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Magnetic skyrmions (skyrmions hereafter) are recently discovered localized vortexlike magnetic structures, defined by their unit topological winding number. From this nontrivial topology, skyrmions inherit unusual physical properties. They have been shown to be particularly robust to deformation, and so they are often referred to as being "topologically protected". In conductive materials, they appear to source electric and magnetic fields. When driven by an applied force, their topology prevents them from moving collinearly with the direction of the applied force; the angle by which they are deflected is known as the skyrmion Hall angle. Large skyrmion Hall angles are known to decrease the depinning threshold for motion under external drives, and skyrmions are known to be sensitive to ultra-low current density spin-transfer and spin-orbit torques. These factors, combined with their nano-scale size, have generated excitement around the prospect that skyrmions could find use as a next-generation information carrier. This led to the publication of dozens of skyrmionic device schematics, each more ingenious than the last. Despite this flurry of applied research, magnetic skyrmions are still far from finding technological use. This can be attributed to two key issues. The first is materials problem; while there are dozens of materials systems that host these topological whirls, no material is known to host skyrmions with the three necessary characteristics of having a diameter on the order of 10 nm, stability at room temperature, and stability at remanence (although, FeGe and CoxZnyMnz satisfy the first two criteria, and many magnetic multilayers meet the last two). The second issue is a lack of physical understanding of the structure and dynamics of magnetic skyrmions, which will be the focus of this thesis. The structural investigation begins with the establishment of the necessary mathematical framework; magnetic skyrmions, and the magnetization textures they coexist with, are first constructed and investigated analytically. Then, the twodimensional morphology of lattices of these objects is investigated experimentally using resonant elastic x-ray scattering, and the first measurement of the magnetic soliton lattice above room temperature is presented, alongside the first measurement of the skyrmion liquid phase. Following this 2D study, the fascinating threedimensional structure of skyrmions is probed; a mathematical discussion of the conical modulation of skyrmion strings is followed by an experimental and theoretical study of the surface-pinned nature of skyrmions. An important model for the description of skyrmion dynamics is Thiele's equation, but this equation suffers from the prerequisite that one must have a priori knowledge of the interaction potential between the magnetization structures whose motion it describes, and their environment. To extend the cases in which Thiele's equation can be used, a general form of the interaction potential between any two magnetization configurations is derived and benchmarked. Thiele's equation in the presence of external spin-transfer torque, spin-orbit torque, and magnetic field gradient drives is derived; this is used to show that, when skyrmions are driven by spinorbit torque down a nanowire, they are only negligibly deflected by the non-uniform magnetic field generated by the current through the wire. Using the knowledge of skyrmion-skyrmion interactions and their coupling to external fields, the properties of large systems of skyrmions are studied numerically by integrating Thiele's equation, revealing the strain and defect driven dynamics of skyrmion crystals. Finally, the first technique that allows for the determination of the all-important skyrmion Hall angle from the skyrmion lattice state is discussed, and used experimentally to perform the first measurement of the skyrmion Hall angle in FeGe.

Heterostructures composed of ferromagnetic layers that are mutually interacting through a nonmagnetic spacer are at the core of magnetic sensor and memory devices. In the present study, layer-resolved ferromagnetic resonance was used to investigate the coupling between the magnetic layers of a Co/MgO/Permalloy magnetic tunnel junction (MTJ) and Co/Sn/Py spin valves. Elemental tin in the a-phase is an intriguing member of the family of topological quantum materials. In thin films, with decreasing thickness, a-Sn transforms from a 3D topological Dirac semimetal to a 2D topological insulator (TI). Getting access to, and making use of its topological surface states is challenging and requires interfacing to a magnetically ordered material. For both types of samples two magnetic resonance peaks were observed for both magnetic layers, as probed at the Co and Ni L₃ x-ray absorption edges, showing a strong interlayer interaction through the insulating MgO barrier. A theoretical model based on the Landau-Lifshitz-Gilbert-Slonczewski equation was developed, including exchange coupling and spin pumping between the magnetic layers. Fits to the experimental data were carried out, both with and without a spin pumping term, and the goodness of the fit was compared using a likelihood ratio test. Evidence of two types of magnetic layer coupling were found for the studied MgO MTJ. A Likelihood ratio test performed between competing models showed that a model with only exchange coupling is insufficient, and the correct description of the experimental data requires inclusion of spin pumping coupling between magnetic layers. The values characterising both the EC and the spin pumping were estimated. A recipe has been developed for spin-vale fabrication incorporating a a-Sn TI spacer layer. Up to 2nm thick a-Sn layers were deposited onto a Co surface. The X-ray detected ferromagnetic resonance (XFMR) study of the a-Sn system has shown a strong exchange coupling interaction between the magnetic layers with no clear evidence for spin pumping. The methods developed in this work can be used to interpret XFMR data, not only in the discussed cases, but potentially for all types of measurements in general. The explored idea of incorporating the TI a-Sn into a spin-valve has shown promising results, and will serves as a solid basis for further research.

