Abstract: Novel quantum phases of matter and developing practical control over their characteristics is one of the primary aims of current condensed matter physics. It offers the potential for a new generation of energy, electronic and photonic technologies. Among all the newly found phases of matter, topological insulators are novel phases of quantum matter with fascinating bulk band topology and surface states protected by specific symmetries. For example, at the boundary of a strong topological insulator and a trivial insulator, metallic surface states appear that are protected by time-reversal symmetry. As a result, the bulk continues to be insulating, while the surface can support exotic high-mobility spin-polarized electronic states. Since there is no such thing as a clean system, impurities and other disorders are always present in materials. Even while impurities appear to be unfavorable to a system at first look, doping the host system with impurities allows us to engineer different electronic properties of systems, such as the Fermi level or electron density. Because of the symmetry protected metallic states in topological insulators, charge transport responds distinctively to magnetic and non-magnetic impurities. This doctoral dissertation explores how the longitudinal charge transport in magnetic topological thin films and the anomalous Hall effect on the surface of 3D magnetic topological insulators is influenced by point-like and randomly distributed dilute magnetic impurities. We are interested in how charge transport in these systems responds to the orientation of the magnetization orientation and how this response evolves based on the system's main characteristics, such as the magnitude of the Fermi level or gate voltage. Because topological insulators have a strong spin-orbit coupling, the interaction between conducting electrons and local magnetic impurities is very anisotropic. We will show that this anisotropy even enhances when magnetic topological thin films are exposed to a substrate or gate voltage. Therefore, to properly capture this anisotropy in charge transport calculations, we rely on a generalized Boltzmann formalism together with a modified relaxation time scheme. We show that magnetic impurities affect the charge transport in topological insulators by inducing a transition selection rule that governs scatterings of electrons between various electronic states. We see that this selection rule is highly sensitive to the spin direction of the magnetic impurities as well as the position of the Fermi level. According to this selection rule and depending on the position of the Fermi level, two different transport regimes are realized in magnetic topological thin films. In one of these regimes, our findings show that a dissipation less charge current can be generated. In other words, even if there are many magnetic impurities in the system, electrons do not notice them and, remarkably, conduct charge without dissipation. Outside this regime, the charge transport is always dissipative and its sensitivity to the spatial orientation of the magnetic impurities can be effectively modulated by a substrate or gate voltage. In this doctoral thesis, we also explore the anomalous Hall effect (AHE) on the surface of 3D magnetic topological insulators. The AHE is generated by three mechanisms: the intrinsic effect (owing to a nonzero Berry curvature), the side jump effect, and the skew scattering effect. They compete to dominate the AHE in distinct regimes. Analytically, we calculate the contributions of all three mechanisms to the scattering of massive Dirac fermions by magnetic impurities. Our results reveal three transport regimes based on the relative importance of the engaged mechanisms. The identification of these three distinctive transport regimes can assist experimentalists in achieving a regime in which each contribution is dominant over the others, allowing them to measure them separately. Typically, this is not feasible empirically since the total value of the experimentally observed AHE conceals the specific information of each of the three contributions. Based on our analytical calculations, we prove that the AHE can change sign by varying the orientation of the surface magnetization, the concentration of impurities, and the location of the Fermi level, which is consistent with previous experimental findings. In addition, we show that by suitably adjusting the given parameters, any contribution to the AHE, or even the entire AHE, can be turned off. For example, in a system with in-plane magnetization, one can turn off the AHE by pushing the system into the completely metallic regime. Furthermore, we demonstrate that any contribution to the AHE, or even the whole AHE, can be turned off by appropriately changing the provided parameters. For example, in a system with in-plane magnetization, the AHE can be turned off by pushing the system into the fully metallic regime.

