Ellipticity effects on diffusive magnon spin and heat transport in easy-plane ferromagnets

When a magnetic material hosts spin-wave excitations, or magnons, the local magnetization can rotate in circular or elliptical orbits, the latter arising naturally in the presence of magnetic anisotropies transverse to the equilibrium magnetization. This article investigates the diffusive transport of elliptical magnons in easy-plane ferromagnets. Our analysis starts with the derivation of the magnon dispersion relation and magnon spin from the Landau-Lifshitz-Gilbert equation with a perpendicular magnetic anisotropy. Then, using the Boltzmann transport equation in the relaxation time approximation and perturbation analysis, the magnon-spin and magnon thermal conductivities are obtained, quantifying the magnon transport in the insulator. Our calculations demonstrate that, in both three- and two-dimensional systems, the effects of ellipticity on magnon transport coefficients result in an enhancement or a decrease, depending on whether magnets with a easy or hard perpendicular-to-plane axis are considered, respectively. On the other hand, our results predict an enhancement of the magnon heat transport for both easy- and hard-axis magnetic systems. Our study supports previous works on magnon ellipticity and makes a step towards clarifying its effect on magnon transport properties.