Non-equilibrium thermodynamic approach to spin pumping and spin Hall torque effects

Abstract

This paper introduces a non-equilibrium thermodynamic approach to describe vector magnetization in the presence of a magnetic moment current. The Larmor term present in the theory describes in this case how the magnetization dynamics can be a source of magnetic moment currents and vice versa. The model discussed here is applied to describe the reciprocity between spin pumping and spin Hall torque effects found in bilayers composed of a metal with a large spin Hall effect (e.g. platinum, Pt) and a ferromagnetic insulator (e.g. yttrium iron garnet, YIG). The result is that the two effects are related to the transport of the magnetic moment between layers of different materials. In particular, for thin YIG the two effects are related each other by two parameters: the diffusion length of Pt, lPt, and the conductance of Pt, , where is a time constant. Both parameters can be determined by comparison with experiments.