Analogy between the magnetic dipole moment at the surface of a magnetoelectric and the electric charge at the surface of a ferroelectric

TL;DR

This paper explores the analogy between surface magnetic dipole moments in magnetoelectric materials and surface charges in ferroelectrics, providing a method to calculate intrinsic surface magnetization from bulk properties.

Contribution

It introduces a framework to relate surface magnetization to bulk magnetoelectric multipolization and demonstrates this for Cr₂O₃, extending the concept to non-magnetoelectric antiferromagnets.

Findings

Surface magnetic dipole moment can be described by bulk magnetoelectric multipolization.

Method demonstrated on Cr₂O₃ matches experimental measurements.

Non-magnetoelectric antiferromagnets may have intrinsic surface magnetization.

Abstract

In honor of Igor Dzyaloshinskii on his 90th birthday, we revisit his pioneering work on the linear magnetoelectric effect in light of the modern theory of ferroelectric polarization. We show that the surface magnetic dipole moment associated with magnetoelectric materials is analogous to the bound surface charge in ferroelectrics, in that it can be conveniently described in terms of a bulk magnetoelectric multipolization that is analogous to the ferroelectric polarization. We define the intrinsic surface magnetization to be this surface magnetic dipole moment per unit area, and provide a convenient recipe for extracting it for any surface plane, from knowledge of the bulk magnetic order. We demonstrate the procedure for the prototypical magnetoelectric material, Cr$_2$O$_3$, in which Dzyaloshinskii first identified the linear magnetoelectric effect, and compare the value of the intrinsic surface magnetization to recent experimental measurements. Finally, we argue that non-magnetoelectric antiferromagnets whose multipolization lattices do not contain zero should have an intrinsic surface magnetization, in the same way that non-polar insulators whose polarization lattices do not contain zero have an intrinsic surface charge.