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M. A. Novotny

Publications and source records attributed to M. A. Novotny.

At least 91 records · Page 5Linked to original sources
arXiv1999

Application of the Projected Dynamics Method to an Anisotropic Heisenberg Model

The Projected Dynamics method was originally developed to study metastable decay in ferromagnetic discrete spin models. Here, we apply it to a classical, continuous Heisenberg model with anisotropic ferromagnetic interactions, which evolves under a Monte Carlo dynamic. The anisotropy is sufficiently large to allow comparison with the Ising model. We describe the Projected Dynamics method and how to apply it to this continuous-spin system. We also discuss how to extract metastable lifetimes and how to extrapolate from small systems to larger systems.

cond-mat.stat-mech↗
arXiv1999

Dynamic Phase Transition and Hysteresis in Kinetic Ising Models

We briefly introduce hysteresis in spatially extended systems and the dynamic phase transition observed as the frequency of the oscillating field increases beyond a critical value. Hysteresis and the decay of metastable phases are closely related phenomena, and a dynamic phase transition can occur only for field amplitudes, temperatures, and system sizes at which the metastable phase decays through nucleation and growth of many droplets. We present preliminary results from extensive Monte Carlo simulations of a two-dimensional kinetic Ising model in a square-wave oscillating field and estimate critical exponents by finite-size scaling techniques adapted from equilibrium critical phenomena. The estimates are consistent with the universality class of the two-dimensional equilibrium Ising model and inconsistent with two-dimensional random percolation. However, we are not aware of any theoretical arguments indicating why this should be so. Thus, the question of the universality class of this nonequilibrium critical phenomenon remains open.

cond-mat.stat-mech↗
arXiv1998

Parallelization of a Dynamic Monte Carlo Algorithm: a Partially Rejection-Free Conservative Approach

We experiment with a massively parallel implementation of an algorithm for simulating the dynamics of metastable decay in kinetic Ising models. The parallel scheme is directly applicable to a wide range of stochastic cellular automata where the discrete events (updates) are Poisson arrivals. For high performance, we utilize a continuous-time, asynchronous parallel version of the n-fold way rejection-free algorithm. Each processing element carries an lxl block of spins, and we employ the fast SHMEM-library routines on the Cray T3E distributed-memory parallel architecture. Different processing elements have different local simulated times. To ensure causality, the algorithm handles the asynchrony in a conservative fashion. Despite relatively low utilization and an intricate relationship between the average time increment and the size of the spin blocks, we find that for sufficiently large l the algorithm outperforms its corresponding parallel Metropolis (non-rejection-free) counterpart. As an example application, we present results for metastable decay in a model ferromagnetic or ferroelectric film, observed with a probe of area smaller than the total system.

cond-mat.stat-mech↗
arXiv1998

Kinetic Ising model in an oscillating field: Avrami theory for the hysteretic response and finite-size scaling for the dynamic phase transition

Hysteresis is studied for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on large systems and strong field amplitudes at a temperature below T_c. In this parameter regime, the magnetization switches through random nucleation and subsequent growth of many droplets of spins aligned with the applied field. Using a time-dependent extension of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of metastable decay, we analyze the statistical properties of the hysteresis-loop area and the correlation between the magnetization and the applied field. This analysis enables us to accurately predict the results of extensive Monte Carlo simulations. The average loop area exhibits an extremely slow approach to an asymptotic, logarithmic dependence on the product of the amplitude and the frequency of the applied field. This may explain the inconsistent exponent estimates reported in previous attempts to fit experimental and numerical data for the low-frequency behavior of this quantity to a power law. At higher frequencies we observe a dynamic phase transition. Applying standard finite-size scaling techniques from the theory of second-order equilibrium phase transitions to this nonequilibrium phase transition, we obtain estimates for the transition frequency and the critical exponents (beta/nu \approx 0.11, gamma/nu \approx 1.84 and nu \approx 1.1). In addition to their significance for the interpretation of recent experiments on switching in ferromagnetic and ferroelectric nanoparticles and thin films, our results provide evidence for the relevance of universality and finite-size scaling to dynamic phase transitions in spatially extended nonstationary systems.