Topological insulators, a type of quantum material, are of intense interest to researchers due to their ability to house time reversal symmetry protected, gapless, linearly dispersed surface states, offering dissipationless conductivity. Through the introduction of magnetic dopants or proximity coupling which induces long-range ferromagnetic order, time reversal symmetry can be broken, introducing a band gap in the surface state. This has led to the experimental observation of exotic quantum effects such as the quantum anomalous Hall (QAH) effect which does not require an externally applied magnetic eld in order to be realised and is the anomalous counter part to the quantum Hall (QH) effect. However, the QAH effect has only previously been observed in magnetic topological insulators (MTI) at sub mK temperatures, limiting the application potential of these extremely promising materials. This thesis presents an investigation into the structural and magnetic properties of 3D MTI thin films grown by molecular beam epitaxy (MBE) using reflection high energy electron diffraction (RHEED), X-ray reflectometry (XRR), X-ray diffraction (XRD), vibrating sample magnetometry (VSM), X-ray absorption spectroscopy (XAS), X-ray magnetic circular dichroism (XMCD) and polarised neutron reflectometry (PNR). The element specific magnetometry of XMCD and magnetic depth profiling capabilities of PNR allows for an in-depth investigation of the different magnetic coupling scenarios which occur in magnetically doped samples as well as magnetic enhancements caused by proximity coupling and interface effects in MTI heterostructure. Firstly, an investigation of single-layered TI thin films and the effects of using different magnetic dopants in the form of the transition metal Cr and the rare earth Dy ions is presented. Using Cr as a dopant in Sb2Te3 is shown to produce samples of a high structural quality with long-range ferromagnetic order which persists up to a TC of 120 K. XRD, XAS and XMCD measurements demonstrate that Cr substitutionally replaces Sb during growth. PNR measurements demonstrate an equal distribution of Cr throughout the sample with no surface enhancement. XMCD measurements demonstrate that the long-range ferromagnetic order is caused by a carrier-mediated coupling mechanism where the exchange interaction is mediated by polarised Te valence holes, leading to the formation of Cr 3d impurity bands near the Fermi level, which is detrimental to the observation of the QAH effect. Using a Dy dopant with Bi2Te3 leads once again to a sample of high structural quality. VSM and XMCD measurements demonstrate that there is no long-range ferromagnetic order induced. PNR measurements combined with Muon spin relaxation measurements show that the Dy dopant leads to a system which displays short-range ferromagnetic order within patches of the material where a large internal magnetic field can be induced at moderate applied fields. Unlike in the case of Cr-doped Sb2Te3, the exchange interaction in the sample is not mediated by the conduction band, as demonstrated by XMCD. In an attempt to enhance the magnetic properties of an MTI system, two transition metal dopants Cr and V are used to co-dope Sb2Te3. This leads to the formation of Cr2Te3 within the sample which is caused by the V acting as a surfactant which prevents the Cr from substitutionally replacing Sb within the MTI structure as demonstrated by XRD, XAS and XMCD measurements. The previous studies conducted on the single layer MTI samples are then used to inform the fabrication of MTI heterostructures in an attempt to investigate proximity coupling and interface effects in multilayer structures. Growing a ferromagnetic Co layer on top of Cr:Sb2Te3 demonstrates the strength of the long-range ferromagnetic order, where Co is unable to polarise the Cr moments contained within the MTI to a significant degree, as demonstrated by Arrott plots which show that the single layer Cr:Sb2Te3 with a TC of 86.7 K is only minimally enhanced to 92.7 K after the deposition of ferromagnetic Co. Producing high quality heterostructures consisting of multiple bilayers of Cr:Sb2Te3/Dy:Bi2Te3 with well dened interfaces leads to the enhancement of the magnetic properties of the Dy:Bi2Te3 layers, where XMCD measurements show that they demonstrate ferromagnetic behaviour up to a temperature of 17 K as determined by Arrott plots. XMCD measurements demonstrate that despite single layer Cr:Sb2Te3 and Dy:Bi2Te3 having an easy axis of magnetisation perpendicular to one another, the average Cr and Dy moments contained within the structure are parallel out-of-plane, demonstrating that the dopants magnetically couple. This research demonstrates the possibility of enhancing MTI systems through the use of magnetic heterostructures. It also shows how XMCD and PNR are powerful techniques for gaining insight into the magnetic properties of such systems in order understand how these materials can be both utilised and enhanced to further the eld of MTIs in the pursuit of a QAH effect realised in a device friendly scenario.

