This thesis reports on recent results which pave the way for future experiments in the emerging field of quantum magnonics. Chapter 1 presents a brief outline of the field of magnonics, which provides the context in which quantum magnonics has begun to develop. Chapter 2 provides an introduction to the theory of spin waves, which is necessary to understand the experiments reported in the thesis. In Chapter 3, the experimental methods and materials used to carry out the investigations in the thesis are described. Chapter 4 describes the coupling of resonant magnon modes in a sphere of yttrium-iron garnet to photon modes in a coplanar-waveguide resonator. Strong coupling is achieved to multiple magnon modes, and a theoretical model is used to identify the magnon modes which couple most strongly to the photon mode. In Chapter 5, the behaviour of propagating magnon modes is investigated in a waveguide formed from a thin film of yttrium-iron garnet. Two different configurations are investigated supporting different types of propagating mode, namely backward-volume and surface spin waves. Simulations are performed which reproduce the main features of the data. Chapter 6 characterises the effect of the gadolinium-gallium garnet substrate on propagating spin waves. The magnitude of this effect is dependent on both the orientation and temperature of the sample. Finally, Chapter 7 provides a short summary of the results of the thesis, and speculates on how they may inform future work in the field.

In this thesis the results of several different experimental techniques are presented. Time-resolved scanning Kerr microscopy and time-resolved optically pumped scanning optical microscopy measurements were made in Exeter on bi-component anti-dot lattices and permalloy films respectively. Magnetic transmission x-ray microscopy measurements were performed on cobalt nanostructures at the Advanced Light Source at the Lawrence Berkeley National Laboratory in Berkeley, California, USA. Time-resolved Kerr microscopy was used to study bi-component 400nm anti-dot lattices with a 1μm lattice constant. At 200 Oe the mode frequencies were obtained using time-resolved measurements. The mode frequencies of the cobalt filled anti-dots (binary sample) are 3 and 4.4 GHz. The 4.4 GHz mode has propagating character; the 3 GHz mode has non-propagating character. The mode frequencies of the air –filled anti-dot arrays (anti-dot reference sample) are 3.84 and 4.72 GHz. The 3.84 GHz mode has propagating character; the 4.72 GHz mode has non-propagating character. The alteration of the internal field by the air-filled anti-dots lowers the propagating mode frequency compared to the binary sample. Scanning Kerr microscopy was used to study the spatial character of the anti-dot modes. By fitting the spatial character the effective damping parameter(s) were determined. The effective damping parameter for the binary sample was 0.023 and 0.044 for the 4.4 and 3.04 GHz modes respectively. The 3.04GHz mode exists through the cobalt filled anti-dots leading to a high effective damping. The effective damping parameters for the anti-dot reference sample 0.026 and 0.028 for the 3.84 and 4.72 GHz modes respectively. Time-resolved optically pumped measurements have been performed on a continuous 20nm permalloy film. This is a new experimental technique developed during my PhD. Early data acquired on the optical microscope is compared with data measured later and attempts are made to explain the discrepancies. With a 500 Oe out-of-plane field initial time resolved signals show an oscillation at 17 GHz, the origin of the oscillation is unknown and is thought to originate from a magnon or phonon contribution. The experiment overlapping sub-micron pump and probe spots makes acquiring consistent time-resolved signals a difficult challenge. Images revealing circular lobe shapes are observed, the origin of these images is not fully understood. Later measurements are compared to the early measurements. In the recent measurements, images of spin waves with a wavelength and frequency of 2.5 μm and 4 GHz respectively are observed. These values are not reconcilable with the wavelengths and frequencies of 1μm and 17GHz seen in the images and time-resolved signals respectively. Recent measurements also revealed a strong dependence on the pump focus position on the measured images. Lastly, magnetic transmission x-ray microscopy measurements are presented on 700nm cobalt anti-dot structures overlaid on continuous permalloy films of thicknesses ranging from 20 to 60nm. The magnetic ground states of the nanostructures are investigated using L3 edge x-ray absorption and x-ray magnetic circular dichroism as a magnetic contrast mechanism. The reversal fields are determined and consistent with hysteresis loops measurements in Exeter. The dipolar fields from the complex shape of the cobalt anti-dots are expected to modulate the magnetic ground state of the permalloy. Reversal of the permalloy occurs suddenly over a consistent field window, starting and finishing between 13 ~ 17 Oe respectively. The reversal process in the cobalt occurs gradually and full saturation is not observed until fields of up to 350Oe.

