A theoretical analysis is described for the spin waves in single- and double-layered nanorings using a microscopic, or Hamiltonian-based, formalism. The calculations, which yield the frequencies and spatially-dependent intensities of the quantized spin waves, are applied to the vortex and onion (bi-domain) states in a single nanoring, as well as to the field-induced switching. In the case of asymmetric double-layered nanorings (with a nonmagnetic spacer) there are coupled spin waves controlled by varying the spacer thickness to change the strength of the inter-ring dipolar interactions. The different possible magnetic states, depending on the applied magnetic field, may involve vortex states (with the same or opposite chirality) in both layers, a vortex state in one layer and onion state in the other, or onion states in both layers. Numerical applications are made to permalloy nanorings with realistic dimensions and magnetic parameter values.
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.
Theoretical studies are reported for the effects of quasiperiodicity on the dipole-exchange spin waves that can propagate in magnonic crystals. The systems under consideration are lateral arrays formed by nanowire stripes of metallic ferromagnets separated by nonmagnetic spacers and with growth rules derived from both the Fibonacci and Thue–Morse sequences. A microscopic (or Hamiltonian-based) approach is used to calculate the spectra of spin-wave bands and gaps for different generations of the sequences. Different origins for the quasiperiodicity, coming from variations in either the nanowire properties or the spacer properties, are compared and contrasted with one another as well as with the behavior in periodic magnonic crystals. The relative importance of dipole–dipole and exchange interactions can be varied by control of the wave vectors for the spin waves.
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