Structure-Induced Phase Transitions in Classic Systems of Dipoles: Unequal Kagome,Truncated Square,and Prismatic Pentagonal Lattices

Several magnetic compounds owe their properties to the particular nature of the dipole–dipole interaction. Changes induced in their structure will vary the total interaction energy in nontrivial fashions. In the present work, systems of identical particles possessing dipole moments arranged on various types of 2D structures are studied. By continuously varying a structural parameter, the state of minimum energy will favor distinct dipole configurations, giving rise to different phases. The ultimate goal is to quantitatively address the relation existing between the minimum possible energy for different systems of classic dipoles and the concomitant dipole phases that appear. The systems of dipoles considered here are studied in detail for the first time. With the exploration, new light will be shed on the existence of structural phase transitions in classical systems even at zero temperature, changes induced by the variation of a continuous parameter, and not the temperature, that resemble the ones occurring in quantum phase transitions.     

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.     

Ground state of magnetic dipoles on a two-dimensional lattice: structural phases in complex plasmas

We study analytically and by molecular dynamics simulations the ground state configuration of a system of magnetic dipoles fixed on a two-dimensional lattice. We find different phases, in close agreement with previous results. Building on this result and on the minimum energy requirement we determine the equilibrium lattice configuration, the magnetic order (ferromagnetic versus antiferromagnetic), and the magnetic polarization direction of a system of charged mesoscopic particles with magnetic dipole moments, in the domain where the strong electrostatic coupling leads to a crystalline ground state. Orders of magnitudes of the parameters of the system relevant to possible future dusty plasma experiments are discussed.     

Polar nano-rods under shear: From equilibrium to chaos

The orientational dynamics of rod-like particles with permanent (electric or magnetic) dipole moments in a plane Couette shear flow is investigated using mesoscopic relaxation equations combined with a generalized Landau free energy. The free energy contribution due to the coupling between average alignment and dipole orientation is derived on a microscopic basis. Numerical results of the resulting eight-dimensional dynamical system are presented for the case of longitudinal dipoles and thermodynamic conditions where the equilibrium state is a (polar or non-polar) nematic. Solution diagrams reveal presence of a large variety of periodic, transient chaotic, and chaotic dynamic states of the average alignment and dipole moment, respectively, appearing as a function of Deborah number and tumbling parameter. Compared to rods without dipoles we observe a significant preference of out-of-plane kayaking-tumbling states and, generally, a higher sensitivity to the initial conditions including bistability. We also demonstrate that the average (electric) dipole moment characterizing most of the observed states yields electrodynamic (magnetic) fields of measurable strength.     

Equilibrium configurations and phase transitions in dipole lattices

Two-dimensional square and hexagonal lattices of magnetic dipoles with the number of rows 1–4 have been studied. Based on the numerical analysis, equilibrium stable domain configurations, including the minimum number of lattice dipoles, have been revealed; the conditions for the creation and destruction of domains have been determined; and their associated changes in the magnetic moment of the lattice and in the energy of the dipole interaction have been found. The conditions for the occurrence of phase transitions that change the configuration of the lattices have been investigated and the conditions for unidirectional propagation of the front of the phase transition have been established. A comparative analysis of different square and hexagonal lattices has been performed in terms of the specific features of the formed domains and the observed orientation phase transitions.     

Surface wave excitation in solids by magnetic dipoles

The paper studies the interaction of magnetic dipole moments with magnetoplasma (in semiconductors) and magnetostatic (in ferromagnets) surface waves. Expressions for energy losses of such dipoles by wave excitation are obtained; experimental realizability of mobile dipole moments are discussed; and estimates are presented. The said interaction is shown to be suitable to detect surface helicons in semiconductors.     

Mathematical Modeling of the Magnetization of a Two-Dimensional System of Magnetic Moments

Using a system that reaches its minimum energy of interaction at equilibrium, the magnetization of a discrete two-dimensional system of interacting magnetic dipoles by an external magnetic field is modeled mathematically. Magnetization curves for rectangular two-dimensional clusters of dipoles and the region of the magnetic domain are calculated.     

