Theory and Simulation of the Microwave Response of Concentric Ferromagnetic Shells

Abstract

Structured ferromagnetic metal-based metamaterials comprised of spherical particles exhibit properties that are attractive for microwave applications, such as a broad frequency bandwidth and higher working frequencies when compared with bulk ferrimagnetic oxides. In this thesis, the dynamical properties of ferromagnetic spherical shells are studied using a combination of analytical and numerical methods, to further understanding and enhance the permeability of these materials towards higher frequencies. Using linearised micromagnetic equations, saturated spherical shells are investigated in the exchange-dominated regime when assuming that surface anisotropy is present at both the inner and outer boundaries. This configuration is amenable to exact solutions for the resonance eigenvalues and to investigate the size/thickness dependence of the resonance frequencies. It is found that the mode frequency can increase with decreasing shell thickness or is driven rapidly towards the ferromagnetic resonance frequency depending on the choice of the surface anisotropy constant at each boundary. Moreover, surface anisotropy introduces a dependence of the zeroth mode on shell thickness, removing the degeneracy with the ferromagnetic resonance and leading to a pronounced size dependence of this mode for thin shells. A generalised resonance theory is further outlined for a multilayered spherical nanoparticle comprised of exchange-coupled concentric layers. It can be used to compute the resonance spectra of core-shell nanoparticles, as in the case of a solid spherical ferromagnetic core surrounded by an outer oxide shell. Detailed micromagnetic modelling of two- and three-dimensional ferromagnetic particles was carried out to study the role of long-range magnetostatic interactions between concentric rings and the influence of realistic domain structures on the dynamic susceptibility. Micromagnetic modelling of such structures demonstrates that a family of higher-order flexural modes is present for spherical shells relaxed into the vortex state, which can reach high-frequencies 20-25 GHz under weak-field excitations. These simulations provide an alternative and more plausible interpretation of observed high-frequency resonance modes in measured permeability spectra of spherical shell particle composites, and aid in the design of high-frequency, light-weight composite materials. The dynamical properties of three-dimensional permalloy elements supporting vortex domain structures were also investigated with micromagnetic simulations and compared with experiment. This is to study the influence of nonuniform field gradients and three-dimensional static magnetisation configurations on 1 the dynamical behaviour. It is found that the permalloy elements support domain walls with perpendicular out-of-plane components which can be switched dynamically in response to specific magnetic pulse parameters. This project further aimed to incorporate the fundamental nonlinear micromagnetic and electromagnetic details, including exchange and magnetocrystalline anisotropy, within the finite-difference time-domain (FDTD) method. This is to study the interaction between magnetic materials and electromagnetic waves in the presence of current and magnetic sources at microwave frequencies. Results are presented for conducting semi-infinite permalloy pillars in the micrometer and sub-micrometer size range. It is found that microwave absorption results primarily from edge modes localised at the boundaries of the pillar in accordance with the skin depth, which appear at a lower frequency than the ferromagnetic resonance