Spin-wave excitations in arrays of asymmetric ferromagnetic nanorings Available to Purchase

Calculations are reported for the spin-wave excitations in asymmetric ferromagnetic nanorings using a Hamiltonian-based formalism. Both the exchange and dipole-dipole interactions are included, as well as an external magnetic field and single-ion anisotropy. The equilibrium configurations of the nanorings are found by minimizing numerically the energy functional with respect to the spin orientation. Depending on the geometry, particularly the degree of asymmetry and the in-plane applied magnetic field, the nanorings can be in a vortex, onion, or other inhomogeneous state. Spin-dependent Green’s functions are calculated to deduce the dispersion spectra and the mode profiles of the spin waves, and the dependence of the spin-wave properties on the asymmetry factor is studied. The effects of inter-ring dipolar coupling on the spin-wave spectrum are also investigated by considering small arrays (e.g., a $3×3$ square array) of nanorings.