Dipole-exchange spin waves and mode hybridization in magnetic nanoparticles
Phys. Rev. B 114, 254406 – Published 10 November, 2026
DOI: https://doi.org/10.1103/44yd-vfgk
Abstract
We investigate spin-wave modes in confined ferromagnetic resonators with spherical and cylindrical geometries across the exchange-dominated, dipole-exchange, and dipolar interaction regimes. Starting from the linearized Landau-Lifshitz-Gilbert equation, we show that the projection of the total angular momentum and mirror parity are conserved quantities in the problem of axially symmetric resonators. These symmetries provide a natural classification of spin-wave modes and explain the degeneracy of exchange modes, as well as its lifting by dipolar interactions. Numerical analysis shows that the nonlocal dipolar interaction removes the exchange degeneracy and hybridizes modes, leading to avoided crossings between modes that belong to the same symmetry sector. To describe this behavior, we develop a coupled-mode theory formulated directly in terms of dynamical magnetization, which reduces the dipole-exchange problem to a finite system of interacting modes. The resulting framework provides a unified description of spin-wave spectra in confined magnetic particles from the exchange limit to the dipolar regime.
