Giant momentum-dependent spin splitting in centrosymmetric low-$\textit{Z}$ antiferromagnets
The energy vs crystal momentum $\textit{E(k)}$ diagram for a solid (band structure) constitutes the road map for navigating its optical, magnetic, 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, as envisioned by Pekar and Rashba, enabling spintronic application. The current paper provides “design principles” for wave-vector dependent spin splitting (SS) of energy bands that parallel the traditional Dresselhaus and Rashba spin-orbit coupling (SOC)–induced splitting, but originates from a fundamentally different source—antiferromagnetism. Here, we identify a few generic antiferromagnetic (AFM) prototypes with distinct SS patterns using magnetic symmetry design principles. These tools allow also the identification of specific AFM compounds with SS belonging to different prototypes. A specific compound—centrosymmetric tetragonal MnF 2 —is used via density functional band-structure calculations to quantitatively illustrate one type of AFM SS. Unlike the traditional SOC-induced effects restricted to noncentrosymmetric crystals, we show that antiferromagnetic-induced spin splitting broadens the playing field to include even centrosymmetric compounds, and gives SS comparable in magnitude to the best known (“giant’” SOC effects, even without traditional SOC, and consequently does not rely on the often-unstable high atomic number elements required for high SOC. We envision that use of the current design principles to identify an optimal antiferromagnet with 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.