First-principles calculation of the bulk magnetoelectric monopolization: Berry phase and Wannier function approaches

TL;DR

This paper develops a first-principles formalism using Berry phase and Wannier functions to calculate the bulk magnetoelectric monopolization in insulators, extending to non-collinear magnetism and applying it to specific materials.

Contribution

It introduces a new computational approach for magnetoelectric monopolization based on Berry phase and Wannier functions, applicable to non-collinear magnetic systems.

Findings

Calculated magnetoelectric monopolizations for LiMnPO4 and Cr2O3.

Found deviations from local spin moment summation in Cr2O3.

Proposed a method to define local magnetic moments unambiguously.

Abstract

We present a formalism to calculate the macroscopic magnetoelectric monopolization from first principles within the density functional theory framework. An expression for the monopolization in the case of insulating collinear magnetism is derived first in terms of spin-polarized Wannier functions then recast as a Berry phase. We propose an extension to the general, non-collinear case which we implement computationally in the Wannier function form and use to calculate the magnetoelectric monopolizations of LiMnPO$_4$ and Cr$_2$O$_3$. We find that, while the former is well approximated by a summation over the formal local spin moments, the latter shows significant deviations from this approximation. We suggest that equating the Berry phase value with a sum over local moments provides an unambiguous route to defining the size of the local magnetic moment in magnetoelectric antiferromagnets containing only one type of magnetic ion.