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Per Arne Rikvold

Publications and source records attributed to Per Arne Rikvold.

At least 91 records · Page 5Linked to original sources
arXiv2002

Soft versus Hard Dynamics for Field-driven Solid-on-Solid Interfaces

Analytical arguments and dynamic Monte Carlo simulations show that the microstructure of field-driven Solid-on-Solid interfaces depends strongly on the dynamics. For nonconservative dynamics with transition rates that factorize into parts dependent only on the changes in interaction energy and field energy, respectively (soft dynamics), the intrinsic interface width is field-independent. For non-factorizing rates, such as the standard Glauber and Metropolis algorithms (hard dynamics), it increases with the field. Consequences for the interface velocity and its anisotropy are discussed.

cond-mat.stat-mech↗
arXiv2001

Numerical Confirmation of Late-time t^{1/2} Growth in Three-dimensional Phase Ordering

Results for the late-time regime of phase ordering in three dimensions are reported, based on numerical integration of the time-dependent Ginzburg-Landau equation with nonconserved order parameter at zero temperature. For very large systems ($700^3$) at late times, $t \ge 150,$ the characteristic length grows as a power law, $R(t) \sim t^n$, with the measured $n$ in agreement with the theoretically expected result $n=1/2$ to within statistical errors. In this time regime $R(t)$ is found to be in excellent agreement with the analytical result of Ohta, Jasnow, and Kawasaki [Phys. Rev. Lett. {\bf 49}, 1223 (1982)]. At early times, good agreement is found between the simulations and the linearized theory with corrections due to the lattice anisotropy.

cond-mat.mtrl-sci↗
arXiv2001

Dynamics of Magnetization Reversal in Models of Magnetic Nanoparticles and Ultrathin Films

We discuss numerical and theoretical results for models of magnetization switching in nanoparticles and ultrathin films. The models and computational methods include kinetic Ising and classical Heisenberg models of highly anisotropic magnets which are simulated by dynamic Monte Carlo methods, and micromagnetics models of continuum-spin systems that are studied by finite-temperature Langevin simulations. The theoretical analysis builds on the fact that a magnetic particle or film that is magnetized in a direction antiparallel to the applied field is in a metastable state. Nucleation theory is therefore used to analyze magnetization reversal as the decay of this metastable phase to equilibrium. We present numerical results on magnetization reversal in models of nanoparticles and films, and on hysteresis in magnets driven by oscillating external fields.

cond-mat.mtrl-sci↗
arXiv2001

Langevin Simulation of Thermally Activated Magnetization Reversal in Nanoscale Pillars

Numerical solutions of the Landau-Lifshitz-Gilbert micromagnetic model incorporating thermal fluctuations and dipole-dipole interactions (calculated by the Fast Multipole Method) are presented for systems composed of nanoscale iron pillars of dimension 9 nm x 9 nm x 150 nm. Hysteresis loops generated under sinusoidally varying fields are obtained, while the coercive field is estimated to be 1979 $\pm$ 14 Oe using linear field sweeps at T=0 K. Thermal effects are essential to the relaxation of magnetization trapped in a metastable orientation, such as happens after a rapid reversal of an external magnetic field less than the coercive value. The distribution of switching times is compared to a simple analytic theory that describes reversal with nucleation at the ends of the nanomagnets. Results are also presented for arrays of nanomagnets oriented perpendicular to a flat substrate. Even at a separation of 300 nm, where the field from neighboring pillars is only $\sim$ 1 Oe, the interactions have a significant effect on the switching of the magnets.

cond-mat.mtrl-sci↗
arXiv2001

Thermal Magnetization Reversal in Arrays of Nanoparticles

The results of large-scale simulations investigating the dynamics of magnetization reversal in arrays of single-domain nanomagnets after a rapid reversal of the applied field at nonzero temperature are presented. The numerical micromagnetic approach uses the Landau-Lifshitz-Gilbert equation including contributions from thermal fluctuations and long-range dipole-dipole demagnetizing effects implemented using a fast-multipole expansion. The individual model nanomagnets are 9 nm x 9 nm x 150 nm iron pillars similar to those fabricated on a surface with STM-assisted chemical vapor deposition [S. Wirth, et al., J. Appl. Phys {\bf 85}, 5249 (1999)]. Nanomagnets oriented perpendicular to the surface and spaced 300 nm apart in linear arrays are considered. The applied field is always oriented perpendicular to the surface. When the magnitude of the applied field is less than the coercive value, about 2000 Oe for an individual nanomagnet, magnetization reversal in the nanomagnets can only occur by thermally activated processes. Even though the interaction from the dipole moment of neighboring magnets in this geometry is only about 1 Oe, less than 1% of the coercive field, it can have a large impact on the switching dynamics. What determines the height of the free-energy barrier is the difference between the coercive and applied fields, and 1 Oe can be a significant fraction of that. The magnetic orientations of the neighbors are seen to change the behavior of the nanomagnets in the array significantly.

