in ferromagnetic metal/non-magnetic metal systems. The large spin-orbit fields at the interface also enable spin-to-charge current conversion at the interface, known as spin-galvanic effect. The results suggest that single crystalline Fe/GaAs interfaces may enable efficient electrical magnetization manipulation.

Manifestation of extrinsic spin Hall effect in superconducting structures: Nondissipative magnetoelectric effects

We present a comprehensive quasiclassical approach for studying transport properties of superconducting diffusive hybrid structures in the presence of extrinsic spin-orbit coupling. We derive a generalized Usadel equation and boundary conditions that in the normal state reduce to the drift-diffusion theory governing the spin-Hall effect in inversion symmetric materials. These equations predict the non-dissipative spin-galvanic effect, that is the generation of supercurrents by a spin-splitting field, and its inverse -- the creation of magnetic moment by a supercurrent. These effects can be seen as counterparts of the spin-Hall, anomalous Hall and their inverse effects in the superconducting state. Our theory opens numerous possibilities for using superconducting structures in magnetoelectronics.

Magnetotransport signatures of the proximity exchange and spin-orbit couplings in graphene

Graphene on an insulating ferromagnetic substrate---ferromagnetic insulator or ferromagnetic metal with a tunnel barrier---is expected to exhibit giant proximity exchange and spin-orbit couplings. We use a realistic transport model of charge-disorder scattering and solve the linearized Boltzmann equation numerically exactly for the anisotropic Fermi contours of modified Dirac electrons to find magnetotransport signatures of these proximity effects: proximity anisotropic magnetoresistance, inverse spin-galvanic effect, and the planar Hall resistivity. We establish the corresponding anisotropies due to the exchange and spin-orbit couplings, with respect to the magnetization orientation. We also present parameter maps guiding towards optimal regimes for observing transport magnetoanisotropies in proximity graphene.

Reprint of : Spin polarization induced by an electric field in the presence of weak localization effects

We evaluate the spin polarization (Edelstein or inverse spin galvanic effect) and the spin Hall current induced by an applied electric field by including the weak localization corrections for a two-dimensional electron gas. We show that the weak localization effects yield logarithmic corrections to both the spin polarization conductivity relating the spin polarization and the electric field and to the spin Hall angle relating the spin and charge currents. The renormalization of both the spin polarization conductivity and the spin Hall angle combine to produce a zero correction to the total spin Hall conductivity as required by an exact identity. Suggestions for the experimental observation of the effect are given.

Valley-dependent spin-orbit torques in two-dimensional hexagonal crystals

We study spin-orbit torques in two dimensional hexagonal crystals such as graphene, silicene, germanene and stanene. The torque possesses two components, a field-like term due to inverse spin galvanic effect and an antidamping torque originating from Berry curvature in mixed spin-$k$ space. In the presence of staggered potential and exchange field, the valley degeneracy can be lifted and we obtain a valley-dependent Berry curvature, leading to a tunable antidamping torque by controlling the valley degree of freedom. The valley imbalance can be as high as 100\% by tuning the bias voltage or magnetization angle. These findings open new venues for the development of current-driven spin-orbit torques by structural design.

Spin polarization induced by an electric field in the presence of weak localization effects

We evaluate the spin polarization (Edelstein or inverse spin galvanic effect) and the spin Hall current induced by an applied electric field by including the weak localization corrections for a two-dimensional electron gas. We show that the weak localization effects yield logarithmic corrections to both the spin polarization conductivity relating the spin polarization and the electric field and to the spin Hall angle relating the spin and charge currents. The renormalization of both the spin polarization conductivity and the spin Hall angle combine to produce a zero correction to the total spin Hall conductivity as required by an exact identity. Suggestions for the experimental observation of the effect are given.

Theory of the spin-galvanic effect and the anomalous phase shiftφ0in superconductors and Josephson junctions with intrinsic spin-orbit coupling

Due to the spin-orbit coupling (SOC) an electric current flowing in a normal metal or semiconductor can induce a bulk magnetic moment. This effect is known as the Edelstein (EE) or magneto-electric effect. Similarly, in a bulk superconductor a phase gradient may create a finite spin density. The inverse effect, also known as the spin-galvanic effect, corresponds to the creation of a supercurrent by an equilibrium spin polarization. Here, by exploiting the analogy between a linear-in-momentum SOC and a background SU(2) gauge field, we develop a quasiclassical transport theory to deal with magneto-electric effects in superconducting structures. For bulk superconductors this approach allows us to easily reproduce and generalize a number of previously known results. For Josephson junctions we establish a direct connection between the inverse EE and the appearance of an anomalous phase-shift $\varphi_{0}$ in the current-phase relation. In particular we show that $\varphi_{0}$ is proportional to the equilibrium spin-current in the weak link. We also argue that our results are valid generically, beyond the particular case of linear-in-momentum SOC. The magneto-electric effects discussed in this study may find applications in the emerging field of coherent spintronics with superconductors.

Transport theory of metallicB20helimagnets

B20 compounds are a class of cubic helimagnets harboring nontrivial spin textures such as spin helices and skyrmions. It has been well understood that the Dzyaloshinskii-Moriya (DM) interaction is the origin of these textures, and the physics behind the DM interaction is the spin-orbital coupling (SOC). However the SOC shows its effect not only on the spins, but also on the electrons. In this paper, we will discuss effects of the SOC on the electron and spin transports in B20 compounds. An effective Hamiltonian is presented from symmetry analysis, and the spin-orbital coupling therein shows anomalous behaviors in anisotropic magnetoresistance (AMR) and helical resistance. New effects such as inverse spin-galvanic effect is proposed, and the origin of the DM interaction is discussed.

