Magnon Spin-Momentum Locking: Various Spin Vortices and Dirac magnons in Noncollinear Antiferromagnets

摘要

We generalize the concept of the spin-momentum locking to magnonic systems and derive the formula to calculate the spin expectation value for one-magnon states of general two-body spin Hamiltonians. We give no-go conditions for magnon spin to be independent of momentum. As examples of the magnon spinmomentum locking, we analyze a one-dimensional antiferromagnet with the Neel order and two-dimensional kagome lattice antiferromagnets with the 120 degrees structure. We find that the magnon spin depends on its momentum even when the Hamiltonian has the z-axis spin rotational symmetry, which can be explained in the context of a singular band point or a U(1) symmetry breaking. A spin vortex in momentum space generated in a kagome lattice antiferromagnet has the winding number Q = -2, while the typical one observed in topological insulator surface states is characterized by Q = +1. A magnonic analogue of the surface states, the Dirac magnon with Q = +1, is found in another kagome lattice antiferromagnet. We also derive the sum rule for Q by using the Poincare-Hopf index theorem.