Guided spin wave in monolayer CrSBr: Localization and spin-orbit coupling from dipolar field

Spin-wave spectrum of monolayer CrSBr waveguides was studied by numerically diagonalizing the Bogoliubov-de Gennes Hamiltonian derived from linearising the Landau-Lifshitz-Gilbert equation. In contrast to its short-range counterparts, the long-range dipolar field acts statically as a confining potential for spin wave, while the dynamic part couples the spin and orbit degrees of freedom, thus giving rise to spin-orbit coupling for spin wave. Due to the inversion symmetry of the Hamiltonian and the spinor structure of the wave function, spin-wave eigenstates form doublets with definite parity. Micromagnetic simulation tallies well with numerical calculation. Our study on spin-wave eigenstates in CrSBr waveguides sheds light on the nature of exchange-dipole spin wave in ferromagnetic slabs. We confirm particularly that the robustness of the Damon-Eshbach mode is not derived from topology, but rather from the static dipolar field. Moreover, a thorough knowledge on spin wave in monolayer CrSBr itself represents a step forward to understanding the more complicated antiferromagnetic resonance in bulk CrSBr.