Towards a theory of surface orbital magnetization

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