Theoretical seminar | 13 May 2026

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.

To demonstrate the broader applicability of our approach, we also apply our coupled‑mode theory to an optomagnonic setting, showing that the inverse Faraday effect induces spin‑wave mode hybridization.

Main paper/arXiv, related to the seminar, and other references, up to 5

• Shuklin, F., Albitskaya, K., Solovyov, S., Chernov, A., & Petrov, M. (2026). Dipole-exchange spin waves and mode hybridization in magnetic nanoparticles. arXiv preprint arXiv:2603.24187.
• Shuklin, F., Albitskaya, K., Chernov, A., & Petrov, M. (2026). Spin-wave hybridization in bismuth iron garnet Mie spheres induced by the inverse Faraday effect. arXiv preprint arXiv:2604.2047.