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  • Open Access

Local Magnetoelectric Effects as Predictors of Surface Magnetic Order

Sophie F. Weber1,2, Andrea Urru3,1, and Nicola A. Spaldin1

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Phys. Rev. X 15, 021094 – Published 17 June, 2025

DOI: https://doi.org/10.1103/7brd-lynv

Abstract

We use symmetry analysis and density functional theory to show that changes in magnetic order at a surface with respect to magnetic order in the bulk can be generically determined by considering local magnetoelectric responses of the crystal. Specifically, analysis of the local atomic-site magnetoelectric responses, or, equivalently, the corresponding atomic-site magnetic multipoles, can be used to predict all surface magnetic modifications arising purely from symmetry lowering via termination of the bulk magnetic order. This analysis applies even in materials with no bulk magnetoelectric response or net surface magnetization. We then demonstrate our arguments for two example antiferromagnets, topological semimetal CuMnAs and rocksalt NiO. We find that the (010) and (11¯0) surfaces of CuMnAs and NiO, respectively, exhibit a series of antiferroically, as well as roughness-sensitive, ferroically ordered, modifications of the surface magnetic dipole moments, via canting or changes in sublattice magnitude, consistent with the bulk ordering of the magnetic multipoles. Our findings demonstrate a universal bulk-boundary correspondence allowing the general prediction of minimal possible surface and interface magnetic modifications, even in materials with no net magnetoelectric response. Furthermore, it paves the way for more accurate interpretations of a wide variety of surface-sensitive measurements.

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Popular Summary

Magnetic materials often behave differently at their surfaces compared to their interiors, but predicting these changes can be difficult—especially in materials without obvious magnetic signals like net magnetization or magnetoelectric effects. In this study, we show that these surface magnetic changes can be predicted using a combination of symmetry analysis and density functional theory. Specifically, we focus on local magnetoelectric responses at atomic sites—essentially how individual atoms react to electric and magnetic fields—to understand how local magnetic changes emerge when a bulk magnetic structure is interrupted by a surface.

We apply this method to two well-known antiferromagnetic materials: the topological semimetal CuMnAs and the rocksalt compound NiO. Although neither material has a net surface magnetization or bulk magnetoelectric response, we find predictable modifications in surface magnetism due to symmetry breaking at specific surface orientations. For CuMnAs (010) and NiO (11¯0), the surface magnetic dipole moments show distinct changes like canting or changes in sublattice magnitude. Some of these changes are sensitive to surface roughness, while others follow the bulk’s magnetic multipole pattern. These behaviors match our predictions based on the atomic-site magnetoelectric responses.

Our findings demonstrate a general principle—a bulk-to-boundary rule—that allows us to predict surface magnetic behavior from bulk magnetic symmetry. This insight improves how we interpret surface-sensitive measurements in antiferromagnets and related materials.

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Phys. Rev. X 15, 021094– Published 17 June, 2025
  • Received 16 December 2024
  • Accepted 27 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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