Excitation of phase transitions in dipole lattices

Phase transitions in hexagonal lattices with three and four rows of dipoles arising as a result of the reorientation of different sets of dipoles by the external field have been studied. The conditions of the implementation of two types of symmetric phase transitions and the asymmetric transitions, when the configurations of the system to the left and to the right of the excitation region are different, have been established. Merging of two regions of the phase transitions has been considered. Unidirectional phase transitions, in which either the left or the right phase transition front propagates from the excitation region along the lattice, have been obtained in a lattice with four rows of dipoles. The variations of the total dipole moment of the system and the energy of the dipole-dipole interaction during the phase transitions have been given.     

Extremely small domain in the lattice of magnetic dipoles

Lattices of magnetic dipoles with 1–4 rows are investigated. Numerical analysis reveals the smallest stationary domains formed in the lattices, necessary conditions for the formation and destruction of such domains are obtained, and the change in the magnetic moment of the lattices during domain formation is considered. It is shown that the action of an external field on one of the dipoles forming a domain is sufficient for its breaking. The lattices in which the orientational phase transition appears upon perturbation of several dipoles and propagates over the entire system are revealed.     

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.     

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.     

Phase transitions in a two-dimensional dipole ferrimagnet

The magnetic configurations of the system of magnetic dipoles that have different values and are arranged in a staggered order on a square lattice are studied. A numerical simulation is used to study the phase transitions in the system when the mismatch between the dipoles changes. The restructuring of the magnetic configuration of the system induced by a change in the mismatch is shown to proceed via sequential second-order phase transitions between collinear and noncollinear phases. The numerical simulation results are supported by analytical calculations performed with trial functions.     

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 2D nano-islands I: Ising spin model

An Ising spin effective field theory (EFT) is developed as a framework for a detailed analysis of the magnetic properties of two-dimensional (2D) nano-islands on a nonmagnetic substrate with an out of plane magnetization. The Hamiltonian with nearest neighbor exchange interactions and single-atom magnetic anisotropy defines the ground state. The calculation yields the single site spin correlations, the magnetizations, and the isothermal susceptibilities for the core and periphery domains, and the island core phase diagrams. The choice of a spin S=1 for the atoms permits the analysis of the effects of spin fluctuations via the single site spin correlations. In particular we investigate the effects due to the different anisotropies and reduced dimensionalities for the core and periphery domains. The present model calculations are developed for different 2D nano-islands lattices. Detailed theoretical results are presented for the square and hexagonal lattices, with numerical applications for the 2D Co nano-islands on Pt. The derived transition temperature for the hexagonal lattice nano-islands is in good agreement with the experimental data for Co nano-islands on Pt. Though both the core and the periphery domains have the same order-disorder transition temperature, the magnetization of each domain attains this transition differently. The temperature behavior of the spin correlations is also fundamentally different for the periphery and core sites, which entails distinctly different isothermal susceptibilities, and yields statistically averaged nano-islands susceptibilities that do not correspond to a second order phase transition. The experimental susceptibility results for 2D Co nano-islands on Pt can be interpreted within our EFT Ising model without reference to a transition from a blocking state of the particle to a superparamagnetic behavior. The results for the different lattices are formally comparable, and demonstrate the robustness and general character of the model.     

Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method

In order to investigate the quantum phase transitions and the time-of-flight absorption pictures analytically in a systematic way for ultracold Bose gases in bipartite optical lattices, we present a generalized Green’s function method. Utilizing this method, we study the quantum phase transitions of ultracold Bose gases in two types of bipartite optical lattices, i.e., a hexagonal lattice with normal Bose–Hubbard interaction and a d-dimensional hypercubic optical lattice with extended Bose–Hubbard interaction. Furthermore, the time-of-flight absorption pictures of ultracold Bose gases in these two types of lattices are also calculated analytically. In hexagonal lattice, the time-of-flight interference patterns of ultracold Bose gases obtained by our analytical method are in good qualitative agreement with the experimental results of Soltan-Panahi, et al. [Nat. Phys. 7, 434 (2011)]. In square optical lattice, the emergence of peaks at \(\left( { \pm \frac{\pi }{a}, \pm \frac{\pi }{a}} \right)\) in the time-of-flight absorption pictures, which is believed to be a sort of evidence of the existence of a supersolid phase, is clearly seen when the system enters the compressible phase from charge-density-wave phase.     

