Antiferromagnets with non-interconvertible spin motif pair

Recent findings of the emergent splitting of spin polarized energy bands in antiferromagnets that does not rely on spin-orbit coupling has drawn great attention due to its profound physics and potential applications. Formal symmetry conditions, including both spin symmetry and magnetic symmetry, telling which antiferromagnets would deliver such exotic spin splitting has been worked out by us previously (Phys. Rev. B 102, 014422 (2020); Phys. Rev. Materials 5, 014409? (2021)). However, the symmetry conditions did not amount to a transparent structural chemistry intuition for the enabling principles. Here, by introduce the concept of spin motif pair -- simple pairs of real space structural motifs carrying opposite magnetic moments in the unit cell -- we show the effect enabling antiferromagnets are those with spin motif pair that cannot be interconverted by translation nor spatial inversion. This real space motif approach provides an intuitive way to understand the abstract symmetry rules needed for the antiferromagnetic-induced spin splitting effect. Insights beyond the symmetry offered by the motif on symmetry breaking and momentum dependent spin splitting has been discussed. We envision the motif approach would accelerate intuitive identifications and design of materials having this effect with sizable magnitude.