Broken spin-Hall accumulation symmetry by magnetic field and coexisted Rashba and Dresselhaus interactions

TL;DR

This study investigates how magnetic fields and coexisting Rashba and Dresselhaus spin-orbit interactions break the symmetry of spin accumulation in a 2DEG, revealing the conditions under which this symmetry is lost.

Contribution

It introduces a real space Landauer-Keldysh formalism analysis of symmetry breaking in spin-Hall accumulation due to magnetic fields and coexisting spin-orbit couplings.

Findings

Magnetic field breaks spin-Hall symmetry in 2DEG.

Interchanging Rashba and Dresselhaus couplings reverses accumulation patterns.

Symmetry breaking depends on the ratio of Zeeman energy to Rashba energy.

Abstract

The spin-Hall effect in the two-dimensional electron gas (2DEG) generates symmetric out-of-plane spin Sz accumulation about the current axis in the absence of external magnetic field. Here we employ the real space Landauer-Keldysh formalism [B. K. Nikolic et al., Phys. Rev. Lett. 95, 046601 (2005); Phys. Rev. B 73, 075303 (2006)] by considering a four-terminal setup to investigate the circumstances in which this symmetry is broken. For the absence of Dresselhaus interaction, starting from the applied out-of-plane B corresponding to Zeeman splitting energy 0 - 0.5 times the Rashba hopping energy tR, the breaking process is clearly seen. The influence of the Rashba interaction on the magnetization of the 2DEG is studied herein. For coexisted Rashba tR and Dresselhaus tD spin-orbit couplings in the absence of B, interchanging tR and tD reverses the entire accumulation pattern.