Spin Diffusion in Spin Glasses Require Two Magnetic Variables, $\vec{M}$ and $\vec{m}$

Abstract

Experiment has established that spin-glasses can support a steady-state spin current $\vec{j}_{i}$. However, the accepted theory of spin glass dynamics permits oscillations but no steady-state spin current. Onsager's irreversible thermodynamics implies that the spin current is proportional to the gradient of a magnetization. We argue, however, that the magnon distribution function associated with the local equilibrium magnetization $\vec{M}$ cannot diffuse because it represents $10^{23}$ variables. We therefore invoke the non-equilibrium magnetization $\vec{m}$, which in spintronics is called the {\it spin accumulation}. Applying the theory of irreversible thermodynamics we indeed find that it predicts spin diffusion, and we consider other experimental consequences of the theory, including a wavelength-dependent coupling between the reactive and the diffusive degrees of freedom.