Equilibrium and passing properties of dislocation dipoles

Static and dynamic properties of dislocation dipoles are investigated under isotropic and anisotropic elasticity. In elastically isotropic systems for a dislocation character between 35 and 40°, a dipole assumes the same stress-free equilibrium angle of 90° as the screw dipole. This can be affected by elastic anisotropy, as in Cu where the equilibrium angle assumed by a screw dipole (≈59°) is unchanged up to a dislocation character of 22°. In contrast, the static properties of near-edge dislocation dipoles are little influenced by elastic anisotropy. Certain dipole passing properties, not the passing stress however, are also modified by elastic anisotropy. For large heights and/or in the case of undissociated dislocations, the minimum passing stress corresponds to a dipole character of ～60° and it exhibits a sharp maximum in screw orientation. Reasonably moderate dislocation reorientations should facilitate the passing of near-screw dislocations in fatigue channels. Within a certain range of applied stresses, the passing of dipoles, comprised of unlike attractive dislocations, is accompanied by the sweeping of one dislocation by the other over a limited distance. Dissociation plays a prominent role in determining both static and dynamic properties for dipole heights less than a few times the dissociation distance of an isolated dislocation.     

Dynamic magnetization reversal in dipole systems

The possibility of magnetization reversal in two different systems of magnetic dipoles by preliminary excitation of certain oscillatory regimes is demonstrated using numerical analysis of bistable states of these systems. Cyclic magnetization reversal of the systems is executed by sequential alternation of the frequency of the applied ac field. The interaction of two ring-shaped dipole systems is analyzed and peculiarities of the change in the total magnetic moments induced by this interaction are revealed.     

基于介质谐振器原理的左手材料设计

本文通过对高介电常数介质基于介质谐振器理论进行分析,明确了利用高介电常数介质产生负介电常数或负磁导率的途径在于介质中产生具有Lorentz谐振形式的电磁响应的电偶极子或磁偶极子,指出了这种偶极子的产生来源于电磁波在介质中形成的驻波,而左手通带的形成正是由于电偶极子和磁偶极子之间的相互影响,破坏了驻波形成的条件所实现的. 模拟结果表明,通过将尺寸相同,介电常数不同的介质进行组合,使二者电谐振和磁谐振的频率点重合从而实现左手通带,最后利用高介电常数,低损耗的陶瓷进行样品制作并测试,测试结果证实了基于这一原理实 关键词： 全介质左手材料 介质谐振器 磁偶极子 电偶极子     

Tunable Wigner states with dipolar atoms and molecules

We study the few-body physics of trapped atoms or molecules with electric or magnetic dipole moments aligned by an external field. Using exact numerical diagonalization appropriate for the strongly correlated regime, as well as a classical analysis, we show how Wigner localization emerges with increasing coupling strength. The Wigner states exhibit nontrivial geometries due to the anisotropy of the interaction. This leads to transitions between different Wigner states as the tilt angle of the dipoles with the confining plane is changed. Intriguingly, while the individual Wigner states are well described by a classical analysis, the transitions between different Wigner states are strongly affected by quantum statistics. This can be understood by considering the interplay between quantum-mechanical and spatial symmetry properties. Finally, we demonstrate that our results are relevant to experimentally realistic systems.     

Vortices in dipolar Bose–Einstein condensates in synthetic magnetic field

We study the formation of vortices in a dipolar Bose–Einstein condensate in a synthetic magnetic field by numerically solving the Gross–Pitaevskii equation. The formation process depends on the dipole strength, the rotating frequency, the potential geometry, and the orientation of the dipoles. We make an extensive comparison with vortices created by a rotating trap, especially focusing on the issues of the critical rotating frequency and the vortex number as a function of the rotating frequency. We observe that a higher rotating frequency is needed to generate a large number of vortices and the anisotropic interaction manifests itself as a perceptible difference in the vortex formation. Furthermore, a large dipole strength or aspect ratio also can increase the number of vortices effectively. In particular, we discuss the validity of the Feynman rule.     

Crystal-field induced dipoles in heteropolar crystals II: Physical significance

The significance of dipole moments induced by crystal fields in heteropolar crystals is discussed with respect to some aspects of solid state physics. Experimental results from structural analyses that provide data on induced dipoles are summarized. The concept of ionic radii is reconsidered, and a new tabulation scheme is proposed in terms of deformed charge distributions. It is shown that spontaneous polarization as well as the pyro- and piezoelectric coefficients are not independent sets of crystallographic constants, but are accounted for by the structural parameters, the ionic polarizabilities and the elastic constants. The dipole concept is extended to statistically induced or random dipoles. They can account for an important part of the binding energy of substitutionally disordered and non-stoichiometric compounds and, therefore, are concluded to stabilize disorder in solids.     

