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Atomistic Spin DynamicsFoundations and Applications$
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Olle Eriksson, Anders Bergman, Lars Bergqvist, and Johan Hellsvik

Print publication date: 2017

Print ISBN-13: 9780198788669

Published to Oxford Scholarship Online: May 2017

DOI: 10.1093/oso/9780198788669.001.0001

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Spin Dynamics at Finite Temperature

Spin Dynamics at Finite Temperature

Chapter:
(p.73) 5 Spin Dynamics at Finite Temperature
Source:
Atomistic Spin Dynamics
Author(s):

Olle Eriksson

Anders Bergman

Lars Bergqvist

Johan Hellsvik

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198788669.003.0005

In Chapter 4 we presented a microscopic mechanism behind the LL equation and its connection to ab-initio results, such as that provided by density functional theory. All the analysis of Chapter 4 was done by considering a temperature T=0 K. Since most magnetic phenomena of interest are observed at finite temperature, it is important to generalize the analysis presented above to incorporate effects of finite temperature. In the discussion of Eqn. 4.1 it was mentioned briefly that finite temperature effects are incorporated in the stochastic field. Details of the coupling between temperature and the stochastic field, is the main topic of this chapter.

Keywords:   Langevin dynamics, three-temperature model, stochastic differential equation, Fokker-Planck equation, canonical ensemble, conservation law

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