Simple microscopic model of the magneto-electric effect in non-collinear magnets

TL;DR

This paper introduces a simplified microscopic model for the magneto-electric effect in non-collinear magnets, capturing key phenomena with fewer assumptions and clarifying the role of spin-orbit coupling.

Contribution

A new, simpler 2-site 2-electron model that accurately describes the magneto-electric effect and clarifies the dependence on spin-orbit coupling.

Findings

Electric dipole moment proportional to R x (S_a x S_b)

Ferroelectric polarization direction matches previous models

Pi vanishes as spin-orbit coupling approaches zero

Abstract

A 2-site 2-electron model with s- and p-states on each site, having constrained average site-spins S_a, S_b, with angle theta between them, simpler than the previous closely-related model of Katsura et al (KNB), is considered. Intra-site Coulomb repulsion and inter-site spin-orbit coupling V_(SO) are included. The ground state has an electric dipole moment pi consistent with the result of KNB, pi proportional to R x (S_a x S_b) = f, R connecting the two sites, and application to a spiral leads to ferroelectric polarization with direction f, also in agreement with the previous result. However, the present result shows the expected behavior pi goes to 0 as V_(SO) goes to 0, unlike the previous one.