Equilibrium values and dynamics of the net magnetic moment of a system of magnetic dipoles

Equilibrium states of different systems formed by coupled spherical bodies with dipole magnetic moments have been investigated using a numerical analysis. The bistable states and the corresponding values of the net magnetic moment are determined for a number of planar and three-dimensional systems of dipoles, and the conditions providing the existence of orientational configurations of coupled dipoles involved in the bistability are analyzed. The disturbances of the magnetic moment due to the quasi-static passage of an additional dipole and the dynamic modes excited by a homogeneous alternating magnetic field and represented by periodic, quasi-periodic, and chaotic oscillations of the magnetic moment of the system are considered for several types of systems. The bifurcation diagrams of the dynamic modes are constructed, and the specific features typical of the systems under consideration are revealed.     

Force law in material media,hidden momentum and quantum phases

We address to the force law in classical electrodynamics of material media, paying attention on the force term due to time variation of hidden momentum of magnetic dipoles. We highlight that the emergence of this force component is required by the general theorem, deriving zero total momentum for any static configuration of charges/currents. At the same time, we disclose the impossibility to add this force term covariantly to the Lorentz force law in material media. We further show that the adoption of the Einstein–Laub force law does not resolve the issue, because for a small electric/magnetic dipole, the density of Einstein–Laub force integrates exactly to the same equation, like the Lorentz force with the inclusion of hidden momentum contribution. Thus, none of the available expressions for the force on a moving dipole is compatible with the relativistic transformation of force, and we support this statement with a number of particular examples. In this respect, we suggest applying the Lagrangian approach to the derivation of the force law in a magnetized/polarized medium. In the framework of this approach we obtain the novel expression for the force on a small electric/magnetic dipole, with the novel expression for its generalized momentum. The latter expression implies two novel quantum effects with non-topological phases, when an electric dipole is moving in an electric field, and when a magnetic dipole is moving in a magnetic field. These phases, in general, are not related to dynamical effects, because they are not equal to zero, when the classical force on a dipole is vanishing. The implications of the obtained results are discussed.     

Tuning the dipolar interaction in quantum gases

We have studied the tunability of the interaction between permanent dipoles in Bose-Einstein condensates. Based on time-dependent control of the anisotropy of the dipolar interaction, we show that even the very weak magnetic dipole coupling in alkali gases can be used to excite collective modes. Furthermore, we discuss how the effective dipolar coupling in a Bose-Einstein condensate can be tuned from positive to negative values and even switched off completely by fast rotation of the orientation of the dipoles.     

Thermodynamic Limit for Dipolar Media

We prove existence of a shape- and boundary-condition-independent thermodynamic limit for fluids and solids of identical particles with electric or magnetic dipole moments. Our result applies to fluids of hard-core particles, to dipolar soft spheres and Stockmayer fluids, to disordered solid composites, and to regular crystal lattices. In addition to their permanent dipole moments, particles may further polarize each other. Classical and quantum models are treated. Shape independence depends on the reduction in free energy accomplished by domain formation, so our proof applies only in the case of zero applied field. Existence of a thermodynamic limit implies texture formation in spontaneously magnetized liquids and disordered solids analogous to domain formation in crystalline solids.     

Magnetic Properties of Dipolar Chains in Ferrofluids

We have investigated the dipole interaction energies per particle and the local dipole field distributions in a frozen-magnetization model of a ferrofluid chain in a saturating magnetic field. A lognormal distribution of particle diameters was assumed. The interaction energies were calculated for one-dimensional arrays of dipoles with moments parallel to the chain. We have computed the energies by various approximations related to the hard sphere particle diameter distribution. A similar approach was followed for the local field distributions. It was found that the energy per particle and mean local field were largely determined by the mean particle diameter, but the distribution of local fields was sensitive to both the mean diameter and the assumptions about spatial correlations between particles of different size. Detailed results are presented for water-soluble Fe₃O₄/PAA (polyacrylic acid).     

Surface-plasmon-polariton-assisted dipole-dipole interaction near metal surfaces

We investigate the surface plasmon polariton (SPP)-assisted interaction between two dipoles near a metal surface. The radiation energy from a dipole can excite SPPs and transport to another dipole through the channel of the localized SPP modes. This energy transfer can be much more efficient than direct energy transfer via dipole-dipole radiation interaction in free space. A simple analytical model is proposed to describe the underlying physics behind the influence of SPP on the dipole-dipole interaction energy, and it predicts a wide variety of complicated interaction features that agree well with rigorous calculations.