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

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