cond-mat.stat-mech↗
arXiv1998

Simulation of Magnetization Switching in Biaxial Single-Domain Ferromagnetic Particles

The magnetization switching dynamics of biaxial single-domain homogeneous ferromagnetic particles, in which the two easy axes are perpendicular to each other, is simulated using a 4-state clock model. A zero-field mapping of the statics between the symmetric 4-state clock model and two decoupled Ising models is extended to non-zero field statics and to the dynamics. This significantly simplifies the analysis of the simulation results. We measure the magnetization switching time of the model and analyze the results using droplet theory. The switching dynamics in the asymmetric model is more complicated. If the easy axis is perpendicular to the stable magnetization direction, the system can switch its magnetization via two different channels, one very fast and the other very slow. A maximum value for the switching field as a function of system size is obtained. The asymmetry affects the switching fields differently, depending on whether the switching involves one single droplet or many droplets of spins in the stable magnetization configuration. The angular dependence of the switching field in symmetric and asymmetric models is also studied.

cond-mat.mtrl-sci↗
arXiv1998

Test of the Kolmogorov-Johnson-Mehl-Avrami picture of metastable decay in a model with microscopic dynamics

The Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory for the time evolution of the order parameter in systems undergoing first-order phase transformations has been extended by Sekimoto to the level of two-point correlation functions. Here, this extended KJMA theory is applied to a kinetic Ising lattice-gas model, in which the elementary kinetic processes act on microscopic length and time scales. The theoretical framework is used to analyze data from extensive Monte Carlo simulations. The theory is inherently a mesoscopic continuum picture, and in principle it requires a large separation between the microscopic scales and the mesoscopic scales characteristic of the evolving two-phase structure. Nevertheless, we find excellent quantitative agreement with the simulations in a large parameter regime, extending remarkably far towards strong fields (large supersaturations) and correspondingly small nucleation barriers. The original KJMA theory permits direct measurement of the order parameter in the metastable phase, and using the extension to correlation functions one can also perform separate measurements of the nucleation rate and the average velocity of the convoluted interface between the metastable and stable phase regions. The values obtained for all three quantities are verified by other theoretical and computational methods. As these quantities are often difficult to measure directly during a process of phase transformation, data analysis using the extended KJMA theory may provide a useful experimental alternative.

cond-mat.mtrl-sci↗
arXiv1998

Slow Forcing in the Projective Dynamics Method

We provide a proof that when there is no forcing the recently introduced projective dynamics Monte Carlo algorithm gives the exact lifetime of the metastable state, within statistical uncertainties. We also show numerical evidence illustrating that for slow forcing the approach to the zero-forcing limit is rather rapid. The model studied numerically is the 3-dimensional 3-state Potts ferromagnet.

cond-mat.mtrl-sci↗
arXiv1998

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 $β$, $γ$ and $ν$.

cond-mat.stat-mech↗
arXiv1998

Magnetic Particles

We present an overview of the subject of Magnetic Particles, starting at a level suitable for advanced high-school students and ending at a level suitable for current practitioners in the field. The sub-topics covered include: Types of Magnetic Materials, Relationships Between the Vector Fields, Magnetic Energies, Dynamics of Magnetic Particles, and Magnetocaloric Effects.

cond-mat.mtrl-sci↗
arXiv1998

Computer Simulations of Thermal Switching in Small-grain Ferromagnets

We present Monte Carlo and Langevin micromagnetic calculations to investigate thermal switching of single-domain ferromagnetic particles. For the Monte Carlo study we place particular emphasis on the probability that the magnetization does not switch by time t. We find that this quantity has different behaviors in different regimes of applied field, temperature, and system size, and we explain this in terms of different reversal mechanisms that dominate in the different regimes. In the micromagnetic study of an array of Ni pillars, we show that the reversal mode is an outside-in mode starting at the perimeter of the array of pillars.

cond-mat.mtrl-sci↗
arXiv1998

Compensation Temperature of a Mixed Ising Ferrimagnetic Model in the Presence of External Magnetic Fields

