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Abstract

Magnetic vortices are topological objects found in magnetic thin films and microstructures. The study of vortices has attracted much attention for their fundamental beauty and because vortices could be constituents of non-volatile storage and sensing devices as well as of radiofrequency and neuro-inspired devices. Many important experimental, theoretical, and simulational contributions have been made to understand the intricate details of the statics and dynamics of magnetic vortices. In this chapter we start from first experimental observations and proceed to the occurence of vortices, their static properties as well as their topology. The polarization of vortex cores and the circularity of their in-plane magnetization are introduced. The minimization of micromagnetic energy contributions that lead to an out-of-plane core region and an in-plane circulation of magnetization are discussed, along with geometries for confinement and their response in static external magnetic fields. We analyze stray fields in the vicinity of a vortex, their hysteresis as well as their thermal stability before we address dynamic properties. The relation between handedness and sense of gyration are described and the harmonic oscillator model for small excitations is introduced. Then modifications of the oscillator model for strong excitations including nonlinearities are mentioned. We proceed to the core switching process that includes the creation, annihilation, and fusion of vortices and their topological counterpart the antivortex. Harmonic and pulsed excitations with fields and currents are discussed as well as the interaction of coupled vortices, where a vortex can be considered as a building block, for linear chains, vortex molecules and magnonic vortex crystals. The chapter concludes with current perspectives and challenges in the field of magnetic vortices.