Quasi-particle simulations of skyrmion dynamics with applications in unconventional computing
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Abstract
Magnetic skyrmions are effectively two-dimensional, topologically stabilized whirls of magnetization that exhibit particle-like behavior and can perform thermal random motion akin to Brownian dynamics. These properties, alongside a variety of external movement-inducing mechanisms, such as current-induced spin torques, make skyrmions promising candidates for applications in data storage and unconventional computing. Computer simulations are a valuable tool for in-silico device development and optimization. However, conventional atomistic and micromagnetic simulation approaches exhibit prohibitive computational costs at large experimentally relevant length and time scales. Here, we focus on the coarse-grained quasi-particle description of skyrmions. In the so-called Thiele framework, these limitations with respect to time and length scales are overcome by representing skyrmions as soft disks without explicitly modeling their internal magnetic structure. In this thesis, statistical physics methods are employed to determine the key parameters for quantitative quasi-particle simulations of skyrmions directly from experimental trajectories. Consequently, these methods do not rely on any assumptions about the underlying magnetic interactions or the skyrmion’s internal structure, while automatically averaging over thermal fluctuations of the latter.
Two methods are developed to ascertain the skyrmion damping parameter and the force acting on a skyrmion in response to an applied current density. The skyrmion damping sets the time scale of the system’s dynamics. Accounting for the interaction with local variations of the magnetic properties is crucial for the time scale conversion between simulation and experiment. These "pinning effects" are unavoidable in state-of-the-art skyrmion systems and act to slow down skyrmion dynamics significantly. Modeling skyrmion pinning via a spatially inhomogeneous energy landscape enables us to isolate its effects from the intrinsic skyrmion damping. Moreover, the current-induced force acting on a skyrmion is determined based on the bias it inflicts on the thermal diffusion and the resulting effective energy landscape. Thereby, this method reveals even the effects of ultra-low current densities and allows us to ascertain the linear relation between the applied current density and the acting force. Furthermore, a strong dependence of pinning effects on the skyrmion size is revealed and explained by going beyond the quasi-particle picture. We exploit this size-dependence to develop a diffusion enhancement mechanism based on periodically changing the skyrmion size via an oscillating magnetic field. This deterministic excitation is shown to drastically increase the skyrmions' random motion even at a constant temperature, which can be particularly valuable for Brownian computing devices.
Unconventional computers within the Brownian computing paradigm leverage (thermal) randomness for the benefit of a specific computer architecture. Here, a skyrmion-based Brownian reservoir computer is developed. Our concept device exploits the complex non-linear behavior of a confined skyrmion performing thermal diffusion, which arises due to a competition of different interactions at similar scales. This design ensures fast learning at a low computational cost and mitigates the obstructive effects of pinning. In addition, access to the skyrmion’s trajectory during operation allows for the interpretation of the trained parameters and the role of thermal activity.