Particle-based computer simulations of magnetic skyrmions
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Abstract
Magnetic skyrmions are topologically stabilized magnetic structures found in multilayer thin film systems. They are often described as two-dimensional quasi-particles evolving according to the Thiele equation. This description allows for computer simulations of skyrmion dynamics using Brownian dynamics simulations with an additional term that takes care of the skyrmion Hall effect. Such simulations are significantly more efficient than conventional methods such as micromagnetic or atomistic spin dynamics simulations and therefore allow for simulating larger skyrmion systems for longer. Modeling specific skyrmion systems with this equation requires knowledge of interaction potentials of skyrmions with each other and with magnetic material boundaries. This thesis presents an approach to determine these potentials directly from experiment without prior assumptions on the potential shape by using the iterative Boltzmann inversion method, which has been previously established in soft-matter systems. The interaction potentials are found to be purely repulsive for the micrometer sized skyrmions studied here. Based on these potentials, further simulations of skyrmion systems are performed showing a good agreement with experiments and allowing for a comparison of simulated and experimental skyrmion lattices. Besides the analysis of phase transitions and ordering, the analysis of large skyrmion systems also comprises the effect of the gyroscopic Magnus force on diffusion of skyrmions. Contrary to other systems containing diffusive particles, an increased skyrmion density can lead to an increase in diffusion if a sufficiently strong Magnus force is present. Moreover, pinning effects and their influence on free and current-induced skyrmion diffusion are investigated. This investigation motivates the development of two different methods to increase skyrmion diffusion at constant temperature by reducing the impact of pinning on skyrmions. The first method uses periodic perpendicular magnetic field excitations to change skyrmion sizes and thereby the effective pinning landscape in which skyrmions move. The second one uses periodic current excitations to move skyrmions out of pinning sites. Finally, the effect of tight confinements on skyrmion dynamics is investigated. Here, the skyrmion dynamics is not only affected by the skyrmion density but also by the commensurability of the skyrmion number with the confinement. When the number of skyrmions is commensurate with the confinement geometry, diffusion is significantly decreased. Building upon these results, the changes in ordering and dynamics of confined skyrmions due to applied currents are analyzed in the context of employing such confined skyrmion systems for reservoir computing.