Ordering classification of columnar lattices formed in magnetic fluid subjected to perpendicular fields

When the thin film of high-quality magnetic fluid is subjected to a perpendicular magnetic field, a separation of particles from the liquid matrix will occur, leading to a phase transition with a phase that is concentrated in particles separating from a dilute phase. The concentrated phase makes up the cylindrical columns that can form two-dimensional lattices. We have explored the field-induced lattices with optical microscopy, digital imaging and computer-video techniques in this study, to classify the ordering property in terms of bond-orientation order.     

Effects of Field Orientation on the Driven Lattice Gas

Steady states of the driven lattice gas (DLG) on triangular, hexagonal and square lattices with the field at several fixed orientations to the principal lattice vectors were studied by Monte Carlo simulation. In most cases a strong field suppressed change to a low-temperature ordered phase. On each lattice, one field orientation that caused nonequilibrium ordering was identified. On triangular and hexagonal lattices, dependence of energy and anisotropy on field strength was studied at those orientations. Anisotropic ordering along the field developed at intermediate temperatures under weak fields. Partial ordering along the field persisted to low temperature under strong fields.     

Thermodynamic and magnetic properties in two artificial frustrated lattices

With the Monte Carlo simulation, we investigate the thermodynamics and magnetic properties of the artificial frustrated square and honeycomb lattices. The results from the Ising-like dipolar model show that there occurs one magnetic order transition for the square lattice while the honeycomb lattice exhibits two magnetic order phase transitions. When the magnetic field is applied perpendicular to one of sublattices, a sharp field-independent peak in the specific heat curves appears at a very low temperature for both frustrated lattices due to the occurrence of a long-range ordered state induced by the magnetic field. For the square lattice, the coercive field slightly increases with the angle of field relative to the vertical axis. For both frustrated lattices, the magnetic reversal is achieved mostly via flipping a chain of the nearest neighbor spins.     

Magnetic properties of <Superscript>3</Superscript>He on the recursive lattices

We considered the Heisenberg model on the recursive lattices with multi-spin interaction in a strong magnetic field as an approximation of the two-dimensional kagome lattice, as well as hexagonal recursive lattices as an approximation of triangular lattice, for solid ³He. In a strong magnetic field it is possible to approximate the Heisenberg model with the Izing one. Using dynamic approach, we obtain exact recursion relations for partition functions. Diagrams of the magnetization versus external magnetic field with different spin-exchange parameters and temperatures are presented. Magnetization plateaux, bifurcation points, and doublings are obtained.     

Formation of two-dimensional lattices of magnetic domains in a harmonic magnetic field

New configurations of two-dimensional lattices of magnetic domains with symmetry described by the P2 and Cmm2 space groups are revealed in studying the formation of domain structures in a harmonic magnetic field. Two-dimensional lattices belonging to five space groups of the orthorhombic and hexagonal systems are observed in a single iron garnet film. Changes in the lattice configurations and in the lattice elements occur upon the variation of only one parameter of the applied magnetic field, namely, its frequency.     

Phase transitions in a driven lattice gas in two planes

We report on a Monte Carlo study of ordering in a nonequilibrium system. The system is a lattice gas that comprises two equal, parallel square lattices with stochastic particle-conserving irreversible dynamics. The particles are driven along a principal direction under the competition of the heat bath and a large, constant external electric field. There is attraction only between particles on nearest-neighbor sites within the same lattice. Particles may jump from one plane to the other; therefore, density fluctuations have an extra mechanism to decay and build up. It helps to obtain the steady-state accurately. Spatial correlations decay with distance according to a power law at high enough temperature, as for the ordinary two-dimensional case. We find two kinds of nonequilibrium phase transitions. The first one has a critical point for half occupation of the lattice, and seems to be related to the anisotropic phase transition reported before for the plane. This transition becomes discontinuous for low enough density. The difference of density between the planes changes discontinuously for any density at a lower temperature. This seems to correspond to a phase transition that does not have a counterpart in equilibrium nor in the two-dimensional nonequilibrium case.     

