arXiv subjects

P. A. Rikvold

Publications and source records attributed to P. A. Rikvold.

At least 55 records · Page 3Linked to original sources

arXiv2003

Effect of Defects on the Line shape of Electron Paramagnetic Resonance Signals from the Single-Molecule Magnet Mn12: A Theoretical Study

We herein estimate the effect of lattice defects on the line shape of electron paramagnetic resonance (EPR) signals from a single crystal of the S=10 single-molecule magnet Mn$_{12}$ with the external magnetic field along the crystal c axis. A second-order perturbation treatment of an effective single-spin Hamiltonian indicates that a small, random, static misorientation of the magnetic symmetry axes in a crystalline lattice can lead to asymmetric EPR peaks. Full spectra are simulated by calculating probability-distribution functions for the resonant fields, employing distributions in the tilt angle of the easy axis from the c axis, in the uniaxial anisotropy parameter, and in the $g$-factor. We discuss conditions under which the asymmetry in the EPR spectra becomes prominent. The direction and magnitude of the asymmetry provide information on the specific energy levels involved with the EPR transition, the EPR frequency, and the distribution in the tilt angle.

cond-mat↗

arXiv2003

Effects of D-strain, g-strain, and dipolar interactions on EPR linewidths of the molecular magnets Fe8 and Mn12

Electron paramagnetic resonance (EPR) measurements on single crystals of the molecular magnets Fe$_8$ and Mn$_{12}$ reveal complex nonlinearities in the linewidths as functions of energy eigenstate, frequency, and temperature. Using a density-matrix equation with distributions of the uniaxial anisotropy parameter $D$, the Landé $g$ factor, and dipolar interactions, we obtain linewidths in good agreement with experiments. Our study shows that the distribution in $D$ is common to the examined molecular magnets Fe$_8$ and Mn$_{12}$ regardless of the qualities of the samples. This could provide the basis for a proposed tunneling mechanism due to lattice defects. The distribution in $g$ is also quite significant for Mn$_{12}$.

cond-mat↗

arXiv2003

Role of dipolar and exchange interactions in the positions and widths of EPR transitions for the single-molecule magnets Fe8 and Mn12

We examine quantitatively the temperature dependence of the linewidths and line shifts in electron paramagnetic resonance experiments on single crystals of the single-molecule magnets Fe$_8$ and Mn$_{12}$, at fixed frequency, with an applied magnetic field along the easy axis. We include inter-molecular spin-spin interactions (dipolar and exchange) and distributions in both the uniaxial anisotropy parameter $D$ and the Landé $g$-factor. The temperature dependence of the linewidths and the line shifts are mainly caused by the spin-spin interactions. For Fe$_8$ and Mn$_{12}$, the temperature dependence of the calculated line shifts and linewidths agrees well with the trends of the experimental data. The linewidths for Fe$_8$ reveal a stronger temperature dependence than those for Mn$_{12}$, because for Mn$_{12}$ a much wider distribution in $D$ overshadows the temperature dependence of the spin-spin interactions. For Fe$_8$, the line-shift analysis suggests two competing interactions: a weak ferromagnetic exchange coupling between neighboring molecules and a longer-ranged dipolar interaction. This result could have implications for ordering in Fe$_8$ at low temperatures.

cond-mat↗

arXiv2003

Scaling analysis of a divergent prefactor in the metastable lifetime of a square-lattice Ising ferromagnet at low temperatures

We examine a square-lattice nearest-neighbor Ising quantum ferromagnet coupled to $d$-dimensional phonon baths. Using the density-matrix equation, we calculate the transition rates between configurations, which determines the specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo simulations, we measure the lifetimes of the metastable state. As the magnetic field approaches $|H|/J=2$ at low temperatures, the lifetime prefactor diverges because the transition rates between certain configurations approaches zero under these conditions. Near $|H|/J=2$ and zero temperature, the divergent prefactor shows scaling behavior as a function of the field, temperature, and the dimension of the phonon baths. With proper scaling, the simulation data at different temperatures and for different dimensions of the baths collapse well onto two master curves, one for $|H|/J>2$ and one for $|H|/J<2$.

cond-mat.stat-mech↗

arXiv2003

Surface scaling analysis of hydrogels: From multiaffine to self-affine scaling

We show that smoothing of multiaffine surfaces that are generated by simulating a crosslinked polymer gel by a frustrated, triangular network of springs of random equilibrium lengths [G.M. Buend{\'ı}a, S.J. Mitchell, P.A. Rikvold, Phys. Rev. E 66 (2002) 046119] changes the scaling behavior of the surfaces such that they become self-affine. The self-affine behavior is consistent with recent atomic force microscopy (AFM) studies of the surface structure of crosslinked polymer gels into which voids are introduced through templating by surfactant micelles [M. Chakrapani, S.J. Mitchell, D.H. Van Winkle, P.A. Rikvold, J. Colloid Interface Sci., in press]. The smoothing process mimics the effect of the AFM tip that tends to flatten the soft gel surfaces. Both the experimental and the simulated surfaces have a non-trivial scaling behavior on small length scales, with a crossover to scale-independent behavior on large scales.

