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Aron, C.; Barci, D.G.; Cugliandolo, L.F.; Arenas, Z.G.; Lozano, G.S. "Magnetization dynamics: Path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation" (2014) Journal of Statistical Mechanics: Theory and Experiment. 2014(9)
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Abstract:

We construct a path-integral representation of the generating functional for the dissipative dynamics of a classical magnetic moment as described by the stochastic generalization of the Landau-Lifshitz-Gilbert equation proposed by Brown (1963 Phys. Rev. 130 1677), with the possible addition of spin-torque terms. In the process of constructing this functional in the Cartesian coordinate system, we critically revisit this stochastic equation. We present it in a form that accommodates for any discretization scheme thanks to the inclusion of a drift term. The generalized equation ensures the conservation of the magnetization modulus and the approach to the Gibbs-Boltzmann equilibrium in the absence of non-potential and time-dependent forces. The drift term vanishes only if the mid-point Stratonovich prescription is used. We next reset the problem in the more natural spherical coordinate system. We show that the noise transforms non-trivially to spherical coordinates acquiring a non-vanishing mean value in this coordinate system, a fact that has been often overlooked in the literature. We next construct the generating functional formalism in this system of coordinates for any discretization prescription. The functional formalism in Cartesian or spherical coordinates should serve as a starting point to study different aspects of the out-of-equilibrium dynamics of magnets. Extensions to colored noise, micro-magnetism and disordered problems are straightforward. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

Registro:

Documento: Artículo
Título:Magnetization dynamics: Path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation
Autor:Aron, C.; Barci, D.G.; Cugliandolo, L.F.; Arenas, Z.G.; Lozano, G.S.
Filiación:Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, United States
Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, United States
Departamento de Física Teórica, Universidade Do Estado Do Rio de Janeiro, Rua São Francisco Xavier 524, Rio de Janeiro, RJ 20550-013, Brazil
Sorbonne Universités, UPMC Univ. Paris 06, UMR 7589, Paris, F-75005, France
Centro Brasileiro de Pesquisas Físicas, National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro, RJ 22290-180, Brazil
Departamento de Física, FCEYN Universidad de Buenos Aires and IFIBA CONICET, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Instituto de Cibernética, Matemática Y Física, Cuba
Palabras clave:electrical and magnetic phenomena (theory); exact results; stochastic processes (theory)
Año:2014
Volumen:2014
Número:9
DOI: http://dx.doi.org/10.1088/1742-5468/2014/09/P09008
Título revista:Journal of Statistical Mechanics: Theory and Experiment
Título revista abreviado:J. Stat. Mech. Theory Exp.
ISSN:17425468
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17425468_v2014_n9_p_Aron

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Citas:

---------- APA ----------
Aron, C., Barci, D.G., Cugliandolo, L.F., Arenas, Z.G. & Lozano, G.S. (2014) . Magnetization dynamics: Path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation. Journal of Statistical Mechanics: Theory and Experiment, 2014(9).
http://dx.doi.org/10.1088/1742-5468/2014/09/P09008
---------- CHICAGO ----------
Aron, C., Barci, D.G., Cugliandolo, L.F., Arenas, Z.G., Lozano, G.S. "Magnetization dynamics: Path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation" . Journal of Statistical Mechanics: Theory and Experiment 2014, no. 9 (2014).
http://dx.doi.org/10.1088/1742-5468/2014/09/P09008
---------- MLA ----------
Aron, C., Barci, D.G., Cugliandolo, L.F., Arenas, Z.G., Lozano, G.S. "Magnetization dynamics: Path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation" . Journal of Statistical Mechanics: Theory and Experiment, vol. 2014, no. 9, 2014.
http://dx.doi.org/10.1088/1742-5468/2014/09/P09008
---------- VANCOUVER ----------
Aron, C., Barci, D.G., Cugliandolo, L.F., Arenas, Z.G., Lozano, G.S. Magnetization dynamics: Path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation. J. Stat. Mech. Theory Exp. 2014;2014(9).
http://dx.doi.org/10.1088/1742-5468/2014/09/P09008