Prediction of low-Z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling
The over 60 years old Rashba-Dresselhaus effect predicts spin-orbit coupling (SOC) induced momentum-dependent spin splitting and spin polarization in materials with noncentrosymmetric structures. Strong SOC induced effects usually require high-atomic number (Z) elements such as rare-earth elements. It has recently been pointed out that antiferromagnets could hold SOC-independent spin splitting and spin polarization. In the present work we develop the spatial and magnetic symmetry conditions enabling such antiferromagnet (AFM)-induced spin splitting, dividing the 1651 magnetic space groups into seven different spin splitting prototypes (SST-1 to SST-7). This analysis places the physics of AFM spin splitting (SST-4) within the broader context of symmetry conditions that enable the more familiar forms of spin splitting, such as ferromagnetic Zeeman effect (SST-5), nonmagnetic no spin splitting (SST-6), and the nonmagnetic Rashba and Dresselhaus effects (SST-7). The AFM-induced spin splitting and spin polarization 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 manipulations. 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—the magnetic symmetry conditions—to search realizable compounds that satisfy these a priori design principles. This process uncovers 422 magnetic space groups (160 centrosymmetric and 262 noncentrosymmetric) 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 and exist even in the absence of SOC effect. We provide the DFT results for all antiferromagnetic spin splitting prototypes (SST-1, SST-2, SST-3, SST-4), and concentrate on two limits of SST-4 that are particularly unusual: When spin splitting is momentum dependent (just like the Rashba effect) but is enabled in antiferromagnets even in the absence of SOC in the Hamiltonian. This includes examples of (a) centrosymmetric SST-4A compounds (e.g., orthorhombic LaMnO 3 illustrating collinear AFM, as well as cubic NiS 2 illustrating noncollinear AFM) and (b) noncentrosymmetric SST-4B compounds (e.g., rhombohedral MnTiO 3 illustrating collinear AFM and hexagonal ScMnO 3 illustrating noncollinear AFM). The symmetry design principles outlined here, along with their transformation into an inverse design material search approach and DFT verification, could open the way to their experimental examination.