Ferromagnetic resonance in square lattices of planar magnetic cross-shaped elements

Ferromagnetic resonance (FMR) in planar thin film structures comprised of magnetic cross-shaped elements arranged into square lattices has been studied by micromagnetic simulation. FMR spectra and spatial distributions of amplitudes of resonant oscillations were determined for vortex and antivortex states of magnetization in lattice crosses. Resonant modes have the shape of rotating magnetization distributions. Herewith, modes with the same configuration of magnetization but rotating in reverse directions are frequency split. The observed nonreciprocity of propagation of resonant spin oscillations is determined by the sign of magnetization distribution vorticity.