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