Making the Grade: Generating & Controlling Spin Waves with a Graded Refractive Index

In this thesis, the magnetic parameters of a ferromagnetic film are varied to create refractive index profiles for spin waves. The properties of this “magnonic” refractive index are studied for different frequency regimes. Analytical theory and numerical modelling are used throughout. The research in this work is along two main themes. The first involves the generation of spin waves from a graded (or stepped) refractive index region. The energy is driven into the system via a harmonic yet spatially-uniform external magnetic field, and it is shown that the graded index feature may then act as a spin wave source. Exchange (short wavelength) spin waves are studied in this case, since their dynamics are described by the Landau-Lifshitz equation that can be linearised to form a Schrödinger-like equation. This exchange regime is therefore ideal for exploring how the features of well-known exactly-solvable models manifest themselves for spin waves. The exactly-solvable models in this case are a square potential barrier and a Pöschl-Teller potential well. The latter naturally occurs as a magnetic domain wall in a ferromagnet, with a fixed potential ‘height’. Spin waves can be generated by both features, but spin wave emission is not guaranteed. The excitation frequency must primarily be above a threshold value, akin to the ‘work function’ energy in quantum mechanics. Furthermore, certain heights of the potential (or frequencies of excitation) can lead to confinement within the potential region. The second theme studied in this work involves using a graded refractive index to focus or steer spin waves. The rotationally-symmetric graded index lenses, well known in optics, are realised here for spin waves in a perpendicularly- magnetised film, for magnetostatic (long wavelength) spin waves. In this regime, the magnetisation only needs to be changed by a tiny amount, of the order of 2%, to create a Luneburg lens. For the steering lenses, which require a singular refractive index in the centre, just a 10% increase in the magnetisation can create the steering lenses almost exactly. The general properties of the magnonic refractive index are also analysed, for the entire range of spin wave wavelengths, from millimetres to nanometres. The magnetostatic regime is found to be ideal for creating extreme changes in the refractive index, theoretically from 1 to over 100.Engineering and Physical Sciences Research Council (EPSRC

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