Fermi Liquid Theory for Spin Current of a Ferromagnet

Abstract

A recent work [arXiv:2402.04639] considered the dynamical equations for ferromagnets using Onsager's irreversible thermodynamics with fundamental variables magnetization $\vec{M}$ and spin current ${\vec{J}}_i$. The resulting equations have the same structure as Leggett's Fermi liquid theory for the nuclear paramagnet ${}^3$He. Specifically, ${\partial }_t{\vec{J}}_i$ contains a term varying as ${\partial }_i\vec{M}$ that we interpret as associated with a vector spin pressure, and a term giving a mean-field along $\vec{M}$, about which ${\vec{J}}_i$ precesses. (There is also a slow decay term in ${\partial }_t\vec{M}$ not normally present in the Leggett equations, which are intended for shorter-time spin-echo experiments.) The present work applies Fermi liquid theory to ${\vec{J}}_i$ of ferromagnets. The resulting dynamical equation for ${\vec{J}}_i$ confirms the form of ${\vec{J}}_i$ found in [arXiv:2402.04639], but now the previously unknown non-dissipative parameters are given in terms of the quasiparticle interaction parameters of Fermi liquid theory. In the paramagnetic limit the present theory agrees with Leggett and related work.

8 pages