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The spin Hall effect provides a new possible way to effectively inject spins into paramagnetic semiconductors. Here, we investigate the spin-Hall effect in a p-type Luttinger semiconductor employing a two-band kinetic equation analysis. The long-range disorder effect on spin-Hall current (SHC) is considered within the self-consistent Born approximation. We find that in addition to the intrinsic SHC proposed previously, there is a nonvanishing SHC that originates from long-range electron-impurity scattering, but which is independent of impurity density in the diffusive regime. This SHC has an opposite sign from the intrinsic one, leading to a significant reduction of the total SHC. We also carry out a numerical analysis of the hole density dependencies of SHC and spin mobility, finding that with increasing hole density, the SHC first increases and then falls, while the spin mobility monotonically decreases.

The influence of magnetic fields on the electron spin in solids involves two basic mechanisms. First, any magnetic field introduces the Zeeman splitting of electron states, thereby modifying spin precession. Second, since the magnetic field affects the electron motion in the plane perpendicular to the field, the spin dynamics is also modified, owing to the spin-orbit interaction. The theory predicts, as a consequence of this influence, unusual properties of the intrinsic spin-Hall effect in two-dimensional systems in the presence of magnetic fields. This paper describes non-monotonic dependence of the spin-Hall conductivity on the magnetic field and its enhancement in the case of weak disorder, as well as multiple jumps of the spin-Hall conductivity owing to the topological transitions (abrupt changes of the Berry phase) induced by the parallel magnetic field.

The spin Hall effect provides a new possible way to effectively inject spins into paramagnetic semiconductors. Here, we investigate the spin-Hall effect in a p-type Luttinger semiconductor employing a two-band kinetic equation analysis. The long-range disorder effect on spin-Hall current (SHC) is considered within the self-consistent Born approximation. We find that in addition to the intrinsic SHC proposed previously, there is a nonvanishing SHC that originates from long-range electron-impurity scattering, but which is independent of impurity density in the diffusive regime. This SHC has an opposite sign from the intrinsic one, leading to a significant reduction of the total SHC. We also carry out a numerical analysis of the hole density dependencies of SHC and spin mobility, finding that with increasing hole density, the SHC first increases and then falls, while the spin mobility monotonically decreases.

We study the effect of magnetic impurities in a two-dimensional topological insulator under voltage bias. The quantized conductance of this system is computed, and we study the influence of magnetic impurities coupling with charge carriers on the transition between phase with conductance (in fundamental units e²/h) of G = 2 (integer quantum spin Hall effect) and G = 1 (anomalous quantum Hall effect). We assume a ferromagnetic coupling between impurities and electron-like carrier, and two kind of coupling with hole-like. We show that the phase G = 1 exists for ferromagnetic hole-impurities coupling, in the strong coupling limit, in contrast with the prediction of the mean field approximation. This result is supported by direct numerical computations using Landauer transport formula, and by analytical calculations of the chemical potential and mass renormalization as a function of the disorder strength, in the self-consistent Born approximation. The transition is related to the suppression of one of the spin conduction channels, for strong enough disorder, by selective spin scattering and localization.

The spin-Hall effect (SHE) and the inverse spin-Hall effect (ISHE) coupled with magnetization dynamics were investigated using a simple Ni₈₁Fe₁₉/Pt film. A spin current generated by magnetization dynamics was detected electrically using ISHE. The observed magnetic field angle dependence of the ISHE signal is well reproduced by a model calculation based on the dc spin pumping and ISHE. In the same system, we found that spin relaxation in the Ni₈₁Fe₁₉ layer is manipulated electrically using SHE. An electric current applied to the Pt layer exerts the spin torque on the entire magnetization of the Ni₈₁Fe₁₉ layer via the macroscopic spin transfer induced by SHE, which modulates spin relaxation in the Ni₈₁Fe₁₉ layer. This spin-relaxation modulation enables quantitative measurements of spin currents without assuming any microscopic parameters.