Scott Wilson Sides

METASTABLE LIFETIMES IN A KINETIC ISING MODEL : DEPENDENCE ON FIELD AND SYSTEM SIZE

The lifetimes of metastable states in kinetic Ising ferromagnets are studied by droplet theory and Monte Carlo simulation, in order to determine their dependences on applied field and system size. For a wide range of fields, the dominant field dependence is universal for local dynamics and has the form of an exponential in the inverse field, modified by universal and nonuniversal multiplicative power-law prefactors. Quantitative droplet-theory predictions for these dependences are numerically verified, and small deviations from the predictions are shown to depend nonuniversally on the details of the dynamics. We identify four distinct field intervals in which the field dependence and statistical properties of the lifetimes are markedly different. The field marking the crossover between the weak-field regime, in which the decay is dominated by a single droplet, and the intermediate-field regime, in which it is dominated by a finite density of droplets, vanishes logarithmically with system size. As a consequence, the slow decay characteristic of the former regime may be observable in systems that are macroscopic as far as their equilibrium properties are concerned.

Kinetic Ising Model in an Oscillating Field: Finite-Size Scaling at the Dynamic Phase Transition

We study hysteresis for a two-dimensional spin-1/2 nearest-neighbor kinetic Ising ferromagnet in an oscillating field using Monte Carlo simulations. The period-averaged magnetization is the order parameter for a proposed dynamic phase transition (DPT). To quantify the nature of this transition, we present the first finite-size scaling study of the DPT for this model. Evidence of a diverging correlation length is given, and we provide estimates of the transition frequency and the critical indices {beta} , {gamma} , and {nu} . {copyright} {ital 1998} {ital The American Physical Society}

Magnetization switching in nanoscale ferromagnetic grains: description by a kinetic Ising model

The magnetic relaxation of ferromagnetic powders has been studied for many years, largely due to its importance to recording technologies. However, only recently have experiments been performed that resolve the magnetic state of individual sub-micron particles. Motivated by these experimental developments, we use droplet theory and Monte Carlo simulations to study the time and field dependence of some quantities that can be observed by magnetic force microscopy. Particular emphasis is placed on the effects of finite particle size. The qualitative agreement between experiments on switching and our simulations in individual single-domain ferromagnets suggests that the switching mechanism in such particles may involve local nucleation and subsequent growth of droplets of the stable phase.

Response of a kinetic Ising system to oscillating external fields: Amplitude and frequency dependence

The S=1/2, nearest‐neighbor, kinetic Ising model has been used to modelmagnetization switching in nanoscale ferromagnets. For this model, earlier work based on the droplet theory of the decay of metastable phases and Monte Carlo simulations has shown the existence of a size dependent spinodal field which separates deterministic and stochastic decay regimes. We extend the above work to study the effects of an oscillating field on the magnetization response of the kinetic Ising model. We compute the power spectral density of the time‐dependent magnetization for different values of the amplitude and frequency of the external field, using Monte Carlo simulation data. We also investigate the amplitude and frequency dependence of the probability distributions for the hysteresis loop area and the period‐averaged magnetization. The time‐dependent response of the system is classified by analyzing the behavior of these quantities within the framework of the distinct deterministic and stochastic decay modes mentioned above.

KINETIC ISING SYSTEM IN AN OSCILLATING EXTERNAL FIELD : STOCHASTIC RESONANCE AND RESIDENCE-TIME DISTRIBUTIONS

Experimental, analytical, and numerical results suggest that the mechanism by which a uniaxial single-domain ferromagnet switches after sudden field reversal depends on the field magnitude and the system size. Here we report new results on how these distinct decay mechanisms influence hysteresis in a two-dimensional nearest-neighbor kinetic Ising model. We present theoretical predictions supported by numerical simulations for the frequency dependence of the probability distributions for the hysteresis-loop area and the period-averaged magnetization, and for the residence-time distributions. The latter suggest evidence of stochastic resonance for small systems in moderately weak oscillating fields.

KINETIC ISING SYSTEMS AS MODELS OF MAGNETIZATION SWITCHING IN SUBMICRON FERROMAGNETS

Experimental techniques, such as magnetic force microscopy (MFM), have recently enabled the magnetic state of individual submicron particles to be resolved. Motivated by these experimental developments, we use Monte Carlo simulations of two‐dimensional kinetic Ising ferromagnets to study the magnetic relaxation in a negative applied field of a grain with an initial magnetization m0=+1. The magnetostatic dipole–dipole interactions are treated to lowest order by adding to the Hamiltonian a term proportional to the square of the magnetization. We use droplet theory to predict the functional forms for some quantities, which can be observed by MFM. One such quantity is the probability that the magnetization is positive, which is a function of time, field, grain size, and grain dimensionality. The relaxation is characterized by the number of droplets larger than a field‐dependent critical size, which form during the switching process. Our simulations of the kinetic Ising model are in excellent agreement with dr...

Hysteresis loop areas in kinetic Ising models: Effects of the switching mechanism

Experiments on ferromagnetic thin films have measured the dependence of the hysteresis loop area on the amplitude and frequency of the external field, A=A(H0,ω), and approximate agreement with numerical simulations of Ising models has been reported. Here we present numerical and theoretical calculations of A in the low-frequency regime for two values of H0, which bracket a temperature and system-size dependent crossover field. Our previous Monte Carlo studies have shown that the hysteretic response of the kinetic Ising model is qualitatively different for amplitudes above and below this crossover field. Using droplet theory, we derive analytic expressions for the low-frequency asymptotic behavior of the hysteresis loop area. In both field regimes, the loop area exhibits an extremely slow approach to an asymptotic, logarithmic frequency dependence of the form A∝−[ln(H0ω)]−1. Our results are relevant to the interpretation of data from experiments and simulations, on the basis of which power-law exponents fo...