This work focuses on characterising the chiral and topological nature of magnetic skyrmions in noncentrosymmetric helimagnets. In these materials, the skyrmion lattice phase appears as a long-range-ordered, close-packed lattice of nearly millimetre-level correlation length, while the size of a single skyrmion is 3-100 nm. This is a very challenging range of lengthscales (spanning 5 orders of magnitude from tens of nm to mm) for magnetic characterisation techniques. As a result, only three methods have been proven to be applicable for characterising certain aspects of the magnetic information: neutron diffraction, electron microscopy, and magnetic force microscopy. Nevertheless, none of them reveals the complete information about this fascinating magnetically ordered state. On the largest scale, the skyrmions form a three-dimensional lattice. The lateral structure and the depth profile are of importance for understanding the system. On the mesoscopic scale, the rigid skyrmion lattice can break up into domains, with the domain size about tens to hundreds of micrometers. The information of the domain shape, distribution, and the domain boundary is of great importance for a magnetic system. On the smallest scale, a single skyrmion has an extremely fine structure that is described by the topological winding number, helicity angle, and polarity. These pieces of information reveal the underlying physics of the system, and are currently the focus of spintronics applications. However, so far, there is no experimental technique that allows one to quantitatively study these fine structures. It has to be emphasised that the word 'quantitative' here means that no speculations have to be made and no theoretical modelling is required to assist the data interpretation -- what has been measured must be straightforward, and give a unique and unambiguous answer. Motivated by these questions, we developed soft x-ray scattering techniques that allow us to acquire much deeper microscopic information of the magnetic skyrmions -- reaching far beyond what has been possible so far. We will show that by using only one technique, all the information about the magnetic structure (spanning 5 orders of magnitude in length) can be accurately measured. The thesis is structured as follows: The key development is the Dichroism Extinction Rule, which is summarised in Chapter 6, and quintessentially summarises the thesis. In Chapter 1, the well-established theory for skyrmions is introduced, reconstructing the picture from single skyrmions to the skyrmion crystal. A few comments about the current characterisation techniques will be given. In Chapter 2, we will start with the largest lengthscale, the long-range-ordered skyrmion lattice phase. This is an intensely studied phase, mostly using neutron diffraction, and we will show that this piece of information can be equivalently (or actually even better) obtained using resonant x-ray diffraction. The theoretical foundation of this technique is also given. In Chapter 3, we will demonstrate imaging technique with which we were able to effectively map the skyrmion domains. The measurements also suggest a way to control the formation of skyrmion domains, which might be the key for enabling skyrmion-based device applications. Chapters 4 and 5 present the highlights of this work, in which we will show that using the dichroism extinction rule, the topological winding number and the skyrmion helicity angle can be unambiguously determined. In this sense, this technique is capable of accurately measuring the internal structure of single skyrmions.

Spin transfer in magnetic multilayers offers the possibility of a new generation of ultra-fast, low-power spintronic devices. New ways to control the resonance frequency and damping in ultrathin films are actively sought, fuelling study of the precessional dynamics and interaction mechanisms in such samples. One effect that has come under particular scrutiny in recent years is the spin-transfer torque, wherein a flow of spins entering a ferromagnet exerts a torque on the magnetisation, inducing precession. A flow of spin angular momentum is usually generated through a spin-polarised electrical current, but a promising alternative is the pure spin current emitted by a ferromagnet undergoing ferromagnetic resonance (FMR). This allows spins to be transferred without a net charge flow. The physics of the generation, transmission and absorption of pure spin currents is a developing field, and holds great promise for both industrial applications and as a means to study fundamental physical phenomena in exotic materials. This thesis presents an investigation into the magnetodynamics of ferromagnetic thin films and heterostructures grown by molecular beam epitaxy and studied using vector-network analyser ferromagnetic resonance (VNA-FMR), x-ray magnetic circular dichroism, vibrating sample magnetometry and x-ray detected ferromagnetic resonance (XFMR). Particular attention is paid to the anisotropy of damping processes that occur in thin films, and the different coupling mechanisms that can exist across non-magnetic spacer layers in spin valves and magnetic tunnel junctions. It is first shown that the static and dynamic magnetic properties of thin Fe films can be effectively tailored by dilute doping with Dy impurities, which introduces a sizeable anisotropy of Gilbert damping. The mechanism underlying this effect is discussed, as is the concurrent modification of the spin and orbital contributions to the magnetic moment. The focus then turns to magnetodynamics of ferromagnetic films coupled across a nonmagnetic spacer layer, examining how different materials permit different interactions. First, an insulating MgO layer is used to separate the FM layers; it is found that this attenuates a spin current in under 1~nm, but permits a static interaction for at least 2 nm. XFMR measurements are used to ascertain the different contributions of the two interactions, and shed light on their interplay. Next, the same techniques are applied to spin valves with a spacer layer of the topological