Spin-wave hybridization in bismuth iron garnet Mie spheres induced by the inverse Faraday effect

We show that the inverse Faraday effect can be used to engineer dipole--exchange spin-wave spectra in ferrimagnetic bismuth iron garnet (BIG) Mie spheres. Internal optical Mie resonances generate spatially structured effective magnetic fields whose symmetry is inherited from the optical near field and which act as controllable perturbations of the magnon Hamiltonian. For circularly polarized light incident collinearly with the equilibrium magnetization, the optical perturbation preserves axial symmetry while breaking mirror parity, thereby enabling hybridization of magnon modes with opposite parity within the same $\widehat{J}_z$ sector. Using coupled-mode theory, we derive the corresponding avoided-crossing spectrum and analytical expressions for the induced level splittings, which scale linearly with pump intensity. Numerical calculations for BIG spheres confirm the predicted hybridization and show that the splitting is maximized near optical Mie resonances, where field enhancement and magneto-optical response are strongest. We further discuss the roles of damping, linewidth, and heating, and show that the predicted MHz--hundreds-of-MHz splittings should be observable under realistic conditions. These results identify BIG Mie resonators as a promising platform for symmetry-selective optical control of spin-wave spectra.