Conditions for the symmetry-compensated magnets to show altermagnetic properties

Discovered in ~2019 phenomenon of spin-split nonrelativistic bands in a compensate antiferromagnet created a unique situation where an entire class of materials that would’ve been classified as antiferromagnets (AFM) exhibits most of the ferromagnetic signatures: anomalous Hall effect, MOKE, etc. Since this discovery was made independently and concurrently by at least four groups, they were alternatively called “spin-split AFM”, “Anti-Kramers AFM”, and “Altermagnets (AM)”. Here we adapt the latter term, suggested by the Mainz spintronics group. One of the urgent challenges is creating a simple tool that would allow experimentalists quickly test, knowing the structure and magnetic pattern, whether a newly synthesized, or revisited, material is AF or AM. To this end, we prove three theorems that allowed us to encode a simple protocol for immediate determination of the AF/AM status. The required input is: (1) the space group # and (2) the list of Wyckoff positions (WP) occupied by magnetic species (usually just one) and, for a multiplicity >2, the up-down spin partitioning. They are:

T1. In order to determine if a material is AM it is enough to verify that no midpoint between spin-up and -down sites is an inversion center.

T2. No matter which WP are actually occupied in the material, it is sufficient to check a general point against the T1.

T3. To check a system for AM, one should use a setting with an inversion center at the origin, and verify that this operation maps every magnetic atom upon an equivalent atom with the opposite spin (in which case it is *not* AM).