Complementary spin-Hall and inverse spin-galvanic effect torques in a ferromagnet/semiconductor bilayer.

Recently discovered relativistic spin torques induced by a lateral current at a ferromagnet/paramagnet interface are a candidate spintronic technology for a new generation of electrically controlled magnetic memory devices. The focus of our work is to experimentally disentangle the perceived two model physical mechanisms of the relativistic spin torques, one driven by the spin-Hall effect and the other one by the inverse spin-galvanic effect. Here, we show a vector analysis of the torques in a prepared epitaxial transition-metal ferromagnet/semiconductor-paramagnet single-crystal structure by means of the all-electrical ferromagnetic resonance technique. By choice of our structure in which the semiconductor paramagnet has a Dresselhaus crystal inversion asymmetry, the system is favourable for separating the torques due to the inverse spin-galvanic effect and spin-Hall effect mechanisms into the field-like and antidamping-like components, respectively. Since they contribute to distinct symmetry torque components, the two microscopic mechanisms do not compete but complement each other in our system.

Spin transport in non-inertial frame

The influence of acceleration and rotation on spintronic applications is theoretically investigated. In our formulation, considering a Dirac particle in a non-inertial frame, different spin related aspects are studied. The spin current appearing due to the inertial spin–orbit coupling (SOC) is enhanced by the interband mixing of the conduction and valence band states. Importantly, one can achieve a large spin current through the k→.p→ method in this non-inertial frame. Furthermore, apart from the inertial SOC term due to acceleration, for a particular choice of the rotation frequency, a new kind of SOC term can be obtained from the spin rotation coupling (SRC). This new kind of SOC is of Dresselhaus type and controllable through the rotation frequency. In the field of spintronic applications, utilizing the inertial SOC and SRC induced SOC term, theoretical proposals for the inertial spin filter, inertial spin galvanic effect are demonstrated. Finally, one can tune the spin relaxation time in semiconductors by tuning the non-inertial parameters.

Effect of spin rotation coupling on spin transport

We have studied the spin rotation coupling (SRC) as an ingredient to explain different spin-related issues. This special kind of coupling can play the role of a Dresselhaus like coupling in certain conditions. Consequently, one can control the spin splitting, induced by the Dresselhaus like term, which is unusual in a semiconductor heterostructure. Within this framework, we also study the renormalization of the spin-dependent electric field and spin current due to the k→⋅p→ perturbation, by taking into account the interband mixing in the rotating system. In this paper we predict the enhancement of the spin-dependent electric field resulting from the renormalized spin rotation coupling. The renormalization factor of the spin electric field is different from that of the SRC or Zeeman coupling. The effect of renormalized SRC on spin current and Berry curvature is also studied. Interestingly, in the presence of this SRC-induced SOC it is possible to describe spin splitting as well as spin galvanic effect in semiconductors.

Gate-controlled persistent spin helix state in (In,Ga)As quantum wells

In layered semiconductors with spin-orbit interaction (SOI) a persistent spin helix (PSH) state with suppressed spin relaxation is expected if the strengths of the Rashba and Dresselhaus SOI terms, $\ensuremath{\alpha}$ and $\ensuremath{\beta}$, are equal. Here we demonstrate gate control and detection of the PSH in two-dimensional electron systems with strong SOI including terms cubic in momentum. We consider strain-free InGaAs/InAlAs quantum wells and first determine a ratio $\ensuremath{\alpha}/\ensuremath{\beta}\ensuremath{\simeq}1$ for nongated structures by measuring the spin-galvanic and circular photogalvanic effects. Upon gate tuning the Rashba SOI strength in a complementary magnetotransport experiment, we monitor the complete crossover from weak antilocalization via weak localization to weak antilocalization, where the emergence of weak localization reflects a PSH-type state. A corresponding numerical analysis reveals that such a PSH-type state indeed prevails even in presence of strong cubic SOI, however no longer at $\ensuremath{\alpha}=\ensuremath{\beta}$.

Interfacial charge current in a magnetised/normal graphene junction

We theoretically investigate a possible interfacial charge current flowing in a magnetised/normal graphene junction where both the intrinsic and extrinsic (Rashba) spin-orbit coupling (SOC) is considered in the normal graphene. It is found that a spin galvanic effect occurs at the interface and the charge current is converted from the spin Hall current flowing at the interface because of the spin exchange field. The evanescent modes dominate the spin galvanic effect for the intrinsic SOC whereas the transmitted modes mainly contribute to the interfacial charge current for the Rashba term. The optimal magnetisation favouring the charge current is perpendicular to the graphene plane for the intrinsic SOC, while the favoured magnetisation for the Rashba SOC is perpendicular to the interface of the junction.

Current-induced magnetization reversal on the surface of a topological insulator

We study dynamics of the magnetization coupled to the surface Dirac fermions of a three di- mensional topological insulator. By solving the Landau-Lifshitz-Gilbert equation in the presence of charge current, we find current induced magnetization dynamics and discuss the possibility of mag- netization reversal. The torque from the current injection depends on the transmission probability through the ferromagnet and shows nontrivial dependence on the exchange coupling. The mag- netization dynamics is a direct manifestation of the inverse spin-galvanic effect and hence another ferromagnet is unnecessary to induce spin transfer torque in contrast to the conventional setup.