Preface

Skyrmions are generally known as nanoscale magnetic vortices, a type of quasiparticles that are driven by ultra-low electrical current. This skyrmion is a point-like region of reversed magnetization in a uniform magnet. The magnetic skyrmions found in magnetic materials exhibit spiral magnetism. Magnetic skyrmions are anticipated to allow for the existence of discrete magnetic states, which are significantly more energetically stable than their single-domain counterparts. Magnetic skyrmions have important applications in microwave communication, logic computing technology, and memory and logic devices in terms of storing information. Magnetic skyrmions within a film or nanotrack can be manipulated using spin currents or spin waves that can have more applications in data storage and spintronic devices and show outstanding magnetic and transport properties. Magnetic skyrmionics is an advanced and active research field that reveals fundamental physics, encourages the development of next-generation high-density efficient information devices, creates and manipulates nanometer-size skyrmions in devices, and develops compatible materials at room temperature by all-electrical means. There are still several challenges such as the interaction of skyrmions with other magnetic textures, the particle-wave duality of skyrmions, skyrmion lattice phase transitions, and the use of skyrmion lattices as magnonic crystals that are needed to address for designing fully functional and competitive skyrmion devices. This book addresses scientific advances and reveals an interesting fact that skyrmions can create and access magnetic skyrmions under ambient room-temperature conditions for next-generation devices.

This book contains six chapters with some of the most exciting theoretical concepts and reviews the development of magnetic skyrmions and their application in magnetic materials. The first three chapters discuss magnetic skyrmions in solids, thin films, and multilayers. The fourth chapter focuses on the modeling of bulk and nanometric dielectric, and the final two chapters deal with specific intermetallic compounds and Heusler alloys. These chapters explain the fundamentals and present current research trends on magnetic skyrmions for technological innovation.

The topics presented here will be very helpful to students, researchers, academicians, and professionals. This book can also be used as a text for those who wish to engage in the physics of skyrmions in magnetic systems and related materials.

I would like to thank the authors who contributed their interesting and informative chapter for this book. Finally, I am pleased to thank all the members of the publishing house who have helped us with editing, revising, and reviewing this book and so much more.

> **Dipti Ranjan Sahu** Department of Natural and Applied Sciences, Namibia University of Science and Technology, Windhoek, Namibia

**Chapter 1**

**Abstract**

**1. Introduction**

**1**

Applications

*and Omar Fassi-Fehri*

information encoding, are also discussed.

Magnetic Skyrmions: Theory and

Magnetic skyrmions have been subject of growing interest in recent years for their very promising applications in spintronics, quantum computation and future low power information technology devices. In this book chapter, we use the field theory method and coherent spin state ideas to investigate the properties of magnetic solitons in spacetime while focussing on 2D and 3D skyrmions. We also study the case of a rigid skyrmion dissolved in a magnetic background induced by the spin-tronics; and derive the effective rigid skyrmion equation of motion. We examine as well the interaction between electrons and skyrmions; and comment on the modified Landau-Lifshitz-Gilbert equation. Other issues, including emergent electrodynamics and hot applications for next-generation high-density efficient

**Keywords:** Geometric phases, magnetic monopoles and topology, soliton and holonomy, skyrmion dynamics and interactions, med-term future applications

During the last two decades, the magnetic skyrmions and antiskyrmions have been subject to an increasing interest in connection with the topological phase of matter [1–4], the spin-tronics [5, 6] and quantum computing [7, 8]; as well as in the search for advanced applications such as racetrack memory, microwave oscillators and logic nanodevices making skyrmionic states very promising candidates for future low power information technology devices [9–12]. Initially proposed by T. Skyrme to describe hadrons in the theory of quantum chromodynamics [13], skyrmions have however been observed in other fields of physics, including quantum Hall systems [14, 15], Bose-Einstein condensates [16] and liquid crystals [17]. In quantum Hall (QH) ferromagnets for example [18, 19], due to the exchange interaction; the electron spins spontaneously form a fully polarized ferromagnet close to the integer filling factor *ν*≃1; slightly away, other electrons organize into an intricate spin configuration because of a competitive interplay between the Coulomb and Zeeman interactions [18]. Being quasiparticles, the skyrmions of the QH system condense into a crystalline form leading to the crystallization of the

skyrmions [20–23]; thus opening an important window on promising applications. In order to overcome the lack of a prototype of a skyrmion-based spintronic devices for a possible fabrication of nanodevices of data storage and logic technologies, intense research has been carried out during the last few years [24, 25]. In this

*Lalla Btissam Drissi, El Hassan Saidi, Mosto Bousmina*

## **Chapter 1**