The behavior of the compensation temperature of a mixed Ising ferrimagnetic system on a square lattice in which the two interpenetrating square sublattices have spins $σ$ ($\pm 1/2$) and spins $S$ ($\pm 1,0$) has been studied with Monte Carlo methods. Our model includes nearest and next-nearest neighbor interactions, a crystal field and an external magnetic field. This model is relevant for understanding bimetallic molecular ferrimagnetic materials. We found that there is a narrow range of parameters of the Hamiltonian for which the model has compensation temperatures and that the compensation point exists only for small values of the external field.

cond-mat.mtrl-sci↗
arXiv1998

Simulated Dynamics of Underpotential Deposition of Cu with Sulfate on Au(111)

Numerical studies of lattice-gas models are well suited to describe multi-adsorbate systems. One example is the underpotential deposition of Cu on Au(111) in the presence of sulfuric acid. Preliminary results from dynamic Monte Carlo simulations of the evolution of the adsorbed layer during potential-step experiments across phase transitions are presented for this particular system. The simulated current profiles reproduce a strong asymmetry seen in recent experiments. Examination of the microscopic structures that occur during the simulated evolution processes raises questions that need to be investigated by further experimental and theoretical study.

cond-mat.stat-mech↗
arXiv1998

A projection method for statics and dynamics of lattice spin systems

A method based on Monte Carlo sampling of the probability flows projected onto the subspace of one or more slow variables is proposed for investigation of dynamic and static properties of lattice spin systems. We illustrate the method by applying it, with projection onto the order-parameter subspace, to the three-dimensional 3-state Potts model in equilibrium and to metastable decay in a three-dimensional 3-state kinetic Potts model.

cond-mat↗
arXiv1998

Hard Simulation Problems in the Modeling of Magnetic Materials: Parallelization and Langevin Micromagnetics

We present recent results on two attempts at understanding and utilizing large-scale simulations of magnetic materials. In the first study we consider massively parallel implementations on a Cray T3E of the n-fold way algorithm for magnetization switching in kinetic Ising models. We find an intricate relationship between the average time increment and the size of the spin blocks on each processor. This narrows the regime of efficient implementation. The second study concerns incorporating noise into micromagnetic calculations using Langevin methods. This allows measurement of quantities such as the probability that the system has not switched within a given time. Preliminary results are reported for arrays of single-domain nanoscale pillars.

cond-mat.mtrl-sci↗
arXiv1998

Stochastic Hysteresis and Resonance in a Kinetic Ising System

We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small systems and weak field amplitudes at a temperature below $T_{c}$. For these restricted parameters, the magnetization switches through random nucleation of a single droplet of spins aligned with the applied field. We analyze the stochastic hysteresis observed in this parameter regime, using time-dependent nucleation theory and the theory of variable-rate Markov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustable parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of larger spatially extended systems. We consider the frequency dependence of the probability density for the hysteresis-loop area and show that its average slowly crosses over to a logarithmic decay with frequency and amplitude for asymptotically low frequencies. Both the average loop area and the residence-time distributions for the magnetization show evidence of stochastic resonance. We also demonstrate a connection between the residence-time distributions and the power spectral densities of the magnetization time series. In addition to their significance for the interpretation of recent experiments in condensed-matter physics, including studies of switching in ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results are relevant to the general theory of periodically driven arrays of coupled, bistable systems with stochastic noise.

cond-mat.mtrl-sci↗
arXiv1998

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, $A$=$A(H_{0},ω)$, 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 $H_{0}$, 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 $A \propto - [\ln (H_{0} ω)]^{-1}$. Our results are relevant to the interpretation of data from experiments and simulations, on the basis of which power-law exponents for the hysteresis-loop area have been reported.

cond-mat.mtrl-sci↗
arXiv1998

Monte Carlo simulation of magnetization reversal via domain-wall motion in Fe sesquilayers on W(110)

Iron sesquilayers are ultrathin films with coverages between one and two atomic monolayers. They consist of an almost defect-free monolayer with compact islands of a second atomic layer on top. This variation of the film thickness results in a strong interaction between domain walls and the island structure. It makes these systems an ideal laboratory to study the dynamics of domain walls driven by weak external fields. We present computer simulations which provide insight into the role of the thermally activated nucleation processes by which a driven domain wall overcomes the obstacles created by the islands.

cond-mat↗