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

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(1) by considering a four-terminal setup to investigate the circumstances in which this symmetry is broken. For absence of Dresselhaus interaction, starting from the applied out-of-plane B corresponding to Zeeman splitting energy ∆ = 0 to 0.5 times the Rashba hopping energy t SO , the breaking process is clearly seen. The influence of the Rashba interaction on the magnetization of the 2DEG is studied herein. For coexisted Rashba t SO and Dresselhaus t SO spin-orbit couplings in the absence of B, interchanging t SO and t SO reverses the entire accumulation pattern.