Advanced Magnetic Metamaterials for Radio, Microwave and Millimetre-Wave Applications

Abstract

This Thesis investigates the static and dynamic time-dependent properties of magnetic thin films, 2D planar nanostructures and 3D curved nanostructures. The results presented in this thesis aid in the understanding of magnetic materials for high-frequency applications that are achievable by exploiting the magnetic domain structure of thin films and nanomagnetic elements. This is achieved by three different approaches. Firstly the fundamentals of the formation of magnetic domains, with particular attention to the vortex magnetic domain state, are investigated. Secondly, the dynamics of fundamental ferromagnetic magnetic resonances (FMR) and propagating spin-waves resonances due to the magnetic domain structure are analysed and tested. Thirdly, the field-dependent behaviour of the resonances within these structures is investigated. The static magnetic ground state for a variety of different 2D nanostructured geometries (discs, squares and teardrops) is investigated experimentally by measuring the magnetisation of the sample in the presence of an externally applied field and by imaging using holographic techniques. The lowest energy ground state is found to be highly dependent on the geometry, thickness/ height ratio and anisotropy energy. Experimental data shows that there is perpendicular anisotropy energy introduced to the system for thin films deposited above 80 nm. This anisotropy increases with increasing film thickness, which is the cause of the complex magnetic domain state imaged as opposed to the vortex state. The introduction of curvature from 2D nanoelements to iii 3D curved nanomagnets is analysed and the change in the resonant frequency spectra and the spin-wave dynamics is discussed. The vortex is the minimum energy ground state for diameters up to 780 nm with only 10 nm thick ferromagnetic film for thin film magnetic hemispherical shells. The magnetic resonant frequency spectra for soft magnetic thin films are analysed. The phenomenon of FMR and high-frequency spin-wave resonances are explored, with saturated planar thin films primarily showing the fundamental resonance modes, and unsaturated nanoelements in the vortex ground state supporting the higher-order spin-wave resonance modes. The generation and propagation of these spin-waves are shown by micromagnetic simulations. The verification of these propagating spin-wave in discs and squares is investigated by holographic imaging and shows that in squares there is a pinning effect, most likely due to surface defects, which stop these waves from propagating. When curvature is introduced the main spin-wave resonance modes split and broaden with decreasing thickness caused by a thickness gradient as a feature of the chosen fabrication method. Both the FMR and spinwave resonances are field-dependent and their frequencies can be varied by an externally applied magnetic field. For planar thin films, the fundamental resonant frequency has a quadratic dependence on the applied field, whereas, for the higher-frequency spin-wave modes in nanoelements with the vortex ground state, the relationship between the frequency of the resonance and the applied field depends on the characteristics of the resonance. With increasing applied field the vortex core is displaced and the overall trend shows that the higher order spin-wave decrease in frequency with increasing applied field until a saturated state is achieved. When included as part of an antenna system, this field-dependent behaviour iv can be exploited. The field-independent patch antenna resonance modes couple to the field-dependent magnetic resonance modes. This effect creates a dynamically tunable antenna when an external field is applied with a tunability of a few GHz. Varying these resonances, by structuring or applying external stimuli, allows the tailoring of magnetic devices that can be utilised in a wide range of high-frequency devices.