Dynamics of magnon fluid in Dzyaloshinskii-Moriya magnet and its manifestation in magnon-Skyrmion scattering

We construct a Holstein-Primakoff Hamiltonian for magnons in an arbitrary slowly varying spin background for a microscopic spin Hamiltonian consisting of ferromagnetic spin exchange, Dzyaloshinskii-Moriya exchange, and the Zeeman term. The Gross-Pitaevskii-type equation for magnon dynamics contains several background gauge fields pertaining to local spin chirality, inhomogeneous potential, and anomalous scattering that violates the boson number conservation. Nontrivial corrections to previous formulas derived in the literature are given. Subsequent mapping to hydrodynamic fields yields the continuity equation and the Euler equation of the magnon fluid dynamics. Magnon wave scattering off a localized Skyrmion is examined numerically based on our Gross-Pitaevskii formulation. The dependence of the effective flux experienced by the impinging magnon on the Skyrmion radius is pointed out, and compared to an analysis of the same problem using the Landau-Lifshitz-Gilbert equation.