Non-equilibrium thermodynamics of the longitudinal spin Seebeck effect

TL;DR

This paper uses non-equilibrium thermodynamics to analyze the longitudinal spin Seebeck effect, identifying the thermodynamic driving force and estimating the spin Seebeck coefficient for YIG, providing insights into optimizing magnetization currents.

Contribution

It introduces a thermodynamic framework for the spin Seebeck effect, defining the driving force as the gradient of an effective field and estimating the spin Seebeck coefficient from experiments.

Findings

Identifies the thermodynamic driving force as $ abla H^*$.

Defines the spin Seebeck coefficient $\\epsilon_M$ relating $ abla H^*$ and $ abla T$.

Estimates $\\epsilon_M \\sim 10^{-2}$ TK$^{-1}$ for YIG.

Abstract

In this paper we employ non equilibrium thermodynamics of fluxes and forces to describe magnetization and heat transport. By the theory we are able to identify the thermodynamic driving force of the magnetization current as the gradient of the effective field $\nabla H^*$. This definition permits to define the spin Seebeck coefficient $\epsilon_M$ which relates $\nabla H^*$ and the temperature gradient $\nabla T$. By applying the theory to the geometry of the longitudinal spin Seebeck effect we are able to obtain the optimal conditions for generating large magnetization currents. Furthermore, by using the results of recent experiments, we obtain an order of magnitude for the value of $\epsilon_{M} \sim 10^{-2}$ TK$^{-1}$ for yttrium iron garnet (Y$_3$Fe$_5$O$_{12}$).