Towards a theory of surface orbital magnetization

TL;DR

This paper develops a theoretical framework for defining and computing surface orbital magnetization in antiferromagnetic materials, linking local markers to observable hinge currents and identifying symmetry conditions for well-defined surface magnetizations.

Contribution

It introduces a quantum local marker approach to calculate surface magnetization, clarifies the role of symmetry, and validates the method using tight-binding models and hinge current comparisons.

Findings

Only pseudoscalar symmetric crystals have well-defined surface magnetizations.

A specific local marker form accurately predicts hinge currents.

Multiple local marker expressions exist, but only one matches physical observables.

Abstract

The theory of bulk orbital magnetization has been formulated both in reciprocal space based on Berry curvature and related quantities, and in real space in terms of the spatial average of a quantum mechanical local marker. Here we consider a three-dimensional antiferromagnetic material having a vanishing bulk but a nonzero surface orbital magnetization. We ask whether the surface-normal component of the surface magnetization is well defined, and if so, how to compute it. As the physical observable corresponding to this quantity, we identify the macroscopic current running along a hinge shared by two facets. However, the hinge current only constrains the difference of the surface magnetizations on the adjoined facets, leaving a potential ambiguity. By performing a symmetry analysis, we find that only crystals exhibiting a pseudoscalar symmetry admit well-defined magnetizations at their surfaces at the classical level. We then explore the possibility of computing surface magnetization via a coarse-graining procedure applied to a quantum local marker. We show that multiple expressions for the local marker exist, and apply constraints to filter out potentially meaningful candidates. Using several tight-binding models as our theoretical test bed and several potential markers, we compute surface magnetizations for slab geometries and compare their predictions with explicit calculations of the macroscopic hinge currents of rod geometries. We find that only a particular form of the marker consistently predicts the correct hinge currents.