cond-mat.stat-mech↗

arXiv2003

Suppressing Roughness of Virtual Times in Parallel Discrete-Event Simulations

In a parallel discrete-event simulation (PDES) scheme, tasks are distributed among processing elements (PEs), whose progress is controlled by a synchronization scheme. For lattice systems with short-range interactions, the progress of the conservative PDES scheme is governed by the Kardar-Parisi-Zhang equation from the theory of non-equilibrium surface growth. Although the simulated (virtual) times of the PEs progress at a nonzero rate, their standard deviation (spread) diverges with the number of PEs, hindering efficient data collection. We show that weak random interactions among the PEs can make this spread nondivergent. The PEs then progress at a nonzero, near-uniform rate without requiring global synchronizations.

cond-mat.stat-mech↗

arXiv2003

Defects, Tunneling, and EPR Spectra of Single-Molecule Magnets

We examine theoretically electron paramagnetic resonance (EPR) lineshapes as functions of resonance frequency, energy level, and temperature for single crystals of three different kinds of single-molecule nanomagnets (SMMs): Mn$_{12}$ acetate, Fe$_8$Br, and the $S=9/2$ Mn$_4$ compound. We use a density-matrix equation and consider distributions in the uniaxial (second-order) anisotropy parameter $D$ and the $g$ factor, caused by possible defects in the samples. Additionally, weak intermolecular exchange and electronic dipole interactions are included in a mean-field approximation. Our calculated linewidths are in good agreement with experiments. We find that the distribution in $D$ is common to the three examined single-molecule magnets. This could provide a basis for a proposed tunneling mechanism due to lattice defects or imperfections. We also find that weak intermolecular exchange and dipolar interactions are mainly responsible for the temperature dependence of the lineshapes for all three SMMs, and that the intermolecular exchange interaction is more significant for Mn$_4$ than for the other two SMMs. This finding is consistent with earlier experiments and suggests the role of spin-spin relaxation processes in the mechanism of magnetization tunneling.

cond-mat.mtrl-sci↗

arXiv2002

Electrosorption of Br and Cl on Ag(100): Experiments and Computer Simulations

We present chronocoulometry experiments and equilibrium Monte Carlo simulations for the electrosorption of Br and Cl on Ag(100) single-crystal electrode surfaces. Two different methods are used to calculate the long-range part of the adsorbate-adsorbate interactions. The first method is a truncated-sum approach, while the second is a mean-field-enhanced truncated-sum approach. To compare the two methods, the resulting isotherms are fit to experimental adsorption isotherms, assuming both a constant electrosorption valency &gamma and also a coverage-dependent &gamma. While a constant &gamma fits the Br/Ag(100) well, a coverage-dependent or potential-dependent &gamma is needed for Cl/Ag(100).

cond-mat.mtrl-sci↗

arXiv2002

The Transition State in Magnetization Reversal

We consider a magnet with uniaxial anisotropy in an external magnetic field along the anisotropy direction, but with a field magnitude smaller than the coercive field. There are three representative magnetization configurations corresponding to three extrema of the free energy. The equilibrium and metastable configurations, which are magnetized approximately parallel and antiparallel to the applied field, respectively, both correspond to local free-energy minima. The third extremum configuration is the saddle point separating these minima. It is also called the transition state for magnetization reversal. The free-energy difference between the metastable and transition-state configurations determines the thermal stability of the magnet. However, it is difficult to determine the location of the transition state in both experiments and numerical simulations. Here it is shown that the computational Projective Dynamics method, applied to the time dependence of the total magnetization, can be used to determine the transition state. From large-scale micromagnetic simulations of a simple model of magnetic nanowires with no crystalline anisotropy, the magnetization associated with the transition state is found to be linearly dependent on temperature, and the free-energy barrier is found to be dominated by the entropic contribution at reasonable temperatures and external fields. The effect of including crystalline anisotropy is also discussed. Finally, the influence of the spin precession on the transition state is determined by comparison of the micromagnetic simulations to kinetic Monte Carlo simulations of precession-free (overdamped) dynamics.

cond-mat.stat-mech↗

arXiv2002

Absence of First-order Transition and Tri-critical Point in the Dynamic Phase Diagram of a Spatially Extended Bistable System in an Oscillating Field

