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Topology in Magnetism pp 75–115Cite as

Magnetic Vortices

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Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 192))

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.

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Notes

  1. 1.

    The word ’vortex’ addresses the magnetization of the ’vortex core’ with its out-of-plane component at the center pointing either up or down plus the surrounding magnetization curling in the plane either clockwise or counter-clockwise. We will try to be as precise as possible to distinguish the ’vortex core’ from the ’vortex’ as well as from the magnetization of a ’vortex state’ within a microdisk or a microsquare, where the latter case even includes four domains and four domain walls. For the sake of readability we will nonetheless sometimes just write vortex to denote one of the three entities, which should then be clear from the context

  2. 2.

    Figure 3.12 and parts of the text in this subchapter are reproduced from the Dissertation Thesis of C. F. Adolff [78].

  3. 3.

    Figures 3.19, 3.20 and 3.21 and parts of the text in this subchapter are reproduced from the Dissertation Thesis of C. F. Adolff [78].

  4. 4.

    Note that only 136 polarization states are non-degenerate with respect to the frequency response (absorption) due to symmetry reasons.

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Acknowledgements

We are grateful to Ulrich Merkt for continuous support and fruitful discussions over many years. This chapter wouldn’t have been possible without the contributions from Markus Bolte, André Drews, Max Hänze, Thomas Kamionka, Peter Lendecke, Michael Martens, Matthias Pues, Falk-Ulrich Stein, and Andreas Vogel. G.M. acknowledges support and new insights provided by Andrea Cavalleri. We acknowledge financial support from the Deutsche Forschungsgemeinschaft via SFB 668 ‘Magnetism from the Single Atom to the Nanostructure’, via Graduiertenkolleg 1286 ‘Functional Metal-Semiconductor Hybrid Systems’, and via excellence cluster ‘The Hamburg Centre for Ultrafast Imaging—Structure, Dynamics and Control of Matter on the Atomic Scale’.

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Authors and Affiliations

  1. Institut für Angewandte Physik und Zentrum für Mikrostrukturforschung, Jungiusstr. 11, 20355, Hamburg, Germany

    Carolin Behncke & Christian F. Adolff

  2. Max-Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761, Hamburg, Germany

    Guido Meier

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  1. Carolin Behncke
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  2. Christian F. Adolff
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  3. Guido Meier
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Correspondence to Carolin Behncke .

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Editors and Affiliations

  1. University of New Hampshire, Durham, NH, USA

    Jiadong Zang

  2. Unité Mixte de Physique CNRS/Thales, Palaiseau, France

    Vincent Cros

  3. Materials Science Division, Argonne National Laboratory, Lemont, IL, USA

    Axel Hoffmann

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Behncke, C., Adolff, C.F., Meier, G. (2018). Magnetic Vortices. In: Zang, J., Cros, V., Hoffmann, A. (eds) Topology in Magnetism. Springer Series in Solid-State Sciences, vol 192. Springer, Cham. https://doi.org/10.1007/978-3-319-97334-0_3

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