Magnetic skyrmions are nanometer-scale spin textures that enjoy topologically-protected stability and exhibit particle-like behavior. Their rich phenomenology has ignited a growing research interest. These features and their novel transport properties have also made them attractive candidates as information carriers in future high-density magnetic-storage and logic devices, as well as integral components of other spintronic applications. Achieving a high degree of control and manipulation of skyrmions is of immense importance to applications and involves understanding fundamental aspects of the dynamics of twisted spin textures with topological charge at the nanoscale.
In chapter five, we have considered zero temperature quantum nucleation of a single skyrmion in magnetic ultrathin films with interfacial Dzyaloshinskii-Moriya interaction (DMI). While a uniform field stabilizes the ferromagnet, an opposing local magnetic field, generated by the tip of a local probe, drives the skyrmion nucleation. Using spin path integrals and a collective coordinate approximation, the tunneling rate from the ferromagnetic to the single skyrmion state is computed as a function of the tip's magnetization and height above the sample surface.
Based on the relation between DMI coupling and skyrmion helicity, the latter must be included as an extra degree of freedom in chiral magnets with a spatially inhomogeneous DMI. In chapter six, an effective description of skyrmion dynamics for an arbitrary inhomogeneous DMI coupling is obtained. The resulting generalized Thiele's equation is a dynamical system for the center of mass position and helicity of the skyrmion. We fully characterize the effective dynamics of a single skyrmion in a particular case of engineered DMI coupling: half-planes with opposite-sign DMI.
In chapter seven, a particle-based model was used to simulate current-driven magnetic skyrmions interacting with random quenched disorder. We show that the Magnus force combined with the random pinning produces an isotropic effective shaking temperature. Spectral analysis of the velocity noise fluctuations can be used to identify dynamical phase transitions and to extract information about the different dynamic phases.
In chapter eight, avalanches of flux-driven magnetic skyrmions in systems with random quenched disorder were also simulated using a particle-based model. The distribution of the avalanche sizes and durations, the associated critical exponents, and the average avalanche shape, were studied for different pinning regimes and Magnus force strengths.