Magnetic dipolar ordering on geometrically frustrated brick-shaped lattices

The magnetic ordering of frustrated arrays of nanoscale islands can be strongly influenced by the array patterns. We theoretically present three kinds of artificial geometrically frustrated systems with different brick-shaped geometries, defined as brick-shaped lattices, and investigate their magnetic dipolar ordering at the ground state using the Monte Carlo method. The simulated results show that the magnetic ordering of three brick-shaped frustrated lattices depends strongly on the strength of dipolar interactions, depending on the lattice spacing. It is found that the long-range dipolar interactions tend to suppress the long-range ordered state and induce the short-range quasi-ice state at each vertex of the lattices. In addition, the correlations for neighboring spin pairs are closely related to not only the dipolar coupling strength but also the geometry of the lattices.     

Simulating cyclotron-Bloch dynamics of a charged particle in a 2D lattice by means of cold atoms in driven quasi-1D optical lattices

Quantum dynamics of a charged particle in a two-dimensional (2D) lattice subject to magnetic and electric fields is a rather complicated interplay between cyclotron oscillations (the case of vanishing electric field) and Bloch oscillations (zero magnetic field), details of which has not yet been completely understood. In the present work we suggest to study this problem by using cold atoms in optical lattices. We introduce a one-dimensional (1D) model which can be easily realized in laboratory experiments with quasi-1D optical lattices and show that this model captures many features of the cyclotron-Bloch dynamics of the quantum particle in 2D square lattices.     

Comparison of diluted antiferromagnetic Ising models on frustrated lattices in a magnetic field

We study diluted antiferromagnetic Ising models on triangular and kagome lattices in a magnetic field, using the replica-exchange Monte Carlo method. We observe seven and five plateaus in the magnetization curve of the diluted antiferromagnetic Ising model on the triangular and kagome lattices, respectively, when a magnetic field is applied. These observations contrast with the two plateaus observed in the pure model. The origin of multiple plateaus is investigated by considering the spin configuration of triangles in the diluted models. We compare these results with those of a diluted antiferromagnetic Ising model on the three-dimensional pyrochlore lattice in a magnetic field pointing in the [111] direction, sometimes referred to as the “kagome-ice” problem. We discuss the similarity and dissimilarity of the magnetization curves of the “kagome-ice” state and the two-dimensional kagome lattice.     

On the possibility of phase transitions in dusty plasma structures in a glow discharge under the action of a magnetic field

The melting of a dusty plasma structure formed in a stratum of a glow discharge caused by application of a magnetic field and its subsequent increase is studied. The images of two-dimensional cross sections of dusty plasma structures previously obtained by the authors are considered. To identify the phase, the correlation functions are calculated and visual comparison with the space lattices of ideal crystals is performed. It is found that, under the conditions of the previous study of the authors, as the magnetic field increases, the phase state of the dusty structure changes from an anisotropic liquidlike (liquid-ice) state to a disordered one. There is a tendency to a change in the type of the space lattice of the structure.     

Vortex deconfinement in the XY model with a magnetic field

We study vortex unbinding for the classical two-dimensional XY model in a magnetic field on square and triangular lattices. A renormalization group analysis combined with duality in the model shows that at high temperature and high field, the vortices unbind as the magnetic field is lowered in a two-step process: strings of overturned spins first proliferate and then vortices unbind. The transitions are highly continuous but are not of the Kosterlitz-Thouless type. The unbound vortex fixed point is shown to inherit properties of the underlying lattice, in particular containing a set of nodal lines that reflect the lattice symmetry.     

Nonlinear magnetotransport in a two-dimensional electron system in a square array of antidots in GaAs/AlAs heterostructures

Nonlinear magnetotransport of two-dimensional electrons in square antidot lattices prepared on the basis of selectively doped GaAs/AlAs heterostructures with the period that is much less than the electron mean free path in the initial GaAs quantum wells but is much larger than their Fermi wavelength has been studied. It has been shown that the character of the nonlinear transport of the two-dimensional electrons in the lateral lattices under study changes from classical to quantum with the decrease in the antidot radius. It has been found that the quantum lifetime increases in the magnetic field corresponding to the condition of equality of the cyclotron diameter of two-dimensional electrons and the antidot lattice period.     