Spintronics is a newly emerging field in physics, aimed at using the spin of electrons to carry information. One of the primary ways in which this could be done is through the use of spin waves. In order to do this, it will be necessary to have a complete understanding of spin waves and how they behave in various materials and structures. In this dissertation, we aim to create a thorough model of spin waves in both one-dimensional and two-dimensional magnonic crystals in an effort to understand and control their dispersion properties and propagation patterns. Using the Landau-Lifshitz-Gilbert equation, we have derived a model for spin waves in magnonic crystals that allowed us to calculate their dispersion and propagation properties. In the first part of this work we considered two-dimensional magnonic crystals consisting of magnetic cylinders arrange in a lattice and embedded in a second magnetic material. The dispersion relations were found to be heavily dependent on the magnetic properties of the two materials, with band gaps appearing more readily when the magnetization was larger in the cylinders than in the host. It was also found that the dipolar field reduced the symmetry of the results, with reflection symmetry not appearing in the dispersion relations even when it was present in the physical lattice. For the propagation of spin waves in two-dimensional magnonic crystals, we found that their directionality was highly dependent on changes in frequency. Propagation patterns varied from roughly isotropic for spin waves in the middle of a band level, to highly directional propagation along the x and y axes for a frequency near the edge of a band. The absence of propagation was also found for frequencies in a band gap. For spin waves in one-dimensional magnonic crystals, we investigated the effects of applying an electric field to the system. When a uniform electric field was applied to a magnonic crystal consisting of a periodic variation in magnetic materials, the band levels were found to shift downward in frequency, with the magnitude of the shift being dependent on the strength of the electric field. While this method could move existing band gaps, it was not capable of creating a band gap in the dispersion relations. Creation of band gaps was found to occur when a periodically varying electric field was applied to a uniform magnetic material. This effect could be used to create a magnonic device where the dispersion properties can be dynamically controlled with an electric field.

Since the discovery of the long-range ferromagnetic order in two-dimensional and multi-layered van der Waals crystals, and the observation of a nontrivial topology of the magnon bulk bands in the chromium trihalides, the bosonic honeycomb lattices have drawn significant attention within the condensed matter community. In this thesis, we employ a Heisenberg model with a Dzyaloshinsky-Moriya interaction in a honeycomb ferromagnetic lattice to study the properties of bulk and edge spin-wave excitations (magnon). By the Holstein-Primakoff transformations in the linear spin-wave approximation, the spin Hamiltonian is written as the bosonic equivalent of the Haldane model for spinless fermions. We present a simple bosonic tight binding formalism which allows us to obtain analytical solutions for the energy spectrum and wavefunctions. We investigate three basic boundaries in the honeycomb lattice: zigzag, bearded and armchair, and we derive analytical expressions for the energy band structure and wavefunctions for the bulk and edge states, and with both zero and nonzero Dzyaloshinsky-Moriya interaction. We find that in a lattice with a boundary, the intrinsic on-site interactions along the boundary sites generate an effective defect and this gives rise to Tamm-like edge states. If a nontrivial gap is induced, both Tamm-like and topologically protected edge states appear in the band structure. The effective defect can be strengthened by an external on-site potential, and the dispersion relation, velocity and magnon density of the edge states all become tunable. We also investigate the bond modulation in the bosonic Haldane model, where by introducing a Kekule bond modulation and with the analysis of the gap closing conditions and the bulk band inversions, we find a rich topological phase diagram for this system yet to be discovered. We identify four topological phases, verified by a numerical calculation of the Chern number, in terms of the Kekule modulation parameter and the Dzyaloshinsky-Moriya interaction. We present the bulk-edge correspondence for the magnons in a honeycomb lattice for both armchair and zigzag boundaries. We believed that our study in this thesis will be important for possible applications of magnons in data process devices such as magnonics.

In the search for low power operation of microelectronic devices, spin-based solutions have attracted undeniable increasing interest due to their intrinsic magnetic nonvolatility. The ability to electrically manipulate the magnetic order using spin-orbit interaction, associated with the recent emergence of topological spintronics with its promise of highly efficient charge-to-spin conversion in solid state, offer alluring opportunities in terms of system design. Although the related technology is still at its infancy, this thesis intends to contribute to this engaging field by investigating the nature of the charge and spin transport in spin-orbit coupled and topological systems using quantum transport methods. We identified three promising building blocks for next-generation technology, three classes of systems that possibly enhance the spin and charge transport efficiency: (i)- topological insulators, (ii)- spin-orbit coupled magnonic systems, (iii)- topological magnetic textures (skyrmions and 3Q magnetic state). Chapter 2 reviews the basics and essential concepts used throughout the thesis: the spin-orbit coupling, the mathematical notion of topology and its importance in condensed matter physics, then topological magnetism and a zest of magnonics. In Chapter 3, we study the spin-orbit torques at the magnetized interfaces of 3D topological insulators. We demonstrated that their peculiar form, compared to other spin-orbit torques, have important repercussions in terms of magnetization reversal, charge pumping and anisotropic damping. In Chapter 4, we showed that the interplay between magnon current jm and magnetization m in homogeneous ferromagnets with Dzyaloshinskii-Moriya (DM) interaction, produces a field-like torque as well as a damping-like torque. These DM torques mediated by spin wave can tilt the imeaveraged magnetization direction and are similar to Rashba torques for electronic systems. Moreover, the DM torque is more efficient when magnons are thermally driven. Chapters 5 and 6 carry throughout tight-binding studies on the topological charge-spin transport in two-dimensional lattices with ferromagnetic skyrmions and 3Q magnetic structure. We use the Landauer-Buttiker formalism and evaluate the robustness of the topological signals. For the 3Q state, a spin-polarized quantum anomalous Hall state with chiral edge modes, unaffected by deformation and disorder, is reachable in zero net magnetization. We finish with concluding remarks and perspectives.

This thesis contains results of numerical investigations of magnetisation dynamics in nanostructed ferromagnetic materials. Magnetic systems have been simulated using the open source micromagnetic solver: Object Oriented Micromagnetic Framework (OOMMF), and thoroughly analysed using my own software: semargl. A systematic study of collective magnonic modes confined in 2D and 3D systems of rectangular ferromagnetic nano-elements is presented. The collective character of the excitations results from the dynamic magnetic dipole field. The magnetization dynamics of isolated rectangular elements is found to be spatially non-uniform which means that the dynamic dipolar coupling is highly anisotropic. A semi-analytical theory of collective magnonic modes has been developed to evaluate the properties of the dynamic magnetic dipole field. It was found that the theory is only valid for certain eigenmodes of the isolated element. In particular the modes where the magnetic dipole coupling between the elements is much lower than the internal energy of the corresponding eigenmodes of the isolated element. It is then demonstrated that the confinement of spin waves is strongly affected by the ground state of the system. In particular it has been found that symmetry properties of the topology of 2D arrays affect the dynamics of the strongly localised modes. The effect is found to be significant for arrays of any number of elements. At the same time the relative contribution of the localized modes to the uniform response decreases with the number of elements in the array. The dispersion relation of spin waves in 2D arrays of rectangular nano-elements has been calculated for the first time using micromagnetic simulations. The form of the dispersion is used to estimate the spatial anisotropy of the dynamic dipolar coupling. Simulations of the 3D confinement of spin waves in stacks of magnetic nano-elements have been performed. The calculation of both the dispersion and spatial profiles of the corresponding magnonic modes facilitates the investigation of the localisation of collective spin waves. Furthermore the dispersion of collective magnonic modes has been calculated for stacks of rectangular nano-elements for a range of in-plane aspect ratios. Finally, a numerical method has been developed to extract the scattering parameters of magnonic logic devices. This method has been demonstrated by applying it to the simplest possible magnonic device so that the results could be compared to an analytical expression of the scattering parameters.

Popis magnetodynamických vlastností nanomagnetů a nanostrukturovaných magnetických materiálů vyžaduje metody vhodné pro zkoumání typické časové odezvy těchto systémů, tj. v řádu nanosekund a méně. Nedostatek technik, vhodných právě pro charakterizaci v časové doméně, je spojen s možnostmi současné elektroniky. Další možný přístup, jak popsat vlastnosti nanomagnetů, je charakterizace ve frekvenční doméně v pásmu GHz. Nejrozšířenější technikou charakterizace ve frekvenční doméně je měření feromagnetické rezonance (FMR). Ze spekter FMR lze získat cenné informace o systému: parametr tlumení, saturační magnetizace atd. Metoda, kterou využíváme k detekci excitací spinových vln, má za cíl zjednodušení charakterizace. Využíváme termoelektrickou detekci spinových vln v magnetických drátech prostřednictvím anomálního Nernstova jevu. Metoda je založena na disipaci tepla uvnitř magnetické vrstvy v důsledku útlumu spinových vln, a proto dochází k vytvoření teplotního gradientu směrem k substrátu (kolmo k povrchu). To vede k vytvoření elektrického pole kolmého jak na teplotní gradient, tak na směr magnetizace. Napětí je obvykle v řádu V, proto může být měřeno obvyklým laboratorním vybavením. Navzdory své jednoduchosti poskytuje tato metoda velmi zajímavé výsledky a může být použita pro charakterizaci magnonických vlnovodů, magnonických metamateriálů, emitorů spinových vln a dalších zařízení, pracujících se spinovými vlnami.

