skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Closing the hierarchy of moment equations in nonlinear dynamical systems
journal, October 1998


Fast spin dynamics algorithms for classical spin systems
journal, June 1998


Instabilities of the harmonic oscillator with fluctuating damping
journal, October 2011


Closure schemes in stochastic nonlinear dynamics: A validation case study
journal, May 2011


Moment closure hierarchies for kinetic theories
journal, June 1996

  • Levermore, C. David
  • Journal of Statistical Physics, Vol. 83, Issue 5-6
  • DOI: 10.1007/BF02179552

Atomistic spin model simulations of magnetic nanomaterials
journal, February 2014


A method for atomistic spin dynamics simulations: implementation and examples
journal, July 2008


Chaotic dynamics of a magnetic particle at finite temperature
journal, January 2017


Numerical integration of the stochastic Landau-Lifshitz-Gilbert equation in generic time-discretization schemes
journal, August 2014

  • Romá, Federico; Cugliandolo, Leticia F.; Lozano, Gustavo S.
  • Physical Review E, Vol. 90, Issue 2
  • DOI: 10.1103/PhysRevE.90.023203

Landau-Lifshitz-Bloch equation for exchange-coupled grains
journal, December 2014


Spin dynamics of magnetic nanoparticles: Beyond Brown’s theory
journal, November 2005


Thermoremanent Magnetization of Fine Powders
journal, January 1953


Dynamics of an ensemble of single-domain magnetic particles
journal, February 1990

  • Garanin, D. A.; Ishchenko, V. V.; Panina, L. V.
  • Theoretical and Mathematical Physics, Vol. 82, Issue 2
  • DOI: 10.1007/BF01079045

Spin-correlations and magnetic structure in an Fe monolayer on 5 d transition metal surfaces
journal, April 2014


Ab Initio Spin Dynamics in Magnets
journal, July 1995

  • Antropov, V. P.; Katsnelson, M. I.; van Schilfgaarde, M.
  • Physical Review Letters, Vol. 75, Issue 4
  • DOI: 10.1103/PhysRevLett.75.729

Classics in Magnetics A Phenomenological Theory of Damping in Ferromagnetic Materials
journal, November 2004


Role of the interpretation of stochastic calculus in systems with cross-correlated Gaussian white noises
journal, July 2014


Massively parallel symplectic algorithm for coupled magnetic spin dynamics and molecular dynamics
journal, November 2018


Thermal fluctuations of magnetic nanoparticles: Fifty years after Brown
journal, December 2012

  • Coffey, William T.; Kalmykov, Yuri P.
  • Journal of Applied Physics, Vol. 112, Issue 12
  • DOI: 10.1063/1.4754272

Generalizations of classical Poisson brackets to include spin
journal, November 1980


Mapping the magnetic exchange interactions from first principles: Anisotropy anomaly and application to Fe, Ni, and Co
journal, November 2010


Ultrafast magnetization dynamics at very high magnetic fields and elevated temperatures
journal, July 2018


Application of Landau-Lifshitz-Bloch dynamics to grain switching in heat-assisted magnetic recording
journal, July 2012

  • McDaniel, Terry W.
  • Journal of Applied Physics, Vol. 112, Issue 1
  • DOI: 10.1063/1.4733311

Ab initio calculations of exchange interactions, spin-wave stiffness constants, and Curie temperatures of Fe, Co, and Ni
journal, October 2001


Large-scale simulation of the spin-lattice dynamics in ferromagnetic iron
journal, July 2008


Mean-field approach to magnetic ordering in highly frustrated pyrochlores
journal, January 1991


Fokker-Planck and Landau-Lifshitz-Bloch equations for classical ferromagnets
journal, February 1997


A Hierarchy of Turbulence Closure Models for Planetary Boundary Layers
journal, October 1974


Thermal fluctuation of fine ferromagnetic particles
journal, September 1979


Closing the hierarchy for non-Markovian magnetization dynamics
journal, April 2016


Towards multiscale modeling of magnetic materials: Simulations of FePt
journal, May 2008


Exchange Narrowing in Paramagnetic Resonance
journal, January 1953


Thermally induced error: Density limit for magnetic data storage
journal, March 2012

  • Evans, R. F. L.; Chantrell, R. W.; Nowak, U.
  • Applied Physics Letters, Vol. 100, Issue 10
  • DOI: 10.1063/1.3691196

Magnetisation switching of FePt nanoparticle recording medium by femtosecond laser pulses
journal, June 2017


Geometrical integration of Landau–Lifshitz–Gilbert equation based on the mid-point rule
journal, November 2005

  • d’Aquino, Massimiliano; Serpico, Claudio; Miano, Giovanni
  • Journal of Computational Physics, Vol. 209, Issue 2
  • DOI: 10.1016/j.jcp.2005.04.001

Non-Markovian Magnetization Dynamics for Uniaxial Nanomagnets
journal, July 2016

  • Thibaudeau, Pascal; Tranchida, Julien; Nicolis, Stam
  • IEEE Transactions on Magnetics, Vol. 52, Issue 7
  • DOI: 10.1109/TMAG.2016.2522502

A multi-state synthetic ferrimagnet with controllable switching near room temperature
journal, May 2018


Spin dynamics in magnets: Equation of motion and finite temperature effects
journal, July 1996


Anisotropic magnetic molecular dynamics of cobalt nanowires
journal, November 2012


    Works referencing / citing this record:

    Dynamic magnetostriction for antiferromagnets
    journal, December 2019


    Probing magneto-elastic phenomena through an effective spin-bath coupling model
    journal, February 2019

    • Nussle, Thomas; Thibaudeau, Pascal; Nicolis, Stam
    • The European Physical Journal B, Vol. 92, Issue 2
    • DOI: 10.1140/epjb/e2019-90539-6