Prediction of low-Z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling

Recent study (Yuan et. al., Phys. Rev. B 102, 014422 (2020)) revealed a SOC-independent spin splitting and spin polarization effect induced by antiferromagnetic ordering which do not necessarily require breaking of inversion symmetry or the presence of SOC, hence can exist even in centrosymmetric, low-Z light element compounds, considerably broadening the material base for spin polarization. In the present work we develop the magnetic symmetry conditions enabling such effect, dividing the 1651 magnetic space groups into 7 different spin splitting prototypes (SST-1 to SST-7). We use the 'Inverse Design' approach of first formulating the target property (here, spin splitting in low-Z compounds not restricted to low symmetry structures), then derive the enabling physical design principles to search realizable compounds that satisfy these a priori design principles. This process uncovers 422 magnetic space groups (160 centrosymmetric and 262 non-centrosymmetric) that could hold AFM-induced, SOC-independent spin splitting and spin polarization. We then search for stable compounds following such enabling symmetries. We investigate the electronic and spin structures of some selected prototype compounds by density functional theory (DFT) and find spin textures that are different than the traditional Rashba-Dresselhaus patterns. We provide the DFT results for all antiferromagnetic spin splitting prototypes (SST-1 to SST-4) and concentrate on revealing of the AFM-induced spin splitting prototype (SST-4). The symmetry design principles along with their transformation into an Inverse Design material search approach and DFT verification could open the way to their experimental examination.M). The symmetry design principles along with their transformation into an Inverse Design material search approach and DFT verification could open the way to their experimental examination.