  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.
