  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.
