Vector Potential and Surface Magnetic Field in Magnetoelectric Antiferromagnetic Materials

TL;DR

This paper develops a formula for the vector potential in antiferromagnetic materials, linking magnetic quadrupoles to boundary conditions, and explores how surface effects influence magnetic fields and magnetoelectric responses.

Contribution

It introduces a general formula for the vector potential in bulk periodic systems and analyzes the effects of surfaces and interfaces on magnetic properties in antiferromagnets.

Findings

Discontinuity in vector potential at surfaces causes interfacial magnetic fields.

Surface and interface relaxations can induce additional magnetization.

Symmetry analysis suggests relaxation responds to potential discontinuities.

Abstract

A general formula for the average vector potential of bulk periodic systems is proposed and shown to set the boundary conditions at magnetic interfaces. For antiferromagnetic materials, the study reveals a unique relation between the macroscopic potential and the orientation-dependent magnetic quadrupole, as a result of the different crystalline and magnetic symmetries. In particular, at surfaces and interfaces of a truncated bulk without inversion and time-reversal symmetries, the average vector potential exhibits a discontinuity, which results in an interfacial magnetic field. In general, however, due to the surface and interface electronic and atomic relaxations, additional magnetization may result. For the experimentally-observed magnetoelectric antiferromagnets, in particular, our symmetry analysis suggest that the relaxation effects could well be a system response to the presence of such a potential discontinuity.