The energy vs. crystal momentum E(k) diagram for a solid ('band structure') constitutes the road map for navigating its optical, thermodynamic and transport properties. By selecting crystals with specific atom types, composition and symmetries one could design a target band structure and thus desired properties. A particularly attractive outcome would be to design energy bands that are split into spin components with a momentum-dependent splitting, enabling spintronic application. The current paper provides theoretical evidence for wavevector dependent spin splitting of energy bands 1 that parallels the traditional Dresselhaus 2 and Rashba 3 spin-orbit coupling (SOC) -induced splitting, but originates from a fundamentally different source -antiferromagnetism. Identifying via theoretically derived design principles a compound (tetragonal MnF2) with the right magnetic symmetry and performing density functional band structure calculations, reveals surprising, hitherto unknown spin behaviors. Unlike the traditional SOC-induced effects 2,3 restricted to noncentrosymmetric crystals, we show that antiferromagnetic-induced spin splitting broadens the playing field to include even centrosymmetric compounds, and is nonzero even without SOC, and consequently does not rely on the often-unstable high atomic number elements required for high SOC, and yet is comparable in magnitude to the best known ('giant') SOC effects. This work identifies predicted fingerprints of the novel spin splitting mechanism to aid its eventual experimental measurements. It envisions that the antiferromagnetic induced spin-split energy bands would be beneficial for efficient spin-charge conversion and spin orbit torque applications without the burden of requiring compounds containing heavy elements.

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.

Hidden Rashba and Dresselhaus spin splittings in centrosymmetric crystals with subunits/sectors having non-centrosymmetric symmetries (the R-2 and D-2 effects) have been predicted theoretically and then observed experimentally, but the microscopic mechanism remains unclear. Here we demonstrate that the spin splitting in the R-2 effect is enforced by specific symmetries, such as non-symmorphic symmetry in the present example, which ensures that the pertinent spin wavefunctions segregate spatially on just one of the two inversion-partner sectors and thus avoid compensation. We further show that the effective Hamiltonian for the conventional Rashba (R-1) effect is also applicable for the R-2 effect, but applying a symmetry-breaking electric field to a R-2 compound produces a different spin-splitting pattern than applying a field to a trivial, non-R-2, centrosymmetric compound. This finding establishes a common fundamental source for the R-1 effect and the R-2 effect, both originating from local sector symmetries rather than from the global crystal symmetry per se.