From spin splitting to projected mass in altermagnetic Chern matter

TL;DR

This paper introduces a projected-mass criterion to distinguish different magnetic topological phases in altermagnetic materials, aiding in their identification and design.

Contribution

It formulates a new diagnostic based on exchange mass projection to differentiate Hall responses and phases in altermagnetic Chern matter.

Findings

The $(C, ext{A})$ diagnostic separates hidden Hall responses from quantum anomalous Hall phases.

The criterion guides interface, thickness, and materials design strategies.

It clarifies the role of exchange mass in defining topological properties.

Abstract

Altermagnetic spin splitting alone does not define Chern matter. The relevant object is the exchange mass projected onto Hall-active surface, valley, orbital or interface sectors. We formulate this projected-mass criterion for compensated magnetic topology. The resulting two-channel $(C,\mathcal{A})$ diagnostic separates hidden compensated Hall responses from additive altermagnetic quantum anomalous Hall phases in a global insulating gap. It also guides interface, thickness and materials design strategies.