It has been well established that spatially extended, bistable systems that are driven by an oscillating field exhibit a nonequilibrium dynamic phase transition (DPT). The DPT occurs when the field frequency is on the order of the inverse of an intrinsic lifetime associated with the transitions between the two stable states in a static field of the same magnitude as the amplitude of the oscillating field. The DPT is continuous and belongs to the same universality class as the equilibrium phase transition of the Ising model in zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed that the DPT becomes discontinuous at temperatures below a tricritical point [M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on observations in dynamic Monte Carlo simulations of a multipeaked probability density for the dynamic order parameter and negative values of the fourth-order cumulant ratio. Both phenomena can be characteristic of discontinuous phase transitions. Here we use classical nucleation theory for the decay of metastable phases, together with data from large-scale dynamic Monte Carlo simulations of a two-dimensional kinetic Ising ferromagnet, to show that these observations in this case are merely finite-size effects. For sufficiently small systems and low temperatures, the continuous DPT is replaced, not by a discontinuous phase transition, but by a crossover to stochastic resonance. In the infinite-system limit the stochastic-resonance regime vanishes, and the continuous DPT should persist for all nonzero temperatures.

cond-mat.stat-mech↗

arXiv2002

Surface Scaling Analysis of a Frustrated Spring-network Model for Surfactant-templated Hydrogels

We propose and study a simplified model for the surface and bulk structures of crosslinked polymer gels, into which voids are introduced through templating by surfactant micelles. Such systems were recently studied by Atomic Force Microscopy [M. Chakrapani et al., e-print cond-mat/0112255]. The gel is represented by a frustrated, triangular network of nodes connected by springs of random equilibrium lengths. The nodes represent crosslinkers, and the springs correspond to polymer chains. The boundaries are fixed at the bottom, free at the top, and periodic in the lateral direction. Voids are introduced by deleting a proportion of the nodes and their associated springs. The model is numerically relaxed to a representative local energy minimum, resulting in an inhomogeneous, ``clumpy'' bulk structure. The free top surface is defined at evenly spaced points in the lateral (x) direction by the height of the topmost spring, measured from the bottom layer, h(x). Its scaling properties are studied by calculating the root-mean-square surface width and the generalized increment correlation functions C_q(x)= <|h(x_0+x)-h(x_0)|^q>. The surface is found to have a nontrivial scaling behavior on small length scales, with a crossover to scale-independent behavior on large scales. As the vacancy concentration approaches the site-percolation limit, both the crossover length and the saturation value of the surface width diverge in a manner that appears to be proportional to the bulk connectivity length. This suggests that a percolation transition in the bulk also drives a similar divergence observed in surfactant templated polyacrylamide gels at high surfactant concentrations.

cond-mat.soft↗

arXiv2002

Microstructure and Velocity of Field-Driven SOS Interfaces: Analytic Approximations and Numerical Results

The local structure of a solid-on-solid (SOS) interface in a two-dimensional kinetic Ising ferromagnet with single-spin-flip Glauber dynamics, which is driven far from equilibrium by an applied field, is studied by an analytic mean-field, nonlinear-response theory [P.A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000)] and by dynamic Monte Carlo simulations. The probability density of the height of an individual step in the surface is obtained, both analytically and by simulation. The width of the probability density is found to increase dramatically with the magnitude of the applied field, with close agreement between the theoretical predictions and the simulation results. Excellent agreement between theory and simulations is also found for the field-dependence and anisotropy of the interface velocity. The joint distribution of nearest-neighbor step heights is obtained by simulation. It shows increasing correlations with increasing field, similar to the skewness observed in other examples of growing surfaces.

cond-mat.stat-mech↗

arXiv2001

Halide Adsorption on Single-crystal Silver Substrates: Dynamic Simulations and ab-initio Density-functional Theory

We investigate the static and dynamic behaviors of a Br adlayer electrochemically deposited onto single-crystal Ag(100) using an off-lattice model of the adlayer. Unlike previous studies using a lattice-gas model, the off-lattice model allows adparticles to be located at any position within a two-dimensional approximation to the substrate. Interactions with the substrate are approximated by a corrugation potential. Using Density Functional Theory (DFT) to calculate surface binding energies, a sinusoidal approximation to the corrugation potential is constructed. A variety of techniques, including Monte Carlo and Langevin simulations, are used to study the behavior of the adlayer. The lateral root-mean-square (rms) deviation of the adparticles from the binding sites is presented along with equilibrium coverage isotherms, and the thermally activated Arrhenius barrier-hopping model used in previous dynamic Monte Carlo simulations is tested.