Magnonika je novým odvětvím výzkumu, který se zabývá fyzikou spinových vln. Magnonika jako vědní obor nabízí nové možnosti například v nediskrétních výpočtech na základě vlnového charakteru spinových vln. Při výrobě magnonických prvků klasickými metodami není možné příliš měnit charakter materiálů, ze kterých jsou jednotlivé prvky vyrobeny. Tento fakt silně omezuje univerzálnost vyrobených struktur. Cílem této práce je aplikovat nový typ materiálu do oboru magnoniky. Specifikum daného materiálu je možnost zápisu magnetických struktur pomocí iontového svazku. Ukazuje se, že tyto struktury mají velice zajímavé magnetické vlastnosti, které lze velice přesně řídit právě strategií ozařování iontovým svazkem. Na základě fázově rozlišené Brillouinovy spektroskopie jsme získali disperzní relaci spinových vln v tomto systému a tím i důležité parametry systému. Pozorování podkládáme mikromagnetickými simulacemi a analytickými modely. Vlastnosti systému pro magnonické aplikace prezentujeme na třech prototypických sadách struktur, které nelze vyrobit pomocí klasických materiálů.

Spinové vlny mají potenciál být použity jako nová platforma pro přenos a zpracování dat, protože mohou dosáhnout vlnových délek v rozsahu nanometrů a frekvencí v rozsahu terahertzů. K tomu, aby bylo možné navrhnout zařízení a logické obvody založené na spinových vlnách, je zapotřebí získat informace o prostorovém rozložení intenzity spinové vlny a pokud je to možné, také o jejich fázi. To lze měřit pomocí fázově rozlišeného fokuso-vaného Brillouinova rozptylu světla (µ -BLS). Předložená práce se zabývá rozšířením stávající optické sestavy o možnost měření fáze, kde doposud bylo možné měřit pouze intenzitu. Toto rozšíření sestavy je důkladně popsáno a charakterizováno. Schopnosti optické sestavy jsou demonstrovány ve studii šíření spinových vln skrz Néelovu doménovou stěnu. Získané 2D mapy intenzity spinových vln ukazují, že propagace přes doménovou stěnu je ovlivněna topologicky vynucenou kruhovou Blochovou čarou ve středu doménové stěny a že režim propagace závisí na frekvenci spinových vln. V prvním režimu propagace se vytvoří dva svazky spinových vlny šířící se kolem kruhové Blochovy čáry, zatímco ve druhém režimu se spinové vlny šíří pouze středem. Fázově rozlišené µ-BLS měření odhaluje fázový po- sun spinových vln pro oba režimy. Mikromagnetické modelování spinových vln ukazuje rozrušení jejich fázových vlnoploch, které je třeba brát v úvahu při interpretaci měření a navrhování potenciálních zařízení. Mikromagnetické simulace ukazují, že vnější magnetické pole může být použito k pohybu kruhové Blochovy čáry ve stěně domény, a tedy k manipulaci spinových vln.

The study of magnons is an essential part of combining quantum information science and spintronics, allowing for the investigation of quantum properties such as entanglement in solid-state devices. Magnons are commonly described using the theory of T. Holstein and H. Primakoff, associating the spin operators with bosonic creation and annihilation operators. The quantum mechanical properties inherent to this description are the commutation relations. These relations must be conserved under transformation of the basis. This requires the application of pseudo-unitary transformations U (p, q) when studying the magnon eigenspectrum for example. Depending on the system at hand, the groups U (1, 1) and U (2, 2) are of particular interest and will be the focus of this work. We present a general formalism that leads to a representation of pseudo-unitary matrices via their self-adjoint elements. We apply this representation in examples involving magnons in antiferromagnets to find an explicit picture in connection to material properties. Finally, we explore numerical methods for determining magnon energies and compare them to the analytical counterpart.