cond-mat.mtrl-sci↗
arXiv2000

Analytic Approximations for the Velocity of Field-Driven Ising Interfaces

We present analytic approximations for the field, temperature, and orientation dependences of the interface velocity in a two-dimensional kinetic Ising model in a nonzero field. The model, which has nonconserved order parameter, is useful for ferromagnets, ferroelectrics, and other systems undergoing order-disorder phase transformations driven by a bulk free-energy difference. The Solid-on-Solid (SOS) approximation for the microscopic surface structure is used to estimate mean spin-class populations, from which the mean interface velocity can be obtained for any specific single-spin-flip dynamic. This linear-response approximation remains accurate for higher temperatures than the single-step and polynuclear growth models, while it reduces to these in the appropriate low-temperature limits. The equilibrium SOS approximation is generalized by mean-field arguments to obtain field-dependent class populations for moving interfaces, and thereby a nonlinear-response approximation for the velocity. The analytic results are compared with Monte Carlo simulations. Excellent agreement is found in a wide range of field, temperature, and interface orientation.

cond-mat.stat-mech↗
arXiv1999

Evolution of speckle during spinodal decomposition

Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary systems which obey a local conservation law, the characteristic domain size is known to grow in time $τ$ as $R = [B τ]^n$ with n=1/3, where B is a constant. The intensities of individual speckles are found to be nonstationary, persistent time series. The two-time intensity covariance at wave vector ${\bf k}$ can be collapsed onto a scaling function $Cov(δt,\bar{t})$, where $δt = k^{1/n} B |τ_2-τ_1|$ and $\bar{t} = k^{1/n} B (τ_1+τ_2)/2$. Both analytically and numerically, the covariance is found to depend on $δt$ only through $δt/\bar{t}$ in the small-$\bar{t}$ limit and $δt/\bar{t} ^{1-n}$ in the large-$\bar{t}$ limit, consistent with a simple theory of moving interfaces that applies to any universality class described by a scalar order parameter. The speckle-intensity covariance is numerically demonstrated to be equal to the square of the two-time structure factor of the scattering material, for which an analytic scaling function is obtained for large $\bar{t}.$ In addition, the two-time, two-point order-parameter correlation function is found to scale as $C(r/(B^n\sqrt{τ_1^{2n}+τ_2^{2n}}),τ_1/τ_2)$, even for quite large distances $r$. The asymptotic power-law exponent for the autocorrelation function is found to be $λ\approx 4.47$, violating an upper bound conjectured by Fisher and Huse.

cond-mat.stat-mech↗
arXiv1999

Micromagnetic simulations of thermally activated magnetization reversal of nanoscale magnets

Numerical integration of a stochastic Landau-Lifshitz-Gilbert equation is used to study dynamic processes in single-domain nanoscale magnets at nonzero temperatures. Special attention is given to including thermal fluctuations as a Langevin term, and the Fast Multipole Method is used to calculate dipole-dipole interactions. It is feasible to simulate these dynamics on the nanosecond time scale for spatial discretizations that involve on the order of 10000 nodes using a desktop workstation. The nanoscale magnets considered here are single pillars with large aspect ratio. Hysteresis-loop simulations are employed to study the stable and metastable configurations of the magnetization. Each pillar has magnetic end caps. In a time-dependent field the magnetization of the pillars is observed to reverse via nucleation, propagation, and coalescence of the end caps. In particular, the end caps propagate into the magnet and meet near the middle. A relatively long-lived defect is formed when end caps with opposite vorticity meet. Fluctuations are more important in the reversal of the magnetization for fields weaker than the zero-temperature coercive field, where the reversal is thermally activated. In this case, the process must be described by its statistical properties, such as the distribution of switching times, averaged over a large number of independent thermal histories.

cond-mat.mtrl-sci↗
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

Universality and Scaling for the Structure Factor in Dynamic Order-Disorder Transitions

