Giant momentum-dependent spin splitting in centrosymmetric low- Z antiferromagnets

The energy vs. crystal momentum 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 [Zh. Eksperim. i Teor. Fiz. 47 (1964)], enabling spintronic application. The current paper provides "design principles" for wavevector dependent spin splitting (SS) of energy bands that parallels the traditional Dresselhaus and Rashba spin-orbit coupling (SOC) - induce splitting, but originates from a fundamentally different source -- antiferromagnetism. We identify a few generic 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 MnF2 -- is used via density functional band structure calculations to quantitatively illustrate one type of AFM SS. Unlike the traditional SOC-induced effects restricted to non-centrosymmetric 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 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.