insulator (TI) Bi2Se3. TIs are the subject of much attention in the physics community, as they hold the potential for dissipationless transport, extremely high spin-orbit torques, and a host of novel physical effects. Here, their ability to absorb and transmit a pure spin current is studied, testing their suitability for incorporation into existing device schemata. VNA-FMR measurements confirm that the TI functions as an efficient angular momentum sink. XFMR measurements, however, demonstrate the presence of a weak interaction between the two ferromagnets, able to persist up to at least 8~nm, and possibly mediated by the topological surface state. Finally, the angle-dependence of spin pumping through a Cr barrier is examined, finding that a strong anisotropy of spin pumping from the source layer can be induced by an angular dependence of the total Gilbert damping parameter in the spin sink layer. VNA-FMR measurements show that anisotropy is suppressed above the spin diffusion length in Cr, which is found to be 8 nm, and is independent of static exchange coupling in the spin valve. XFMR results confirm induced precession in the spin sink layer, with isotropic static exchange and an anisotropic dynamic exchange. Taken together, these studies provide an insight not only into the magnetisation dynamics of thin films (and ways to modify them) but a demonstration of the power of ferromagnetic resonance techniques, and their applicability across materials and concepts. The results offer valuable information on the transmission and absorption of spin currents by different materials, and several mechanisms by which enhanced spin torques and angular control of damping may be realized for next-generation spintronic devices.

The three key areas of this thesis are crystal synthesis strategies, growth mechanisms, and new types of quantum materials nanowires. The highlights are introduction of a new catalyst (TiO2) for nanowire growth and application to Bi2Se3, Bi2Te3, SnO2, and Ge nanowires; demonstration of step-flow growth, a new growth mechanism, for Bi2Te3 sub-micron belts; and the characterisation of the first quasi-one dimensional topological insulator (orthorhombic Sb-doped Bi2Se3) and topological Dirac semimetal nanowires (Cd3As2). Research into new materials has been one of the driving forces that have contributed to the progress of civilisation from the Bronze Age four thousand years ago to the age of the semiconductor in the 20th century. At the turn to the 21st century novel materials, so-called quantum materials, started to emerge. The fundamental theories for the description of their properties were established at the beginning of the 20th century but expanded significantly during the last three decades based, for example, on a new interpretation of electronic states by topological invariants. Hence, topological insulator (TI) materials such as mercury-telluride are one manifestation of a quantum material. In theory, TIs are characterised by an insulating interior and a surface with spin-momentum locked conduction. In real crystals, however, the bulk can be conducting due to crystal imperfections. Nanowires suppress this bulk contribution inherently by their high surface-to-volume ratio. Additionally, trace impurity elements can be inserted into the crystal to decrease the conductance further. These optimised TI nanowires could provide building blocks for future electronic nanodevices such as transistors and sensors. Initial synthesis efforts using vapour transport techniques and electronic transport studies showed that TI nanowires hold the promise of reduced bulk contribution. This thesis expands the current knowledge on synthesis strategies, crystal growth mechanisms, and new types of quantum materials nanowires. Traditionally, gold catalyst nanoparticles were used to grow TI nanowires. We demonstrate that they are suitable to produce large amounts of nanowires but have undesired side-effects. If a metaloxide catalyst nanoparticle is used instead, quality and even quantity are significantly improved. This synthesis strategy was used to produce a new TI which is built from chains of atoms and not from atomic layers as in case of previously known TIs. The growth of large nanowires with a layered crystal structure leads to step-flowgrowth, an intriguing phenomenon in the growth mechanism: New layers grow on top of previous layers with a single growth frontmoving fromthe root to the tip. These wires are ideal for further electronic characterisation that requires large samples. The nanowire growth of tin-oxide will also be discussed, a side project that arose from my growth studies, which is useful for sensor applications. Under certain conditions it forms tree-like structures in a single synthesis step. All of the aforementioned growth studies are carried out at atmospheric pressure. A separate growth study is carried out in ultra-high vacuum to assess the transferability of the growth process towards the cleanliness requirements of the semiconductor industry. If two quantum materials are joined together, exotic physics may emerge at the interface. One of the goals of TI research is the experimental observation of Majorana fermions, exotic particles which are their ownantiparticles with potential applications in quantum computing that may appear in superconductor/TI hybrid structures. We have synthesised such structures and initial characterisation suggests that the resistivity increases when they are cooled below the critical temperature of the superconductor. Beyond TIs, a new type of quantum material, called a topological Dirac semimetal, opens new realms of exotic physics to be discovered. Nanowires are grownfroma material which has recently been discovered to be a topological Dirac semimetal. Their growth mechanism is characterised and an extremely high electron mobility at room temperature is measured. The contribution of this thesis to the field is summarised in Fig. 1. Its core is the study of the growth mechanism of quantum materials which will be vital for future development of applications and fundamental research.

