Generalized Dynamics for Nanostructured Magnetic Systems
magnetization dynamics, excitation spectra, state density, dynamic susceptibility tensor.
Microwave emission by magnetic materials at well-localized frequencies is of great interest for future nanotechnology applications. Theoretical models were developed in this work to study the excitation spectra of nanostructured magnetic systems. We use micromagnetic simulations, the Landau-Lifshitz resolvent matrix and a generalized dynamic susceptibility tensor. The first part of this work is devoted to setting the Landau-Lifshitz equations of motion for a nanostructured system composed, according to the micromagnetic theory, and the elements of the Landau-Lifshitz equations resolvent matrix, as well as the elements of the dynamic susceptibility tensor. The theoretical models are then applied to describe the excitation spectra of systems such as uniformly magnetized ferromagnetic nanostripes, domain walls of ferromagnetic nanostripes coupled to antiferromagnetic vicinal substrates and magnetic vortices of circular nanodisks. The resolvent matrix allows obtaining the spectral density of states, and is applied to the study the spectra of domain walls, allowing the characterization of some modes of walls oscillations in a frequency range below the magnetic domain spectral band. Using the dynamic susceptibility tensor, the spatial distribution of resonance modes along the entire nanostructure could be identified. Thus, the similarities and differences between the domain, domain wall and vortex magnetic excitations can be investigated using the theoretical models developed in this study. Thus, we suggest, it possible to predict microwave field values to excite each of the observed oscillation modes.