J.D. Hannay

Computational approaches to thermally activated fast relaxation

The formalism allowing the simulation of thermally activated magnetisation reversal based on the Langevin equation is described. Intrinsically, thermal effects are introduced by the inclusion of a random field in the deterministic (Landau-Lifshitz) equation, whose statistical properties are determined by the fluctuation-dissipation theorem. Using this approach for a single spin, breakdown of the exponential relaxation law for short timescales is demonstrated. Application of the Langevin equation approach to a chain of interacting spins leads to a magnetic response in the form of correlated magnetisation fluctuations (spin waves). An alternative formalism is finally given which takes explicit account of the magnetisation fluctuations. This leads naturally to the prediction of spin wave spectra.

High speed switching in magnetic recording media

The theoretical formalism behind the introduction of thermal activation into the micromagnetic approach is reviewed. The theory is introduced via an application to a single spin which shows a rapid increase of coercivity at short timescales of the order of nanoseconds. Interaction effects are shown to increase relaxation times. A model of thermally activated spin-waves is presented.

SIMULATIONS OF FAST SWITCHING IN EXCHANGE COUPLED LONGITUDINAL THIN-FILM MEDIA

We have developed a Langevin dynamic simulation of high speed switching in longitudinal thin-film media. The model assumes a randomly placed set of grains with a particle size distribution which interact via magnetostatic and exchange fields. The dynamic properties of the material are simulated using the Langevin dynamic formalism which is essentially the Landau–Lifshitz–Gilbert equation of motion augmented by a random field whose properties are determined by the fluctuation–dissipation theorem. We have simulated pulsed-field magnetization and remanence curves which are obtained by applying a field pulse to a system in the remanent magnetization state. Calculations of the time dependence of the magnetization, and the time dependence of the coercivity have been made. The high frequency dynamic behavior of the systems is found to be strongly dependent on the value of the exchange coupling between the grains.

Thermal field fluctuations in a magnetic tip / implications for magnetic resonance force microscopy

Thermally excited magnetic fluctuations are fundamental to the behavior of small ferromagnetic particles and have practical consequences for the proposed detection of individual spins by magnetic resonance force microscopy (MRFM). In particular, fluctuating fields from a nearby magnetic tip can increase the relaxation rate of spins in a sample if there is significant spectral density of field fluctuation at the Larmor frequency of the target spin. As an initial step toward understanding this issue, magnetic field fluctuations have been simulated which emanate from a magnetic tip with dimensions 60 nm×60 nm×2 μm. It was found that the fluctuations in a cobalt magnetic tip were too strong for MRFM experiments aimed at detecting individual electron spins. However, the results obtained for a PrFeB tip fell within the tolerance required.

Simulation of magnetic relaxation by a Monte Carlo technique with correlations and quantified time steps

A new integrated numerical approach for simulation of fast and slow relaxation in magnets has been developed. It is based on Monte Carlo calculations which additionally take into account important dynamic information provided by the Langevin dynamics method. Real time quantification of Monte Carlo steps has been achieved by the new technique for a simple one-dimensional modelled system of interacting spins.

Recent studies in thermal activation and spin waves

Abstract Some recent results in computational approaches to thermally activated fast reversal in magnetic recording media are reviewed. In particular, recent results reported in the simulation of pulsed-field-induced magnetisation reversal and thermal activation of spin waves are described. The short time scale breakdown of the Arrhenius–Neel law for a single moment is demonstrated and explained in terms of the dynamics of the precessional motion. The variation in response as a function of the damping parameter is found to be an important factor determining the remanent magnetisation for a given pulse width. The effects of interactions between moments are described, including the apparent increase in effective damping. It is shown that interactions between moments can be described in terms of thermally excited spin waves. The spectrum of relaxation times for systems consisting of coupled moments is explained in terms of the thermal excitation of spin waves.

A computational model of thermally activated high speed magnetisation reversal in longitudinal thin film media

Abstract A computational model of thermally activated magnetisation reversal in longitudinal thin film recording media is described. We introduce thermal effects into the simulation by adding a random field term to the local field of each spin, thus converting the deterministic Landau–Lifshitz–Gilbert equation of motion into the stochastic Langevin equation of the problem. The model includes anisotropic crystalline, magnetostatic (dipole), and exchange interactions. Methods of perturbing and expanding a system of grains which initially form a regular lattice has given a physically realistic system of grains which lie on an isotropic physical structure having a log-normal grain size distribution and also a random distribution of in plane easy axes.

Thermally activated magnetisation reversal

A model of thermally activated magnetisation reversal is presented. The approach is based on the numerical solution of the Langevin equation of the problem. It is shown that the random thermal perturbations give rise to correlated magnetisation fluctuations (spin waves) in coupled systems. Simulations of longitudinal thin films are presented which show an effective non-local damping arising from spin waves.