Degeneracy removal of spin bands in antiferromagnets with non-interconvertible spin motif pair

Energy bands in antiferromagnets are generally spin degenerate in the absence of spin-orbit coupling (SOC). Recent studies [Physical Review B 102, 014422 (2020)] identified formal symmetry conditions for crystals for which this degeneracy can be lifted even in the zero SOC limit. Such materials could enable "spin-split" antiferromagnetic spintronics without the burden of use of heavy atom compounds. Here, we show that these formal symmetry conditions can be interpreted in terms of easy-to-visualize local motif pair, such as octahedra or tetrahedra, each carrying opposite magnetic moments. Collinear antiferromagnets with such spin motif pair whose components interconvert by neither translation nor spatial inversion will show splitting of spin bands. Such real-space motif-based approach enables an easy way to identify and design of materials having spin splitting without the need for spin orbit coupling, and offers insights on the magnitude of spin splitting.