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Title: Hierarchies of Landau-Lifshitz-Bloch equations for nanomagnets: A functional integral framework

Abstract

We propose a functional integral framework for the derivation of hierarchies of Landau-Lifshitz-Bloch (LLB) equations that describe the flow toward equilibrium of the first and second moments of the magnetization. The short-scale description is defined by the stochastic Landau-Lifshitz-Gilbert equation, under both Markovian or non-Markovian noise, and takes into account interaction terms that are of practical relevance. Depending on the interactions, different hierarchies on the moments are obtained in the corresponding LLB equations. Two closure Ansätze are discussed and tested by numerical methods that are adapted to the symmetries of the problem. Our formalism provides a rigorous bridge between the atomistic spin dynamics simulations at short scales and micromagnetic descriptions at larger scales.

Authors:
 [1];  [2];  [3]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. CEA DAM/Le Ripault, Monts (France)
  3. Univ. d'Orleans (France)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1477321
Alternate Identifier(s):
OSTI ID: 1475088
Report Number(s):
SAND-2018-10424J
Journal ID: ISSN 2470-0045; PLEEE8; 668215
Grant/Contract Number:  
AC04-94AL85000; NA0003525
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 98; Journal Issue: 4; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Tranchida, Julien, Thibaudeau, Pascal, and Nicolis, Stam. Hierarchies of Landau-Lifshitz-Bloch equations for nanomagnets: A functional integral framework. United States: N. p., 2018. Web. doi:10.1103/PhysRevE.98.042101.
Tranchida, Julien, Thibaudeau, Pascal, & Nicolis, Stam. Hierarchies of Landau-Lifshitz-Bloch equations for nanomagnets: A functional integral framework. United States. doi:10.1103/PhysRevE.98.042101.
Tranchida, Julien, Thibaudeau, Pascal, and Nicolis, Stam. Mon . "Hierarchies of Landau-Lifshitz-Bloch equations for nanomagnets: A functional integral framework". United States. doi:10.1103/PhysRevE.98.042101. https://www.osti.gov/servlets/purl/1477321.
@article{osti_1477321,
title = {Hierarchies of Landau-Lifshitz-Bloch equations for nanomagnets: A functional integral framework},
author = {Tranchida, Julien and Thibaudeau, Pascal and Nicolis, Stam},
abstractNote = {We propose a functional integral framework for the derivation of hierarchies of Landau-Lifshitz-Bloch (LLB) equations that describe the flow toward equilibrium of the first and second moments of the magnetization. The short-scale description is defined by the stochastic Landau-Lifshitz-Gilbert equation, under both Markovian or non-Markovian noise, and takes into account interaction terms that are of practical relevance. Depending on the interactions, different hierarchies on the moments are obtained in the corresponding LLB equations. Two closure Ansätze are discussed and tested by numerical methods that are adapted to the symmetries of the problem. Our formalism provides a rigorous bridge between the atomistic spin dynamics simulations at short scales and micromagnetic descriptions at larger scales.},
doi = {10.1103/PhysRevE.98.042101},
journal = {Physical Review E},
number = 4,
volume = 98,
place = {United States},
year = {2018},
month = {10}
}

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