Multicanonical sampling of the space of states of ℋ(2, <Emphasis Type="Italic">n</Emphasis>)-vector models

Problems of temperature behavior of specific heat are solved by the entropy simulation method for Ising models on a simple square lattice and a square spin ice (SSI) lattice with nearest neighbor interaction, models of hexagonal lattices with short-range (SR) dipole interaction, as well as with long-range (LR) dipole interaction and free boundary conditions, and models of spin quasilattices with finite interaction radius. It is established that systems of a finite number of Ising spins with LR dipole interaction can have unusual thermodynamic properties characterized by several specific-heat peaks in the absence of an external magnetic field. For a parallel multicanonical sampling method, optimal schemes are found empirically for partitioning the space of states into energy bands for Ising and SSI models, methods of concatenation and renormalization of histograms are discussed, and a flatness criterion of histograms is proposed. It is established that there is no phase transition in a model with nearest neighbor interaction on a hexagonal lattice, while the temperature behavior of specific heat exhibits singularity in the same model, in case of LR interaction. A spin quasilattice is found that exhibits a nonzero value of residual entropy.     

Vortex structures in planar lattices of magnetic dipoles in the presence of exchange coupling

Vortex equilibrium states of planar square lattices of magnetic dipoles in the presence of the exchange interaction have been studied. It has been shown that the vortex equilibrium configurations differ in the position of the vortex center and, correspondingly, in the magnitude and direction of the total magnetic moment of the system. In the case of the position of the vortex center in the center of the array, the total magnetic moment of the system is zero. The vortex center moves in the direction perpendicular to the field under the action of the external planar magnetic field on the system. Thus, the transitions between different equilibrium vortex configurations are implemented and the magnetic moment of the system of dipoles is controlled.     

Fe原子薄片的磁性:第一性原理计算

使用基于密度泛函理论的第一原理方法,对Fe单层原子薄片在二维正方、二维六角晶格下的电子结构和磁学性质进行了系统研究.结果表明,二维正方、二维六角以及bcc晶格在平衡晶格常数下都具有磁性,其单位原子磁矩分别为2.65,2.54和2.20μ_В.对二维晶格在被压缩和被拉伸时的磁性计算表明,随着晶格的被拉伸,当最近邻原子间距大于4.40时,铁原子间的键合被拉断,体系单位原子的磁矩趋于孤立Fe原子的磁矩4μ_В;随着原子键长的减小,各体系的磁矩 关键词： Fe 原子薄片 磁性 从头计算     

A mean—field approximation scheme containing the spatial parameter and its application to a surface—reaction—like cellular automaton model

Using an AB2 Surface-reaction-like cellular automaton model,we present a modified mean-field approximation scheme for describing some dynamic lattice models,in which a lattice freedom parameter N is introduced as a variable,We obtain the phase diagrams of the example model for linear,hexagonal,square and triangular lattices,and we reveal a second-order phase transiton which has not been found using using traditional approaches.     

Dynamics of the lattice of magnetic nanodipoles with cubic anisotropy

The 5 × 5 square lattices of magnetic dipoles with cubic crystallographic anisotropy were investigated by the computer simulation method. The conditions for implementing the random orientation of lattice configurations, each of which are characterized by a certain response to the influence of an external magnetic pulse, as well as by the established regime of the oscillation of the total magnetic moment under the influence of an alternating field, are revealed. Regular vibration modes with a doubled frequency and quasi-periodic and chaotic modes are detected. The dependence of the system response on the parameters of the magnetic field pulse is studied.     

Hamiltonian walks and polymer configurations

Kasteleyn's treatment of the hamiltonian walk problem on lattice graphs is briefly reviewed. The asymptotic behaviour of the number of hamiltonian walks on the kth covering of a closed oriented lattice graph is expressed in terms of the asymptotic behaviour of the number of oriented trees on the lattice graph. Asymptotic results on the enumeration of hamiltonian walks are presented for the covering and underlying lattices of the Manhattan oriented square lattice, and the covering lattices of certain orientations of the diamond and cubic lattices. The effect of boundary conditions is examined.Relations are established between hamiltonian walks and close-packed polymer configurations. An analysis of the assumptions in lattice models of the melting and glass transitions in polymers shows that the Flory-Huggins approximation underestimates the total number of polymer configurations, but that corrections can be made without altering the principal features of the models thus permitting better agreement with the experimental data.     