Topological insulators (TIs) are recently predicted, and much studied, new quantum materials. These materials are characterised by their unique surface electronic properties; namely, behaving as band insulators within their bulk, but with spin-momentum locked surface or edge states at their interface. These surface/edge crossing states are protected by the underlying time-reversal symmetry (TRS) of the bulk band structure, leading to a robust topological surface state (TSS) that is resistant to scattering from impurities which do not break TRS. Their surface band dispersion has a characteristic crossing at time reversal invariant momenta (TRIM) called a Dirac cone. It has been predicted that the introduction of a TRS breaking effect, through ferromagnetic order for instance, will open a band-gap in this Dirac cone. It can be seen that magnetic fields are not time reversal invariant by considering a solenoid. If time is reversed, the current will also reverse in the solenoid and so the magnetic field will also be reversed. So it can be seen that magnetic fields transform as odd under time reversal, the same will be true of internal magnetisation. By manipulating this gapped surface state a wide range of new physical phenomena are predicted, or in some cases, already experimentally observed. Of particular interest is the recently observed quantum anomalous Hall effect (QAHE) as well as, e.g., topological magneto-electric effect, surface Majorana Fermions and image magnetic monopoles. Building on these novel physical effects, it is hoped to open new pathways and device applications within the emerging fields of spintronics and quantum computation. This thesis presents an investigation of the nature of magnetic doping of the chalcogenide TIs Bi2Se3 and Bi2Te3 using 3d transition-metal dopants (Mn and Cr). Samples were grown by molecular beam epitaxy (MBE), an ideal growth method for the creation of high-quality thin film TI samples with very low defect densities. The grown films were investigated using a range of complementary lab-based and synchrotron-based techniques to fully resolve their physical structure, as well as their magnetic and electronic properties. The ultimate aim being to form a ferromagnetic ground state in the insulating material, which may be expanded into device applications. Samples of bulk Mn-doped Bi2Te3 are presented and it is shown that a ferromagnetic ground state is formed below a measured TC of 9-13 K as determined by a range of experimental methodologies. These samples are found to have significant inhomogeneities within the crystal, a problem that is reduced in MBE-grown crystals. Mn-doped Bi2Se3 thin films were grown by MBE and their magnetic properties investigated by superconducting quantum interference device (SQUID) magnetometry and x-ray magnetic circular dichroism (XMCD). These reveal a saturation magnetisation of 5.1 μB/Mn and show the formation of short-range magnetic order at 2.5 K (from XMCD) with indication of a ferromagnetic ground state forming below 1.5 K. Thin films of Cr-doped Bi2Se3 were grown by MBE, driven by the recent observation of the QAHE in Cr-doped (Bi1−xSbx)2Te3. Investigation by SQUID shows a ferromagnetic ground state below 8.5 K with a saturation magnetisation of 2.1 μB/Cr. Polarised neutron reflectometry shows a uniform magnetisation profile with no indication of surface enhancement or of a magnetic dead layer. Further studies by extended x-ray absorption fine structure (EXAFS) and XMCD elucidate the electronic nature of the magnetic ground state of these materials. It is found that hybridisation between the Cr d and Se p orbitals leads to the Cr being divalent when doping on the Bi3+ site. This covalent character to the electronic structure runs counter to the previously held belief that divalent Cr would originate from Cr clusters within the van der Waals gap of this material. The work overall demonstrates the formation of a ferromagnetic ground state for both Cr and Mn doped material. The transition temperature, below which ferromagnetic order is achieved, is currently too low for usable device applications. However, these materials provide a promising test bed for new physics and prototype devices.