The universal form for the average scattering intensity from systems undergoing order-disorder transitions is found by numerical integration of the Langevin dynamics. The result is nearly identical for simulations involving two different forms of the local contribution to the free energy, supporting the idea that the Model A dynamical universality class includes a wide range of local free-energy forms. An absolute comparison with no adjustable parameters is made to the forms predicted by the theories of Ohta-Jasnow-Kawasaki and Mazenko. The numerical results are well described by the former theory, except in the cross-over region between scattering dominated by domain geometry and scattering determined by Porod's law.

cond-mat.stat-mech↗
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

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↗
arXiv1997

Speckle from phase ordering systems

The statistical properties of coherent radiation scattered from phase-ordering materials are studied in detail using large-scale computer simulations and analytic arguments. Specifically, we consider a two-dimensional model with a nonconserved, scalar order parameter (Model A), quenched through an order-disorder transition into the two-phase regime. For such systems it is well established that the standard scaling hypothesis applies, consequently the average scattering intensity at wavevector _k and time t' is proportional to a scaling function which depends only on a rescaled time, t ~ |_k|^2 t'. We find that the simulated intensities are exponentially distributed, with the time-dependent average well approximated using a scaling function due to Ohta, Jasnow, and Kawasaki. Considering fluctuations around the average behavior, we find that the covariance of the scattering intensity for a single wavevector at two different times is proportional to a scaling function with natural variables mt = |t_1 - t_2| and pt = (t_1 + t_2)/2. In the asymptotic large-pt limit this scaling function depends only on z = mt / pt^(1/2). For small values of z, the scaling function is quadratic, corresponding to highly persistent behavior of the intensity fluctuations. We empirically establish a connection between the intensity covariance and the two-time, two-point correlation function of the order parameter. This connection allows sensitive testing, either experimental or numerical, of existing theories for two-time correlations in systems undergoing order-disorder phase transitions. Comparison between theory and our numerical results requires no adjustable parameters.

cond-mat.stat-mech↗
arXiv1997

Equilibrium and nonequilibrium applications of lattice-gas models in electrochemistry

We discuss applications of statistical-mechanical lattice-gas models to study static and dynamic aspects of electrochemical adsorption. The strategy developed to describe specific systems includes microscopic model formulation, calculation of zero-temperature phase diagrams, numerical simulation of thermodynamic and structural quantities at nonzero temperatures, and estimation of effective, lateral interactions. We briefly review earlier work, including studies by Monte Carlo simulation of the adsorption of urea on Pt(100). As an illustrative example, we discuss in some detail recent applications to the underpotential deposition of Cu with sulfate on Au(111). Experimental and numerical results are included for equilibrium coverages and voltammetric currents at slow potential sweep rates, and new results from dynamic Monte Carlo simulations are presented. In particular, we present simulated results for current transients far from equilibrium, following sudden changes in the electrode potential.

cond-mat↗
arXiv1996

Effects of boundary conditions on magnetization switching in kinetic Ising models of nanoscale ferromagnets

Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this article we consider the effects of boundary conditions on the switching phenomena. A rich range of behaviors is predicted by droplet theory: the specific mechanism by which switching occurs depends on the structure of the boundary, the particle size, the temperature, and the strength of the applied field. The theory predicts the existence of a peak in the switching field as a function of system size in both systems with periodic boundary conditions and in systems with boundaries. The size of the peak is strongly dependent on the boundary effects. It is generally reduced by open boundary conditions, and in some cases it disappears if the boundaries are too favorable towards nucleation. However, we also demonstrate conditions under which the peak remains discernible. This peak arises as a purely dynamic effect and is not related to the possible existence of multiple domains. We illustrate the predictions of droplet theory by Monte Carlo simulations of two-dimensional Ising systems with various system shapes and boundary conditions.

cond-mat↗
arXiv1996

Numerical simulations of scattering speckle from phase ordering systems

The scattering of coherent X-rays from dynamically evolving systems is currently becoming experimentally feasible. The scattered beam produces a pattern of bright and dark speckles, which fluctuate almost independently in time and can be used to study the dynamics of the system. Here we report large-scale computer simulations of the speckle dynamics for a phase ordering system, using a two-dimensional model quenched through an order--disorder transition into the two-phase regime. The intensity at each wave vector ${\bf k}$ is found to be an exponentially distributed random variable. The scaling hypothesis is extended to the two-time correlation function of the scattering intensity at a given wave vector, $Corr({\bf k};t_1,t_2)$. The characteristic decay time difference for the correlation function, $|t_1 - t_2|_c$, is found to scale as $k|t_1 + t_2|^{1/2}$.

cond-mat↗