Dipole-exchange spin waves in unsaturated ferromagnetic nanorings with interfacial Dzyaloshinski-Moriya interactions

A theoretical analysis is made for the quantized spin waves in single-layered ferromagnetic nanorings with the added effect of interfacial Dzyaloshinski-Moriya interactions (DMI). A microscopic, or Hamiltonian-based, formalism is employed that includes competing terms for the symmetric (bilinear) exchange interactions, the antisymmetric DMI, the magnetic dipole-dipole interactions, and applied magnetic field. It is found that, in our model, the transition field value between vortex and onion states is shifted by the inclusion of DMI effects. Significantly, the spin-wave frequencies are also modified with the effects being largest in the onion state close to the transition field. We present combined analytical and numerical results obtained for the static and dynamical magnetization, including the frequencies and amplitudes (with relative phase) of the spin waves when interfacial DMI is present. Published under an exclusive license by AIP Publishing.