Monte Carlo technique with a quantified time step: Application to the motion of magnetic moments

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
American Physical Society
Google Scholar
Research Projects
Organizational Units
Journal Issue
The viability of the time quantified Metropolis Monte Carlo technique to describe the dynamics of magnetic systems is discussed. Similar to standard Brownian motion, the method is introduced basing on the comparison between the Monte Carlo trial step and the mean squared deviation of the direction of the magnetic moment. The Brownian dynamics approach to the time evolution of a magnetic moment is investigated and expressions for the mean square deviations are obtained. However, the principle difference between the standard Brownian motion and the magnetic moments dynamics is the presence of the spin precession which constitutes the reversible part of the dynamics. Although some part of the precession contributes to the diffusion coefficient, it also gives rise to athermal, energy conserving motion which cannot be taken into account by Monte Carlo methods. It is found that the stochastic motion of a magnetic moment falls into one of two possible regimes: (i) precession dominated motion, (ii) nonprecessional motion, according to the value of the damping constant and anisotropy strength and orientation. Simple expressions for the diffusion coefficient can be obtained in both cases for diffusion dominated motion, i.e., where the athermal precessional contribution can be neglected. These simple expressions are used to convert the Monte Carlo steps to real time units. The switching time for magnetic particles obtained by the Monte Carlo with time quantification is compared with the numerical integration of the Landau-Lifshitz-Gilbert equations with thermal field contribution and with some well known asymptotic formulas.
O.C. acknowledges the hospitality and support from Durham University, U.K., Duisburg University, Germany, and Seagate Research Center, Pittsburgh, where a part of this work was done. R.S.-R. thanks Durham University, U.K., for hospitality and support. M.A.W. thanks ICMM, Madrid, Spain for hospitality and support, and acknowledges the EPSRC who supported this project under Grant No.R040 318.
Unesco subjects
W. F. Brown, Phys. Rev. 130, 1677 (1963). D. T. Gillespie, J. Comput. Phys. 22, 403 (1976). Y. Kanai and S. H. Charap, IEEE Trans. Magn.27, 4972 (1991). Y. Zhang and H.N. Bertram, IEEE Trans.Magn. 34, 3786 (1998). W. F. Brown, IEEE Trans. Magn. MAG-15 (1979). A. Aharoni, Phys. Rev. 177, 793 (1969). H. B. Braun, Phys. Rev. Lett. 71, 3557 (1993). W.T.Coffey, D.S. F. Crothers, J. L. Dormann, L. J. Geoghan, and E. C. Kennedy, Phys. Rev. B 58, 3249 (1998). U.Nowak, R.W.Chantrell, and E. C. Kennedy, Phys. Rev. Lett. 84, 163 (2000). R.Smirnov-Rueda, O.Chubykalo, U.Nowak, R. W. Chantrell,and J.M.Gonzalez, J.Appl. Phys. 87, 4798 (2000). O. A. Chubykalo, J. Kaufman, B. Lengsfield, and R. Smirnov-Rueda, J.Magn. Magn. Mater. 242-245 (2002). D.Stauffer,F. W. Hehl, V. Winkelmann, and J. G. Zabolitzky, Computer Simulation and Computer Algebra (Springer-Verlag, Berlin, 1993). K. Binder and D. W. Heermann, in Monte Carlo Simulation in Statistical Physics, edited by P. Fulde( Springer-Verlag, Berlin, 1997). R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics(Springer-Verlag, Berlin, 1985). F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1967). K. Kikuchi, M.Yosida, T.Mackawa,and H.Watanabi,Chem.Phys. Lett. 185, 335 (1991). E. Meiburg, Phys. Fluids 29, 3107 (1986). J. M. Gonzalez, R. Ramirez, R. Smirnov-Rueda, and J. Gonzalez, Phys. Rev. B 52, 16 034 (1995). J. M.Gonzalez,O.A. Chubykalo,and R.Smirnov-Rueda,J.Magn. Magn. Mater. 203, 18 (1999). O. A. Chubykalo, J. M. Gonzalez, G. R. Aranda, and J. Gonzalez, J. Magn. Magn. Mater. 35, 314 (2000). R. Smirnov-Rueda, O. A. Chubykalo, J. M. Gonzalez, and J. Gonzalez, J. Appl. Phys. 83, 6509 (1998). J.L.Garcia- Palacios and F.-J Lázaro,Phys. Rev. B 58,14 937 (1998). A. Lyberatos, D. V. Berkov, and R. W. Chantrell, J. Phys.: Condens. Matter 5, 8911 (1993). F. Vesely, Computational Physics (Universitätsverlag, Wien, 1993). D. Hinzke and U. Nowak, Phys. Rev. B 61, 6734 (2000). D.Hinzke and U.Nowak,J.Magn.Magn.Mater. 221, 365(2000). R. Smirnov-Rueda, J. D. Hannay, O. Chubykalo, R. W. Chantrell, and J. M. González, IEEE Trans. Magn. 35, 3730 (1999). O. A. Chubykalo, B. Lengsfield, B. Jones, J. Kaufman, J. M. González, R. W. Chantrell, and R. Smirnov - Rueda, J. Magn. Magn. Mater. 221, 132 (2000).