Hybrid modes of a cavity photon coupled with multiple magnons in ferromagnetic nanostructures

By using a microscopic dipole-exchange theory within a Green's function formalism, we study the coupling regime of microwave cavity photons to magnons in nanostructures. The ferromagnetic nanostructures considered are single- and double-layer films, nanowires with rectangular cross-sections, and one-dimensional magnonic crystal arrays of nanowires. In contrast with previous studies of magnon-photon hybrid systems, where either bulklike magnetic samples or macroscopic spheres or films were utilized, a discrete lattice of effective spins is employed to establish a microscopic theory for describing the dependence of the magnon frequencies on the wave vector. We explore hybrid systems derived from the discrete magnons in nanostructures and a selected microwave cavity photon, where strong photon-magnon coupling is expected. This may extend the functionality of the existing hybrid systems or may introduce new functionality. The dependence of the hybridized frequency modes on applied magnetic field are calculated and it is shown that the results are significantly modified compared with those for magnetic bulk materials. In particular, a series of anticrossing phenomena of the cavity mode and multiple magnon modes of ferromagnetic nanostructures are reported. Our findings are important for future applications in integrated hybrid systems for quantum magnonics.