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

Tranchida, Julien; Thibaudeau, Pascal; Nicolis, Stam

doi:10.1103/PhysRevE.98.042101

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:

Tranchida, Julien ^[1]; Thibaudeau, Pascal ^[2]; Nicolis, Stam ^[3]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
CEA DAM/Le Ripault, Monts (France)
Univ. d'Orleans (France)

Publication Date:: Mon Oct 01 00:00:00 EDT 2018

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.

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                    Tranchida, Julien, Thibaudeau, Pascal, & Nicolis, Stam. Hierarchies of Landau-Lifshitz-Bloch equations for nanomagnets: A functional integral framework.  United States.  https://doi.org/10.1103/PhysRevE.98.042101

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                    Tranchida, Julien, Thibaudeau, Pascal, and Nicolis, Stam. Mon .  
"Hierarchies of Landau-Lifshitz-Bloch equations for nanomagnets: A functional integral framework".  United States.  https://doi.org/10.1103/PhysRevE.98.042101.  https://www.osti.gov/servlets/purl/1477321.

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@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         = {Mon Oct 01 00:00:00 EDT 2018},

  month        = {Mon Oct 01 00:00:00 EDT 2018}

}

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Works referencing / citing this record:

Dynamic magnetostriction for antiferromagnets
journal, December 2019

Nussle, Thomas; Thibaudeau, Pascal; Nicolis, Stam
Physical Review B, Vol. 100, Issue 21
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Probing magneto-elastic phenomena through an effective spin-bath coupling model
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arXiv
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Title: Hierarchies of Landau-Lifshitz-Bloch equations for nanomagnets: A functional integral framework

Abstract

Citation Formats

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

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

Symplectic analytically integrable decomposition algorithms: classification, derivation, and application to molecular dynamics, quantum and celestial mechanics simulations journal, April 2003

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

Dynamics of Hierarchical Systems book, January 1986

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

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

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

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

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

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

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

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

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

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

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

Dynamic magnetostriction for antiferromagnets journal, December 2019

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

Probing magneto-elastic phenomena through an effective spin-bath coupling model text, January 2018

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

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

Symplectic analytically integrable decomposition algorithms: classification, derivation, and application to molecular dynamics, quantum and celestial mechanics simulations
journal, April 2003

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

Dynamics of Hierarchical Systems
book, January 1986

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

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

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

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

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

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

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

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

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

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

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

Dynamic magnetostriction for antiferromagnets
journal, December 2019

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

Probing magneto-elastic phenomena through an effective spin-bath coupling model
text, January 2018