Statistical moment equations for stochastic spin dynamics in phase space: A uniaxial paramagnet subjected to a dc bias field of arbitrary orientation

Yuri P. Kalmykov, Serguey V. Titov, and William T. Coffey
Phys. Rev. B 86, 104435 – Published 28 September 2012

Abstract

Spin dynamics in a dissipative environment are treated via the evolution (master) equation for the quasiprobability density function of spin orientations in the phase space of the polar and azimuthal angles in the weak spin-bath coupling and high-temperature limits. The explicit solution is written for an arbitrary spin Hamiltonian as a finite series of spherical harmonics analogous to the (infinite) Fourier series representation of the classical case governed by the Fokker–Planck equation. Therefore, the expansion coefficients, i.e., the statistical averages of the spherical harmonics, may be determined as before from a differential-recurrence relation, yielding the stochastic spin dynamics for arbitrary spin number S. For large S the differential-recurrence relations reduce to those generated by the Fokker–Planck equation. Thus, the spin dynamics may be treated in a manner transparently linking to the classical representations, thereby providing quantum corrections to classical averages. The method is illustrated via the magnetization relaxation of a uniaxial paramagnet with a dc field H0 applied at an arbitrary angle to the easy axis, which is the quantum version of the most basic model in classical superparamagnetism.

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  • Received 17 July 2012

DOI:https://doi.org/10.1103/PhysRevB.86.104435

©2012 American Physical Society

Authors & Affiliations

Yuri P. Kalmykov1,*, Serguey V. Titov2, and William T. Coffey3

  • 1Université de Perpignan Via Domitia, Laboratoire de Mathématiques et Physique, EA 4217, F-66860, Perpignan, France
  • 2Kotel'nikov's Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Vvedenskii Square 1, Fryazino, Moscow Region, 141120, Russia
  • 3Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland

  • *Corresponding author: kalmykov@univ-perp.fr

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Issue

Vol. 86, Iss. 10 — 1 September 2012

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