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.

1 Magnetism and topology Andre' Thiaville, Jacques Miltat, and Stanislas Rohart 2 Materials for skyrmionics Kai Litzius and Mathias Klaui 3 Characterizing magnetic skyrmions at their fundamental length and time scales Peter Fischer and Sujoy Roy 4 Mapping the magnetic field of skyrmions and spin spirals by scanning probe microscopy Hans J. Hug 5 Scanning probe microscopy methods for imaging skyrmions and spin spirals with atomic resolution Hans J. Hug 6 Static properties of magnetic skyrmions  Roberto Zivieri and Oksana Chubykalo-Fesenko 7 Dynamics of magnetic skyrmions Riccardo Tomasello, Luis Sa¿nchez-Tejerina, and Mario Carpentieri 8 Electrical nucleation and detection of magnetic skyrmions  Felix Buttner and William Legrand 9 Topological Hall effect  Igor Rozhansky and Konstantin Denisov 10 Skyrmions in ferrimagnets Xichao Zhang, Yan Zhou, and Seonghoon Woo 11 Skyrmions in antiferromagnets Oleg A. Tretiakov 12 Multiple skyrmionic states and oblique spirals in bulk cubic helimagnets Andrey O. Leonov and Catherine Pappas 13 Conventional applications of skyrmions Xichao Zhang, Jing Xia, Laichuan Shen, Motohiko Ezawa, Xiaoxi Liu, and Yan Zhou 14 Unconventional applications of skyrmions Wang Kang, Sai Li, Xing Chen, Daoqian Zhu, Xueying Zhang, Na Lei, and Weisheng Zhao 15 Introduction to topology Gabriele Bonanno and Giuseppina D'Agui`