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

TL;DR

This paper proposes that spin diffusion in spin glasses requires two magnetic variables, $oldsymbol{M}$ and $oldsymbol{m}$, to reconcile experimental observations with thermodynamic theory, introducing a new framework for understanding spin transport.

Contribution

It introduces a dual-variable model involving $oldsymbol{M}$ and $oldsymbol{m}$ to explain steady-state spin currents in spin glasses, extending existing thermodynamic theories.

Findings

Spin diffusion in spin glasses depends on both $oldsymbol{M}$ and $oldsymbol{m}$.

The theory predicts wavelength-dependent coupling between reactive and diffusive spin degrees of freedom.

Experimental implications include the necessity of considering non-equilibrium magnetization for spin transport.

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.