Spin Dynamics of a Fermi Liquid in an Electric Field

TL;DR

This paper explores how an external electric field influences the spin dynamics of a Fermi liquid, generalizing existing equations and revealing electric field-induced phase shifts in spin flow.

Contribution

It extends Leggett's equations to include electric field effects and derives new spin dynamics equations for strongly polarized liquids at zero temperature.

Findings

Electric field causes an additional phase shift in spin flow.

Generalized equations incorporate covariant derivatives for electric fields.

Phase shift magnitude is comparable to superfluid $^3$He-$B$ effects.

Abstract

The influence of an external electric field on the spin dynamics of an electrically neutral Fermi liquid is considered, the mechanism of such an influence being the relativistic spin-orbital interaction. As a result, Leggett's equations for the spin dynamics of weakly polarized Fermi liquids are generalized to the case of non-zero external electric field. In addition, we obtained the transverse spin dynamics equation for strongly spin-polarized liquids in an electric field at zero temperature. In both situations covariant derivatives depending on the electric field are shown to be substituted for spatial gradients in line with the SU(2) gauge invariance of the microscopic Hamiltonian. The new equations are applied to the study of spin flow along a channel, where an electric field is found to bring about an additional phase shift of the order of magnitude of the phase shift in superfluid $^3$He-$B$ but growing with time.