Lamellar-like structures in ferrofluids placed in strong magnetic fields

We consider a ferrofluid system consisting of magnetic particles interacting with a magnetic dipole–dipole interaction. We study the strong magnetic field regime where all magnetic dipoles are completely polarized in the direction of the magnetic field. We introduce a lattice gas model that serves to describe space ordering phenomena in such systems. It is found that, within mean field theory, this model predicts a second order phase transition to a phase with inhomogeneous lamellar-like ordering below a certain critical temperature.     

Some dynamical properties of a two-dimensional Wigner crystal

Results for the static part of the ground state energy of the square and hexagonal two-dimensional Wigner lattices are given. The hexagonal lattice has the lower energy. Phonon dispersion curves and the vibrational zeropoint energy are calculated for the hexagonal lattice. The dielectric susceptibility tensor of a two-dimensional Wigner crystal χ_αβ(q) has been determined in the long wavelength limit in the presence of a static magnetic field perpendicular to the crystal, and explicit expressions have been obtained for the hexagonal lattice. Applying the analysis developed by Chiu and Quinn, the results for the susceptibility have been used to obtain the dispersion relation for the plasma oscillations in the electron crystal on the assumption that the crystal is embedded in a dielectric medium. The dispersion curves have been calculated for differing magnitudes of the applied magnetic field.     

Cyclotron dynamics of neutral atoms in optical lattices with additional magnetic field and harmonic trap potential

We analytically and numerically discuss the stability and dynamics of neutral atoms in a two-dimensional optical lattice subjected to an additional harmonic trap potential and artificial magnetic field. The harmonic trap potential plays a key role in modifying the equilibrium state properties of the system and stabilizing the cyclotron orbits of the condensate.Meanwhile, the presence of the harmonic trap potential and lattice potential results in rich cyclotron dynamics of the condensate. The coupling effects of lattice potential, artificial magnetic field, and harmonic trap potential lead to single periodic, multi-periodic or quasi-periodic cyclotron orbits of the condensate. So we can control the cyclotron dynamics of neutral atoms in optical lattice by manipulating the strength of harmonic confinement, artificial magnetic field, and initial conditions. Our results provide a direct theoretical evidence for the cyclotron dynamics of neutral atoms in optical lattices exposed to the artificial gauge magnetic field and harmonic trap potential.     

Magnetism in artificial lattices

We compare magnetism in two artificial lattice structures, a quantum dot array formed in a two-dimensional electron gas and an optical lattice loaded with repulsive, contact-interacting fermionic atoms. When the tunneling between the lattice sites is strong, both lattices are non-magnetic. With reduced tunneling in the tight-binding limit, the shell-filling of the single-site quantum wells combined with Hund's rule determines the magnetism. This leads to a systematic magnetic phase diagram with non-magnetic, ferromagnetic and antiferromagnetic phases.     

Incommensurateness effects in a lattice Ginzburg-Landau model

This paper discusses the effect of magnetic translational symmetry on the vortex structure in superconducting crystals with a large basis in artificial Josephson media (regular lattices of superconducting clusters) prepared with opal as the base material. For external magnetic fields lower than the upper critical field, the lattice Ginzburg-Landau model reduces to the two-dimensional Frenkel’-Kontorova model which in some cases is exactly solvable, in which the crystal lattice plays the role of an “hard sublattice” while the deformable vortex lattice plays the role of a “soft sublattice.” It is shown that static shear waves in the vortex lattice are solutions to the two-dimensional sine-Gordon equation with an additional condition of incompressibility implied by flux quantization. The pinning energy is found as a function of the magnetic field, nearness to the transition line, and the crystal lattice constant. Fiz. Tverd. Tela (St. Petersburg) 39, 1158–1162 (July 1997)     

Stable spiral domains in ferrite-garnet films

Stable spiral domain structures—spiral domains stabilized by a bubble lattice and lattices of spiral domains—in epitaxial ferrite-garnet films have been experimentally investigated. The thermodynamic approach based on the concept of magnetostatic pressure is applied to explain the behavior of a spiral domain structure with a change in temperature or magnetic field. It is shown that phase transitions in spiral domains are related to phase transitions in the bubble lattice.     

Mean fields and self consistent normal ordering of lattice spin and gauge field theories

Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived.