Monte Carlo Simulations of Ultrathin Magnetic Dots

In this work we study the thermodynamic properties of ultrathin ferromagnetic dots using Monte Carlo simulations. We investigate the vortex density as a function of the temperature and the vortex structure in monolayer dots with perpendicular anisotropy and long-range dipole interaction. The interplay between these two terms in the hamiltonian leads to an interesting behavior of the thermodynamic quantities as well as the vortex density.Comment: 10 figure

Phase transition in ultrathin magnetic films with long-range interactions: Monte Carlo simulation of the anisotropic Heisenberg model

Ultrathin magnetic films can be modeled as an anisotropic Heisenberg model with long-range dipolar interactions. It is believed that the phase diagram presents three phases: An ordered ferromagnetic phase I, a phase characterized by a change from out-of-plane to in-plane in the magnetization II, and a high-temperature paramagnetic phase III. It is claimed that the border lines from phase I to III and II to III are of second order and from I to II is first order. In the present work we have performed a very careful Monte Carlo simulation of the model. Our results strongly support that the line separating phases II and III is of the BKT type.Comment: 7 page

Escape configuration lattice near the nematic-isotropic transition: Tilt analogue of blue phases

We predict the possible existence of a new phase of liquid crystals near the nematic-isotropic ($NI$) transition. This phase is an achiral, tilt-analogue of the blue phase and is composed of a lattice of {\em double-tilt}, escape-configuration cylinders. We discuss the structure and the stability of this phase and provide an estimate of the lattice parameter.Comment: 5 pages, 6 figures (major revision, typos corrected, references added

Orientational transition in a nematic liquid crystal at a patterned surface

T. J. Atherton and J. Roy Sambles, Physical Review E, Vol. 74, article 022701 (2006) "Copyright © 2006 by the American Physical Society."We consider a semi-infinite nematic in contact with a periodic patterned surface with alternate planar and homeotropic stripes. Extending the work of Barbero et al., we find the free energy (assuming K1=K3) for the situations where the easy direction on the planar stripe is either perpendicular or parallel to the length of the stripes. We find the bulk free energy difference between the structures to be proportional to √ K2/K1 and so we consider the possibility of a spontaneous transition between the two states if the azimuthal anchoring energy is sufficiently weak and K1≠K2. We compute the critical azimuthal anchoring energy for such a transition in terms of the relative width of the stripes and the period of the pattern and find it to be ~10−6 J m−2, comparable to experimental values

Magnetic friction due to vortex fluctuation

We use Monte Carlo and molecular dynamics simulation to study a magnetic tip-sample interaction. Our interest is to understand the mechanism of heat dissipation when the forces involved in the system are magnetic in essence. We consider a magnetic crystalline substrate composed of several layers interacting magnetically with a tip. The set is put thermally in equilibrium at temperature T by using a numerical Monte Carlo technique. By using that configuration we study its dynamical evolution by integrating numerically the equations of motion. Our results suggests that the heat dissipation in this system is closed related to the appearing of vortices in the sample.Comment: 6 pages, 41 figure

Layer dynamics of a freely standing smectic-A film

We study the hydrodynamics of a freely-standing smectic-A film in the isothermal, incompressible limit theoretically by analyzing the linearized hydrodynamic equations of motion with proper boundary conditions. The dynamic properties for the system can be obtained from the response functions for the free surfaces. Permeation is included and its importance near the free surfaces is discussed. The hydrodynamic mode structure for the dynamics of the system is compared with that of bulk systems. We show that to describe the dynamic correlation functions for the system, in general, it is necessary to consider the smectic layer displacement $u$ and the velocity normal to the layers, $v_z$, together. Finally, our analysis also provides a basis for the theoretical study of the off-equilibrium dynamics of freely-standing smectic-A films.Comment: 22 pages, 4 figure

Switching dynamics of surface stabilized ferroelectric liquid crystal cells: effects of anchoring energy asymmetry

We study both theoretically and experimentally switching dynamics in surface stabilized ferroelectric liquid crystal cells with asymmetric boundary conditions. In these cells the bounding surfaces are treated differently to produce asymmetry in their anchoring properties. Our electro-optic measurements of the switching voltage thresholds that are determined by the peaks of the reversal polarization current reveal the frequency dependent shift of the hysteresis loop. We examine the predictions of the uniform dynamical model with the anchoring energy taken into account. It is found that the asymmetry effects are dominated by the polar contribution to the anchoring energy. Frequency dependence of the voltage thresholds is studied by analyzing the properties of time-periodic solutions to the dynamical equation (cycles). For this purpose, we apply the method that uses the parameterized half-period mappings for the approximate model and relate the cycles to the fixed points of the composition of two half-period mappings. The cycles are found to be unstable and can only be formed when the driving frequency is lower than its critical value. The polar anchoring parameter is estimated by making a comparison between the results of modelling and the experimental data for the shift vs frequency curve. For a double-well potential considered as a deformation of the Rapini-Papoular potential, the branch of stable cycles emerges in the low frequency region separated by the gap from the high frequency interval for unstable cycles.Comment: 35 pages, 15 figure

Constant-angle surfaces in liquid crystals

We discuss some properties of surfaces in R3 whose unit normal has constant angle with an assigned direction field. The constant angle condition can be rewritten as an Hamilton-Jacobi equation correlating the surface and the direction field. We focus on examples motivated by the physics of interfaces in liquid crystals and of layered fluids, and discuss the properties of the constant-angle surfaces when the direction field is singular along a line (disclination) or at a point (hedgehog defect

Geometrically-controlled twist transitions in nematic cells

We study geometrically-controlled twist transitions of a nematic confined between a sinusoidal grating and a flat substrate. In these cells the transition to the twisted state is driven by surface effects. We have identified the mechanisms responsible for the transition analytically and used exact numerical calculations to study the range of surface parameters where the twist instability occurs. Close to these values the cell operates under minimal external fields or temperature variations