Minimal models for altermagnetism

Altermagnets feature vanishing net magnetization, similar to antiferromagnets, but exhibit time-reversal symmetry breaking and spin-split band structures. This work constructs minimal models for altermagnetism based on symmetry arguments considering two magnetic atoms in the unit cell and demonstrates that these can capture key properties of the band structure and altermagnetic spin splitting for the material candidate RuO${}_{2}$. Notably, the models have altermagnetic ground states and give rise to a Berry curvature and a conductivity linear in the spin-orbit coupling.