Noether spin current in noncollinear kagome antiferromagnet models

Noncollinear antiferromagnets (AFMs) Mn₃X (X=Ir, Sn, Ge, etc.) have recently attracted attention in the emerging field of antiferromagnetic spintronics because of their various interesting transport, magnetic, and optical properties. Due to the noncollinear magnetic order, spin is in general not a conserved quantity even without explicitly considering spin-orbit coupling, making it difficult to understand the transfer of angular momentum among different subsystems. Here we study the conserved Noether current and charge associated with spin rotation symmetry in noncollinear AFMs by considering a two-dimensional kagome lattice model with classical spins forming different noncollinear orders. Explicit formulas of the Noether spin current and charge were derived based on the continuum Lagrangian obtained through gradient expansion of the lattice model. We found that the Noether spin current of noncollinear AFMs carries information of the underlying lattice and ground state, and is inherently anisotropic even when the spin rotation symmetry is intact. We show the consequences of this unusual anisotropy by numerically studying evolutions of magnon wave packets scattered by magnetic domain walls.