Spin Hall Effect in a Simple Classical Picture of Spin Forces

Abstract

Spin Hall effect (SHE) in a 2D-Rashba system has been treated in the spin-dependent precession [J. Sinova et al.: Phys. Rev. Lett. 92 (2004) 126603] and the time-space gauge [T. Fujita et al.: New J. Phys. 12 (2010) 013016] approaches, both yielding SHE conductivity of σyz = e/8π. Separate studies based on the concept of spin transverse force [S.-Q. Shen: Phys. Rev. Lett. 95 (2005) 187203] provide a heuristic but not a quantifiable indication of SHE. We provide complete description of the SHE using the Heisenberg approach, unifying the Yang–Mills force, the Heisenberg spin force, and the SHE σyz under the classical notion of accelerations. Central to this paper is the spin force equations that are satisfied by both σyz and σxz, Yang–Mills, and Heisenberg spin forces. By linking σyz to the spin forces, one sees that the physics of SHE in a 2D-Rashba system is also a simple classical Lorentz force picture.