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Energy bands in antiferromagnets are generally spin degenerate in the absenceof spin-orbit coupling (SOC). Recent studies [Physical Review B 102, 014422(2020)] identified formal symmetry conditions for crystals for which thisdegeneracy can be lifted even in the zero SOC limit. Such materials couldenable "spin-split" antiferromagnetic spintronics without the burden of use ofheavy atom compounds. Here, we show that these formal symmetry conditions canbe interpreted in terms of easy-to-visualize local motif pair, such asoctahedra or tetrahedra, each carrying opposite magnetic moments. Collinearantiferromagnets with such spin motif pair whose components interconvert byneither translation nor spatial inversion will show splitting of spin bands.Such real-space motif-based approach enables an easy way to identify and designof materials having spin splitting without the need for spin orbit coupling,and offers insights on the magnitude of spin splitting.

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