Theory of spin-charge interconversion in an electron gas

Abstract

The dissertation work focuses on understanding the theory of spin orientation induced by currents. The microscopic origin of this phenomenon is the spin-orbit coupling (SOC). Usually, the SOC is classified as intrinsic and extrinsic, depending on the origin of the electrical potential. The intrinsic SOC arises due to the structure inversion asymmetry (Rashba) or due to bulk inversion asymmetry (Dresselhaus). On the other hand, the extrinsic SOC is due to the atomic potential of random impurities, which determine the transport properties of a given material. Among the many interesting effects which arise from SOC, the two effects, known as inverse spin-galvanic effect (ISGE) and spin-galvanic effect (SGE), are the focus of intensive experimental and theoretical research both for their intrinsic interest and for their potential exploitation in the realization of new spintronic functionalities. The non-equilibrium generation of a spin polarization perpendicular to an externally applied electric field is referred to as the ISGE even in the absence of external magnetic field, whereas the SGE is its Onsager reciprocal, whereby a spin polarization injected through a nonmagnetic material creates a charge current in the direction perpendicular to the spin polarization. In this work, we evaluate the ISGE generated by an externally applied electric field by analyzing the interplay of intrinsic (Rashba and Dresselhaus) and extrinsic SOC. To do so, we derive the Bloch equations governing the spin dynamics by identifying the various relaxation mechanisms and spin generation torques. The results are valid to first order beyond the Born approximation. They are obtained first by the standard diagrammatic techniques and then by the SU(2) gauge-field formulation of the Rashba-Dresselhaus SOC. We show how the interplay of intrinsic and extrinsic mechanisms modifies the Bloch equations. More precisely, the extrinsic SOC affects the spin relaxation time by adding the Elliott–Yafet spin relaxation to the D’yakonov–Perel’ spin relaxation. Furthermore, it changes the non equilibrium value of the ISGE by introducing an additional spin torque. This additional spin torque derives in the context of the diagrammatic approach and the SU(2) gauge-field formulation. We also investigate the side-jump and skew scattering contributions due to the extrinsic SOC to the ISGE by using the standard Kubo formula diagrammatic method. These lead to the renormalization of the spin Hall angle in the expression of the spin generation torque. In order to make the comparison with the experiments, we solve the Bloch equations numerically. Our theory, which is able to show a negative differential relation between the ISGE and spin-orbit field, finds to qualitatively agree with the recent experimental results. To describe the mechanisms in a quantum well, where the cubic SOC is important, we propose a theoretical description of the model in the presence of both linear and cubic Rashba-Dresselhaus SOC. For this purpose, we investigate the ISGE by using the method of quasiclassical Green functions. To this aim, we first derive the Eilenberger equation for the quasiclassical Green function for the case of a generic SOC. Then we apply it to derive the Bloch equations for the spin dynamics of carriers in the case of the linear Rashba-Dresselhaus SOC. One of the advantages of this approach is to include also the behavior of the ISGE beyond the diffusive regime, which is hard to study in comparison to the diffusive regime. In the case of linear SOC, we analyze the Bloch equations both analytically and numerically. Next, we describe the case when only the cubic Rashba and Dresselhaus SOCs are present. In this case, we show that the ISGE does not appear. However, when both the linear and cubic SOC are present, we find new terms in the Bloch equations, both in the spin relaxation rate tensor and in the spin generation torque. The new terms arise from the interplay between the linear and cubic SOCs.