M.A. Wongsam

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.

Numerical simulation of 2D thin films using a finite element method

Abstract A numerical method in micromagnetics is described. The 2D method is used to investigate the dependence of coercivity on grain size as well as the effects of magnetic interactions. Hysteresis behaviour of the film were studied on an array of interacting polycrystalline grains. The coercivity and remanence are found to decrease with increasing grain size. The coupling between the grains is found to influence the magnetic structure of the thin film. There is good agreement between our theoretical results and some experimental observation.

Modelling the evolution of domains in nanoelements using finite elements

Investigation into the theoretical magnetic behaviour of permalloy is described. The material is discretised into a structure of nanoelements, so that we may employ micromagnetic simulations in order to investigate the material behaviour. In this paper we describe the formation and structure of domains in an array of interacting nanoelements with varying space between them. The simulations begin at saturation and end when the nanoelements are in a zero field equilibrium state. The time evolution of the system is described by the Landau-Lifschitz equation of motion and the field calculations are carried out by the use of a finite element spatial discretisation scheme.

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.

Micromagnetics of polycrystalline two‐dimensional platelets

A numerical micromagnetic technique is used to simulate magnetization processes in two‐dimensional thin metallic platelets. The platelets are modeled as an array of interacting polycrystalline grains. The technique assumes a triangular discretization at the subgrain level with the magnetization varying linearly over each triangle. The coupling between the grains has a profound effect on the magnetic structure of the platelets as does the grain size. For systems with strongly exchange coupled grains, approximately solenoidal magnetization structures exist. A single domain behavior exists for systems with weakly coupled grains. The magnetization pattern of the platelets has been characterized by the vorticity of the magnetization vector field.

Hamiltonian descriptions of the micromagnetics of finite continuous media in the effective field formalism

The equations of motion describing the response of a ferromagnetic system in the micromagnetic approximation can be developed by applying Hamiltons principle to an action functional constructed from a Lagrangian density composed of the usual free energy expression, together with a suitably chosen expression for the kinetic energy density so as to produce the characteristic Larmour precession associated with magnetic spin systems under the influence of an external field. If a Hamiltonian density functional is introduced through the usual Legendre transformation, it can be shown that by a suitable choice of the form of the generalised momenta and the standard form of the Rayleigh dissipation energy density functional, equations of motion are derived which are formally equivalent to the Landau-Lifshitz-Gilbert form. However, the form of the equations of motion permits a substantial increase in the time step. An alternative description which avoids the introduction of a kinetic energy term, but which retains all the essential attributes of the former approach, is described. The model is applied to small rectangular polycrystalline cobalt samples with in-plane randomly oriented uniaxial anisotropy directions.

THE EQUATIONS OF MOTION OF MICROMAGNETICS IN HAMILTONIAN FORM

Abstract The equations of motion describing the response of a ferromagnetic system in the micromagnetic approximation are developed by applying Hamiltons principle to an action functional constructed from a Lagrangian density composed of the usual free energy expression, together with a suitably chosen expression for the kinetic energy density so as to produce the characteristic Larmor precession associated with magnetic spin systems under the influence of an external field. A suitable choice of the form of the generalised momenta and the standard form of the Rayleigh dissipation energy density functional, leads to equations of motion which exhibit similar behaviour to the Landau-Lifshitz-Gilbert form. It is shown that with our Hamiltonian formulation, micromagnetic simulations of systems with very many degrees of freedom can be performed with a substantial increase in the upper limit on the timestep size.

A Hamiltonian description of FMR in finite continuous media

Abstract A Hamiltonian dynamical framework is applied to the ferromagnetic resonance of finite, continuous distributions of magnetisation in media which evolve via non-uniform magnetisation processes. The theory takes into account the cooperative motion of the coupled moments of the system and is applied to regularly shaped two-dimensional platelets under the influence of in-plane bias fields and small transverse dynamic perturbations. Resonance spectra are obtained showing a significant broadening of the linewidth over that expected for systems with independent moments.

Spin wave resonances of cobalt based multilayers

A formulation of micromagnetics based on equations of motion in the Hamiltonian form is applied to the simulation of ferromagnetic resonance in Cobalt based magnetic/nonmagnetic multilayers. A two-peak feature in the field swept FMR absorption curve recently observed experimentally is reproduced. A semiclassical micromagnetic spin wave theory is presented and used to calculate the dispersion curves and amplitude spectra of the multilayers at various values of the external field. It is found that uniform precession dominates all in-plane modes, and that the features in the FMR absorption curve coincide with the sudden excitation of the first spin wave mode in the perpendicular direction.