Weakly spin-dependent band structures of antiferromagnetic perovskite LaMO$_3$ (M = Cr, Mn, Fe)

We investigate spin-dependent electronic states of antiferromagnetic (AFM) lanthanum chromite (LaCrO$_3$), lanthanum manganite (LaMnO$_3$), and lanthanum ferrite (LaFeO$_3$) using spin-polarized first-principles density functional theory (DFT) with Hubbard U correction. The band structures are calculated for 15 types of their different AFM structures. It is verified for these structures that there is a very simple rule to identify which wave number k exhibits spin splitting or degeneracy in the band structure. This rule uses the symmetry operations that map the up-spin atoms onto the down-spin atoms. The resulting spin splitting is very small for the most stable spin configuration of the most stable experimental structure. We discuss a plausible benefit of this characteristic, i.e., the direction-independence of the spin current, in electrode applications.