Abstract: The precise control of skyrmionics and magnonics in magnetic materials is key to the development of novel spin-based technology and information transport applications. Essentially, the inherent stability of magnetic skyrmions (provided by their topological charge) together with their extremely small size (down to a few nanometers) and the ultralow threshold current necessary to move them in nanostructures are the main advantages of skyrmionics. Not least, magnonics offers lower power consumption compared to electronics and the excitation of high frequency (sub-100~nm wavelength) magnons makes it possible for the creation of nanometric devices for ultrafast information transport. Even though extensive research has been carried out in recent years, the precise manipulation of skyrmions and spin waves (magnons) in nanostructures is not fully mastered and needs to be addressed before making functional skyrmionic and magnonic devices. In this thesis, we reveal multiple alternatives for the manipulation of skyrmions and spin-waves in different materials, such as bulk chiral magnets, heterochiral structures, magnet-supperconductor hybrids and two-dimentional magnetic materials. We make use of a multiscale model to numerically simulate the magnetic states at each considered material, from micromagnetic to atomistic control. We first explore the different nucleation mechanisms, activation energy, and the time evolution of the skyrmion formation in chiral magnetic films, crucial for the realization of skyrmion-based devices. We show that the skyrmion lattice is formed from the conical phase progressively, most probably by the formation of chiral bobbres, followed by the cylindrical growth of individual skyrmions from the film surface. That reflects a rod-like (one-dimensional) nucleation of the skyrmion phase, with an activation barrier of several electronvolts per skyrmion for the case of MnSi (Manganese monosilicide). In addition, we reveal the interesting blinking (creation-annihilation) behavior of skyrmions close to the phase boundary between the conical and skyrmion phases, where we recall that such switching between topologically distinct states has been proposed as a bit operation for information storage. Next, we discuss the motion of ferromagnetic and antiferromagnetic skyrmions in heterochiral magnets. We report the characteristic deflection of ferromagnetic skyrmions when moving across a heterochiral interface, where the extent of such deflection is tuned by the applied spin-polarized current and the magnitude of Dzyaloshinskii-Moriya interaction. Following, we show that the antiferromagnetic skyrmion achieves much higher velocities than its ferromagnetic counterpart, yet experiences far stronger confinement in nanoengineered heterochiral tracks, which reinforces antiferromagnetic skyrmions as a favorable choice for skyrmion-based devices. After that, we study the interesting coupling of magnetic skyrmions and superconducting vortices in magnet-superconductor heterostructures. We perform numerical simulations, based on experimental observations, to demonstrate that the stray field of magnetic skyrmions can nucleate antivortices in an adjacent superconducting film, giving rise to a hybrid topological object, the skyrmion-vortex pair, which harbor promising features for skyrmionics and quantum computing applications. We then explore the manipulation of a single skyrmion-vortex pair when currents are applied into both superconducting and magnetic parts of the heterostructure, which is of importance for the facilitated skyrmion guidance in racetrack applications. Afterwards, we make use of the high tunability of magnetic parameters in two-dimensional magnetic materials to reveal the rich phase diagram of exotic magnetic configurations in magnetic monolayers with suppressed nearest-neighbour exchange, where we show that several unique cycloidal, checkerboard, row-wise and spin-ice states are stabilized by the competition between the second-nearest-neighbor exchange, Dzyaloshinskii-Moriya, and dipolar interactions. Additionally, we show the coexistence of ferromagnetic and antiferromagnetic spin-cycloids, as well as novel types of skyrmions and chiral domain walls. Finally, in the last part of the thesis, we present the spin wave properties in the two-dimensional magnetic materials CrBr$3$ and CrI$3$. Using spin-dynamics simulations parametrized from first principles, we reveal that the spin wave dispersion in such materials can be tuned in a broad range of frequencies by strain-engineering, and that a designed pattern of strain, as well as structural defects (halide vacancies) can be turned useful in the design of spin-wave guides. Lastly, we discuss the realization of magnonic crystals by moiré-periodic modulation of magnetic parameters in van der Waals heterostructures, where we show that the several nanometer small periodicities in such samples are ideal for the interference of terahertz spin waves. Recalling the wide range of possibilities for manipulating spin waves in such two-dimensional materials, we therefore suggest these systems as a front-runner for prospective terahertz magnonic applications.