cond-mat.mtrl-sci↗

arXiv2001

Scaling Analysis of Surfactant Templated Polyacrylamide Gel Surfaces

Surfaces of surfactant-templated polyacrylamide hydrogels were imaged by atomic force microscopy (AFM), and the surface morphology was studied by numerical scaling analysis. The templated gels were formed by polymerizing acrylamide plus a cross-linker in the presence of surfactants, which were then removed by soaking in distilled water. Gels formed in the presence of over 20% surfactant (by weight) formed clear, but became opaque upon removal of the surfactants. Untemplated gels formed and remained clear. The surface morphology of the gels was studied by several one- and two-dimensional numerical scaling methods. The surfaces were found to be self-affine on short length scales, with a roughness (Hurst) exponent in the range 0.85 to 1, crossing over to a constant root-mean-square surface width on long scales. Both the crossover length between these two regimes and the saturation value of the surface width increased significantly with increasing surfactant concentration, coincident with the increase in opacity. We propose that the changes in the surface morphology are due to a percolation transition in the system of voids formed upon removal of the surfactants from the bulk.

cond-mat.soft↗

arXiv2001

Going through Rough Times: from Non-Equilibrium Surface Growth to Algorithmic Scalability

Efficient and faithful parallel simulation of large asynchronous systems is a challenging computational problem. It requires using the concept of local simulated times and a synchronization scheme. We study the scalability of massively parallel algorithms for discrete-event simulations which employ conservative synchronization to enforce causality. We do this by looking at the simulated time horizon as a complex evolving system, and we identify its universal characteristics. We find that the time horizon for the conservative parallel discrete-event simulation scheme exhibits Kardar-Parisi-Zhang-like kinetic roughening. This implies that the algorithm is asymptotically scalable in the sense that the average progress rate of the simulation approaches a non-zero constant. It also implies, however, that there are diverging memory requirements associated with such schemes.

cond-mat.stat-mech↗

arXiv2001

Thermal and Dynamic Effects in Langevin Simulation of Hysteresis in Nanoscale Pillars

Dynamic quantities related to hysteresis have been measured in micromagnetic simulations of single-domain nanoscale magnets at nonzero temperature. The hysteresis-loop area and magnetization-field correlation display the characteristics of resonance, and the resonance frequency is found to be temperature dependent. The period-averaged magnetization displays symmetry breaking at high frequencies.

cond-mat.mtrl-sci↗

arXiv2000

Static and Dynamic Monte Carlo Simulations of Br Electrodeposition on Ag(100)

We study the static and dynamic properties of bromine electrosorption onto single-crystal silver (100) electrodes by Monte Carlo simulation. At room temperature the system displays a second-order phase transition between a low-coverage disordered phase at more negative electrode potentials and a c(2x2) ordered phase with bromine coverage 1/2 at more positive potentials. We explore the phase diagram and demonstrate that the broad shoulder observed in room-temperature cyclic voltammograms is due to local fluctuations resembling ordered phases with coverage 1/4 which exist in the model at much lower temperatures. We construct a dynamic Monte Carlo algorithm using a thermally activated stochastic barrier-hopping model for the microscopic dynamics. We use this algorithm to study the phase ordering and disordering processes following sudden potential steps between the disordered phase and the c(2x2) phase and to study the sweep-rate dependence in simulated cyclic-voltammetry experiments.

cond-mat.mtrl-sci↗

arXiv2000

Dynamic Phase Transition in a Time-Dependent Ginzburg-Landau Model in an Oscillating Field

The Ginzburg-Landau model below its critical temperature in a temporally oscillating external field is studied both theoretically and numerically. As the frequency or the amplitude of the external force is changed, a nonequilibrium phase transition is observed. This transition separates spatially uniform, symmetry-restoring oscillations from symmetry-breaking oscillations. Near the transition a perturbation theory is developed, and a switching phenomenon is found in the symmetry-broken phase. Our results confirm the equivalence of the present transition to that found in Monte Carlo simulations of kinetic Ising systems in oscillating fields, demonstrating that the nonequilibrium phase transition in both cases belongs to the universality class of the equilibrium Ising model in zero field. This conclusion is in agreement with symmetry arguments [G. Grinstein, C. Jayaprakash, and Y. He, Phys. Rev. Lett. 55, 2527 (1985)] and recent numerical results [G. Korniss, C.J. White, P. A. Rikvold, and M. A. Novotny, Phys. Rev. E (submitted)]. Furthermore, a theoretical result for the structure function of the local magnetization with thermal noise, based on the Ornstein-Zernike approximation, agrees well with numerical results in one dimension.

cond-mat.stat-mech↗