Vortices are point-like topological defects in superconductors whose motion dictates superconducting properties and controls device performance. In superconductor-ferromagnet heterostructures, vortices interact with topological defects in the ferromagnet such as line-like domain walls. While in previous heterostructure generations, vortex-domain wall interactions were mediated by stray fields; in new heterostructure families, more important become exchange fields and spin-orbit coupling. However, spin-orbit coupling's role in vortex-domain wall interactions remains unexplored. Here we uncover, via numerical simulations and Ginzburg-Landau theory, that Rashba spin-orbit coupling induces magnetoelectric interactions between vortices and domain walls that crucially depend on the wall's winding direction$-$its helicity. The wall's helicity controls whether vortices are pushed or dragged by N\'eel walls, and their gliding direction along Bloch walls. Our work capitalizes on interactions between topological defects from different order parameters and of different dimensionality to engineer enhanced functionality.

Majorana zero modes are quasiparticles that hold promise as building blocks for topological quantum computing. However, the litmus test for their detection, the observation of exotic non-abelian statistics revealed by braiding, has so far eluded experimental efforts. Here we take advantage of the fact that skyrmion-vortex pairs in superconductor-ferromagnet heterostructures harboring Majorana zero modes can be easily manipulated in two spatial dimensions. We adiabatically braid the hybrid topological structures and explicitly confirm the non-abelian statistics of the Majorana zero modes numerically using a self-consistent calculation of the superconducting order parameter. Our proposal of controlling skyrmion-vortex pairs provides the necessary leeway toward a scalable topological quantum computing platform.

We propose that the nonlinear radio-frequency dynamics and nanoscale size of topological magnetic structures associated with their well-defined internal modes advocate their use as in materio scalable frequency multipliers for spintronic systems. Frequency multipliers allow for frequency conversion between input and output frequencies, and thereby significantly increase the range of controllably accessible frequencies. In particular, we explore the excitation of eigenmodes of topological magnetic textures by fractions of the corresponding eigenfrequencies. We show via micromagnetic simulations that lowfrequency perturbations to the system can efficiently excite bound modes with a higher amplitude. For example, we excite the eigenmodes of isolated ferromagnetic skyrmions by applying half, a third, and a quarter of the corresponding eigenfrequency. We predict that frequency multiplication via magnetic structures is a general phenomenon that is independent of the particular properties of the magnetic texture and works for magnetic vortices, droplets, and other topological textures.

In this thesis we investigate the existence of Majorana zero modes in ferromagnetsuperconductor heterostructures. A promising feature of these modes is the property of non-abelian statistics. Such statistics of exchanging two quasiparticles is the key ingredient to building a topological quantum computer which implements quantum error correction on a hardware level. At the moment there is no experimental technique which shows unambiguously the existence of Majorana modes. Hence, the only way to prove if the observed modes are the desired ones is to braid them and verify their nonabelian statistics. Therefore, it is vital to find a system where the latter can be realized. In order to analyse the considered systems, we diagonalize the corresponding Bogoliubovde Gennes Hamiltonian and self-consistently calculate the superconducting gap. Within this method the energy of the system is minimized. Thereby, we obtain a stable solution, which makes it more probable to be found in an experimental setup. As a main result, we find the existence of Majorana zero modes in skyrmion-vortex pairs. Due to the drivability of the skyrmion and the attraction between a skyrmion and a vortex, skyrmion-vortex pairs could be a way to actually braid the Majorana zero modes. As a starting point, we prove that the used method fulfils the concepts derived for the Kitaev Chain. In the course of this thesis, we expand the model to skyrmionvortex pairs. Finally, the generation of effective spin-orbit coupling by a skyrmion with winding number two is an unstable solution in our method.

We examine the current-induced dynamics of a skyrmion that is subject to both structural and bulk inversion asymmetry. There arises a hybrid type of Dzyaloshinskii-Moriya interaction (DMI) which is in the form of a mixture of interfacial and bulk DMIs. Examples include crystals with symmetry classes C-n as well as magnetic multilayers composed of a ferromagnet with a noncentrosymmetric crystal and a nonmagnet with strong spin-orbit coupling. As a striking result, we find that, in systems with a hybrid DMI, the spin-orbit-torque-induced skyrmion Hall angle is asymmetric for the two different skyrmion polarities (+/- 1 given by out-of-plane core magnetization), even allowing one of them to be tuned to zero. We propose several experimental ways to achieve the necessary straight skyrmion motion (with zero Hall angle) for racetrack memories, even without antiferromagnetic interactions or any interaction with another magnet. Our results can be understood within a simple picture by using a global spin rotation which maps the hybrid DMI model to an effective model containing purely interfacial DMI. The formalism directly reveals the effective spin torque and effective current that result in qualitatively different dynamics. Our work provides a way to utilize symmetry breaking to eliminate detrimental phenomena as hybrid DMI eliminates the skyrmion Hall angle.