Momentum-dependent spin splitting by collinear antiferromagnetic ordering

We clarify the macroscopic symmetry and microscopic model-parameter conditions for emergence of spin-split electronic band structure in collinear antiferromagnets without atomic spin–orbit coupling. By using the microscopic multipole descriptions, we elucidate the fundamental degree of freedom in a cluster unit of an antiferromagnet giving rise to an effective spin–orbit interaction through the anisotropic kinetic motions of electrons. We show a correspondence of the ordering patterns and resultant momentum-dependent spin splitting for 32 crystallographic point groups after demonstrating two intuitive examples of four-sublattice pyrochlore and tetragonal systems. Our study unveils potential features of collinear antiferromagnets with considerably weak spin–orbit coupling in light-element materials and 3d transition metal oxides, which can be utilized for a spin-current generation by electric (thermal) current and a magneto-striction effect.