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.     

Exact wave-based Bloch analysis procedure for investigating wave propagation in two-dimensional periodic lattices

This paper presents an exact, wave-based approach for determining Bloch waves in two-dimensional periodic lattices. This is in contrast to existing methods which employ approximate approaches (e.g., finite difference, Ritz, finite element, or plane wave expansion methods) to compute Bloch waves in general two-dimensional lattices. The analysis combines the recently introduced wave-based vibration analysis technique with specialized Bloch boundary conditions developed herein. Timoshenko beams with axial extension are used in modeling the lattice members. The Bloch boundary conditions incorporate a propagation constant capturing Bloch wave propagation in a single direction, but applied to all wave directions propagating in the lattice members. This results in a unique and properly posed Bloch analysis. Results are generated for the simple problem of a periodic bi-material beam, and then for the more complex examples of square, diamond, and hexagonal honeycomb lattices. The bi-material beam clearly introduces the concepts, but also allows the Bloch wave mode to be explored using insight from the technique. The square, diamond, and hexagonal honeycomb lattices illustrate application of the developed technique to two-dimensional periodic lattices, and allow comparison to a finite element approach. Differences are noted in the predicted dispersion curves, and therefore band gaps, which are attributed to the exact procedure more-faithfully modeling the finite nature of lattice connection points. The exact method also differs from approximate methods in that the same number of solution degrees of freedom is needed to resolve low frequency, and arbitrarily high frequency, dispersion branches. These advantageous features may make the method attractive to researchers studying dispersion characteristics, band gap behavior, and energy propagation in two-dimensional periodic lattices.     

Dimer problem on the cylinder and torus

We obtain explicit expressions of the number of close-packed dimers and entropy for three types of lattices (the so-called 8.8.6, 8.8.4, and hexagonal lattices) with cylindrical boundary condition and the entropy of the 8.8.6 lattice with toroidal boundary condition. Our results and the one on 8.8.4 and hexagonal lattices with toroidal boundary condition by Salinas and Nagle [S.R. Salinas, J.F. Nagle, Theory of the phase transition in the layered hydrogen-bonded SnCl²⋅2H₂O crystal, Phys. Rev. B 9 (1974) 4920-4931] and Wu [F.Y. Wu, Dimers on two-dimensional lattices, Inter. J. Modern Phys. B 20 (2006) 5357-5371] imply that the 8.8.6 (or 8.8.4) lattices with cylindrical and toroidal boundary conditions have the same entropy whereas the hexagonal lattices have not. Based on these facts we propose the following problem: under which conditions do the lattices with cylindrical and toroidal boundary conditions have the same entropy?     

Bubble-domain lattices in the vicinity of the compensation point

The behavior of a hexagonal lattice of bubble domains in thin uniaxial films of garnet ferrites is studied in the temperature range from the compensation point to the Néel temperature. Two types of first-order phase transitions (preserving and not preserving the total number of domains in the bubble-domain lattice) occurring with variation of the temperature were studied. It is shown that the type of a phase transition is determined by the temperature dependence of the characteristic length of the film. The existence of two types of phase transitions is explained in terms of magnetostatic pressure existing in a bubble-domain lattice.     

Response of a magnetic nanoparticle lattice to a magnetic field pulse near the stability boundary

The dynamic response of a system being near the stable equilibrium boundary to an external magnetic field pulse is studied for 2D lattices of magnetic nanoparticles with cubic crystallographic anisotropy. The conditions under which magnetic moment oscillations from individual dipoles propagate to the entire system are revealed. This effect results in the lattice response are significantly larger in the external pulse duration and with an amplitude rather weakly depending on initial conditions and external field parameters, the processes during which the pulse results in reorientation of only individual lattice dipoles.     

Imaging of a vortex lattice transition in YNi2B2C by scanning tunneling spectroscopy

The vortex lattices in YNi2B2C under the magnetic fields H up to 3 T applied along both the a and the c axes have been studied by scanning tunneling spectroscopy at 4.2 K. The vortex lattice transition has been found to occur in different manners for H parallela and H parallelc; in H parallela a slightly distorted hexagonal vortex lattice has been found to transform to a nearly square one above 1.0 T with increasing H, while in H parallelc the transition occurs at a much lower field around 0.1 T. The unconventional steep increase of the quasiparticle density of states outside the vortex core has also been found well below H(c2).