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Handbook of Materials Modeling pp 1–28Cite as

Landau-Lifshitz-Bloch Approach for Magnetization Dynamics Close to Phase Transition

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Abstract

Micromagnetic modeling has recommended itself as a useful tool for the design of magnetic nanostructures in multiple applications. The standard micromagnetics based on the integration of the Landau-Lifshitz-Gilbert equation is a valid approach at low temperatures only. In multiple recent applications such as heat-assisted magnetic recording or ultrafast magnetic dynamics, the temperatures often go close to the Curie temperature Tc and above. Here we review the micromagnetic approach valid in this temperature range, based on the use of the Landau-Lifshitz-Bloch equation. The essential part of this approach is the presence of the temperature-dependent longitudinal relaxation with the characteristic time diverging at Tc. We review this approach in its classical and quantum formulations and for one- and two-component materials. The behavior of longitudinal relaxation time is discussed. Finally, we present examples of the use of this micromagnetics related to the modeling of ultrafast magnetization dynamics.

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Acknowledgements

This work was supported by the Spanish Ministry of Economy and Competitiveness under the project FIS201678591-C3-3-R. P.N. acknowledges support from EU Horizon 2020 Framework Programme for Research and Innovation under Grant Agreement No. 686056, NOVAMAG.

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Authors and Affiliations

  1. Instituto de Ciencia de Materiales de Madrid, Spanish National Research Council – CSIC, Madrid, Spain

    Oksana Chubykalo-Fesenko

  2. International Research Center in Critical Raw Materials and Advanced Industrial Technologies, Universidad de Burgos, Burgos, Spain

    Pablo Nieves

Authors
  1. Oksana Chubykalo-Fesenko
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  2. Pablo Nieves
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Corresponding author

Correspondence to Oksana Chubykalo-Fesenko .

Editor information

Editors and Affiliations

  1. Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Wanda Andreoni

  2. Department of Nuclear Science & Engineering , Massachusetts Institute of Technology , Cambridge, MA, USA

    Sidney Yip

Section Editor information

  1. Department of Physics, Trinity College, Dublin, Ireland

    Stefano Sanvito

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Chubykalo-Fesenko, O., Nieves, P. (2018). Landau-Lifshitz-Bloch Approach for Magnetization Dynamics Close to Phase Transition. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling . Springer, Cham. https://doi.org/10.1007/978-3-319-42913-7_72-1

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  • DOI: https://doi.org/10.1007/978-3-319-42913-7_72-1

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  • Print ISBN: 978-3-319-42913-7

  • Online ISBN: 978-3-319-42913-7

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