  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.
