Dynamics Of Metastable Magnetic Skyrmions

The energy cost associated with modern information technologies has been increasing exponentially over time, stimulating the search for alternative information storage and processing devices. Magnetic skyrmions are solitonic nanometer-scale quasiparticles whose unique topological properties can be thought of as that of a Mobius strip. Skyrmions are envisioned as information carriers in novel information processing and storage devices with low power consumption and high information density. As such, they could contribute to solving the energy challenge. In order to be used in applications, isolated skyrmions must be thermally stable at the scale of years. In this work, their stability is studied through two main approaches: the Kramers' method in the form of Langer's theory, and the forward flux sampling method. Good agreement is found between the two methods. We find that small skyrmions possess low internal energy barriers, but are stabilized by a large activation entropy. This is a direct consequence of the existence of stable modes of deformation of the skyrmion. Additionally, frustrated exchange that arises at some transition metal interfaces leads to new collapse paths in the form of the partial nucleation of the corresponding antiparticle, as merons and antimerons.

Magnetic skyrmions are particle-like objects described by localized solutions of non-linear partial differential equations. Up until a few decades ago, it was believed that magnetic skyrmions only existed in condensed matter as short-term excitations that would quickly collapse into linear singularities. The contrary was proven theoretically in 1989 and evidentially in 2009. It is now known that skyrmions can exist as long-living metastable configurations in low-symmetry condensed matter systems with broken mirror symmetry, increasing the potential applications possible. Magnetic Skyrmions and their Applications delves into the fundamental principles and most recent research and developments surrounding these unique magnetic particles. Despite achievements in the synthesis of systems stabilizing chiral magnetic skyrmions and the variety of experimental investigations and numerical calculations, there have not been many summaries of the fundamental physical principles governing magnetic skyrmions or integrating those concepts with methods of detection, characterization and potential applications. Magnetic Skyrmions and their Applications delivers a coherent, state-of-the-art discussion on the current knowledge and potential applications of magnetic skyrmions in magnetic materials and device applications. First the book reviews key concepts such as topology, magnetism and materials for magnetic skyrmions. Then, charactization methods, physical mechanisms, and emerging applications are discussed. Covers background knowledge and details the basic principles of magnetic skyrmions, including materials, characterization, statics and dynamics Reviews materials for skyrmion stabilization including bulk materials and interface-dominated multilayer materials Describes both well-known and unconventional applications of magnetic skyrmions, such as memristors and reservoir computing

Abstract: We review the recent progress on the magnetic skyrmions in chiral magnetic materials. The magnetic skyrmion is a topological spin configuration with localized spatial extent, which could be thought of as an emergent rigid particle, owing to its particular topological and chiral properties. Static skyrmionic configurations have been found in various materials with different transport and thermodynamic properties. The magnetic skyrmions respond to externally applied fields in a very unique way, and their coupling to other quasiparticles in solid-state systems gives rise to the emergent electrodynamics. Being not only theoretically important, the magnetic skyrmion is also very promising to be the information carrier in next generation spintronic devices.

Magnetic skyrmionics is an advanced and active research field, which involves fundamental physics, the creation of efficient next-generation high-density information devices, the formation and manipulation of nanometer-size skyrmions in devices, and the development of compatible materials at room temperature. The magnetic skyrmions found in magnetic materials exhibit spiral magnetism. This book presents a basic overview of magnetic skyrmions along with current research on magnetic skyrmions, emphasizing formation mechanisms and materials design strategies. This book is suitable for an interdisciplinary audience of undergraduates, graduates, engineers, scientists, and researchers in the development of the next generation of spintronic devices.

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.

Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several field theories.