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

This brief reviews current research on magnetic skyrmions, with emphasis on formation mechanisms, observation techniques, and materials design strategies. The response of skyrmions, both static and dynamical, to various electromagnetic fields is also covered in detail. Recent progress in magnetic imaging techniques has enabled the observation of skyrmions in real space, as well as the analysis of their ordering manner and the details of their internal structure. In metallic systems, conduction electrons moving through the skyrmion spin texture gain a nontrivial quantum Berry phase, which provides topological force to the underlying spin texture and enables the current-induced manipulation of magnetic skyrmions. On the other hand, skyrmions in an insulator can induce electric polarization through relativistic spin-orbit interaction, paving the way for the control of skyrmions by an external electric field without loss of Joule heating. Because of its nanometric scale, particle nature, and electric controllability, skyrmions are considered as potential candidates for new information carriers in the next generation of spintronics devices.

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.

This book summarizes some of the most exciting theoretical developments in the topological phenomena of skyrmions in noncentrosymmetric magnetic systems over recent decades. After presenting pedagogical backgrounds to the Berry phase and homotopy theory, the author systematically discusses skyrmions in the order of their development, from the Ginzburg-Landau theory, CP1 theory, Landau-Lifshitz-Gilbert theory, and Monte Carlo numerical approaches. Modern topics, such as the skyrmion-electron interaction, skyrmion-magnon interaction, and various generation mechanisms of the skyrmion are examined with a focus on their general theoretical aspects. The book concludes with a chapter on the skyrmion phenomena in the cold atom context. The topics are presented at a level accessible to beginning graduate students without a substantial background in field theory. The book can also be used as a text for those who wish to engage in the physics of skyrmions in magnetic systems, or as an introduction to the various theoretical methods used in studying current condensed-matter systems.

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 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.

This book discusses theoretical and experimental advances in metamaterial structures, which are of fundamental importance to many applications in microwave and optical-wave physics and materials science. Metamaterial structures exhibit time-reversal and space-inversion symmetry breaking due to the effects of magnetism and chirality. The book addresses the characteristic properties of various symmetry breaking processes by studying field-matter interaction with use of conventional electromagnetic waves and novel types of engineered fields: twisted-photon fields, toroidal fields, and magnetoelectric fields. In a system with a combined effect of simultaneous breaking of space and time inversion symmetries, one observes the magnetochiral effect. Another similar phenomenon featuring space-time inversion symmetries is related to use of magnetoelectric materials. Cross-coupling of the electric and magnetic components in these material structures, leading to the appearance of new magnetic modes with an electric excitation channel – electromagnons and skyrmions – has resulted in a wealth of strong optical effects such as directional dichroism, magnetochiral dichroism, and rotatory power of the fields. This book contains multifaceted contributions from international leading experts and covers the essential aspects of symmetry-breaking effects, including theory, modeling and design, proven and potential applications in practical devices, fabrication, characterization and measurement. It is ideally suited as an introduction and basic reference work for researchers and graduate students entering this field.