Direct calculation of the attempt frequency of magnetic structures using the finite element method

A numerical implementation of the transition state theory is presented which can be used to calculate the attempt frequency f0 of arbitrary shaped magnetic nanostructures. The micromagnetic equations are discretized using the finite element method. The climbing image nudged elastic band method is used to calculate the saddle point configuration, which is required for the calculation of f0. Excellent agreement of the implemented numerical model and analytical solutions is obtained for single domain particles. The developed method is applied to compare f0 for single phase and graded media grains of advanced recording media. f0 is predicted to be comparable if the maximum anisotropy is the same in these two media types.

[1]  J. Langer,et al.  Hydrodynamic Model of the Condensation of a Vapor near Its Critical Point , 1973 .

[2]  D. A. Smith,et al.  A classical theory of superparamagnetic relaxation , 1976 .

[3]  H. Thomas,et al.  Integrable and nonintegrable classical spin clusters , 1988 .

[4]  P. Loxley,et al.  Theory for nucleation at an interface and magnetization reversal of a two-layer nanowire , 2006 .

[5]  Statistical mechanics of nonuniform magnetization reversal. , 1994, Physical review. B, Condensed matter.

[6]  D. Suess.  Multilayer exchange spring media for magnetic recording , 2006 .

[7]  P. Visscher,et al.  Thermal stability of graded exchange spring media under the influence of external fields , 2008 .

[8]  W. Coffey,et al.  EFFECT OF AN OBLIQUE MAGNETIC FIELD ON THE SUPERPARAMAGNETIC RELAXATION TIME. II. INFLUENCE OF THE GYROMAGNETIC TERM , 1998 .

[9]  William T. Coffey,et al.  Crossover formulas in the kramers theory of thermally activated escape rates—application to spin systems , 2007 .

[10]  C. Gardiner.  Handbook of Stochastic Methods , 1983 .

[11]  D. J. McCarthy,et al.  Interpolation formula between very low and intermediate-to-high damping Kramers escape rates for single-domain ferromagnetic particles. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  G. Henkelman,et al.  A climbing image nudged elastic band method for finding saddle points and minimum energy paths , 2000 .

[13]  R. Stamps,et al.  Spin wave valve in an exchange spring bilayer , 2006 .

[14]  W. Coffey,et al.  Thermally Activated Relaxation Time of a Single Domain Ferromagnetic Particle Subjected to a Uniform Field at an Oblique Angle to the Easy Axis: Comparison with Experimental Observations , 1998 .

[15]  W. Brown.  Thermal Fluctuations of a Single‐Domain Particle , 1963 .

[16]  Thomas Schrefl,et al.  Validation of the transition state theory with Langevin-dynamics simulations , 2010 .

[17]  T. Schrefl,et al.  Reliability of Sharrocks equation for exchange spring bilayers , 2007 .

[18]  H. Kramers.  Brownian motion in a field of force and the diffusion model of chemical reactions , 1940 .

[19]  J. W. Brown.  Thermal fluctuation of fine ferromagnetic particles , 1979 .

[20]  Nonlinear response of superparamagnets with finite damping: An analytical approach , 2004, cond-mat/0404445.

[21]  Werner Scholz,et al.  Time resolved micromagnetics using a preconditioned time integration method , 2002 .

[22]  Werner Scholz,et al.  A path method for finding energy barriers and minimum energy paths in complex micromagnetic systems , 2002 .