Dynamic spin-Hall effect and driven spin helix for linear spin-orbit interactions

TL;DR

This paper investigates how ac electric fields induce non-uniform spin polarization in 2D semiconductors with linear spin-orbit interactions, revealing a driven spin helix mode that can be enhanced by magnetic resonance.

Contribution

It derives boundary conditions for ac-induced spin accumulation and uncovers the driven spin-helix mode in finite channels, extending understanding of spin dynamics under ac fields.

Findings

AC electric fields generate non-zero out-of-plane spin polarization.

Driven spin-helix mode can be excited and amplified by magnetic resonance.

Finite size effects and balanced Rashba-Dresselhaus SOI enhance the helix mode.

Abstract

We derive boundary conditions for the electrically induced spin accumulation in a finite, disordered 2D semiconductor channel. While for DC electric fields these boundary conditions select spatially constant spin profiles equivalent to a vanishing spin-Hall effect, we show that an in-plane ac electric field results in a non-zero ac spin-Hall effect, i.e., it generates a spatially non-uniform out-of-plane polarization even for linear intrinsic spin-orbit interactions. Analyzing different geometries in [001] and [110]-grown quantum wells, we find that although this out-of-plane polarization is typically confined to within a few spin-orbit lengths from the channel edges, it is also possible to generate spatially oscillating spin profiles which extend over the whole channel. The latter is due to the excitation of a driven spin-helix mode in the transverse direction of the channel. We show that while finite frequencies suppress this mode, it can be amplified by a magnetic field tuned to resonance with the frequency of the electric field. In this case, finite size effects at equal strengths of Rashba- and Dresselhaus SOI lead to an enhancement of the magnitude of this helix mode. We comment on the relation between spin currents and boundary conditions.