Structure and melting of dipole clusters

Two-dimensional clusters of particles, repelling due to dipole-dipole interactions and confined by an external parabolic potential, are considered. The model describes different physical systems, particularly electrons in semiconductor structures, or electrons above a drop of He near a metal electrode, a drop of colloid liquid etc. Two kinds of ordering are in competition in the clusters: a triangular lattice and a shell structure. The ground-state configurations corresponding to the local and global minima of the potential energy for clusters with N = 1 – 40 “particles” are calculated. The structure, the potential energy and the radial and angular r.m.s. displacements as functions of temperature are also calculated. Analysing these quantities the melting of clusters is studied. One- or two-stage melting occurs depending on the number of particles in the cluster. In the case of clusters consisting of two shells melting has two stages: at lower temperature reorientation of neighbouring shells (“orientational melting”) arises; at much higher temperatures the radial shell order disappears. In clusters consisting of more than two shells total melting occurs as a first-order one-stage transition (analogously to a dipole crystal). This is connected with the barrier of rotation being less than the barrier of interchange of particles between shells for small microclusters while the barriers are of equal order for clusters with a greater number of particles.     

Structure, melting, and potential barriers in mesoscopic clusters of repulsive particles

This paper discusses two-dimensional mesoscopic clusters of particles that repel according to dipole, Coulomb, and logarithmic laws and are confined by an external parabolic potential. These models describe a number of physical systems, in particular, electrons in semiconductor structures or on a liquid-helium surface allowing for image forces, indirect excitons in coupled semi-conductor dots, and a small number of vortices in an island of a second-order superconductor or in superfluid helium. Two competing forms of ordering are detected in the particles in the mesoscopic clusters-the formation of a triangular lattice or of a shell structure. The temperature dependences of the potential energy, the mean-square radial and angular deviations, the radial and angular distributions of the particles, and the distribution of the particles over the local minima are studied. Melting in mesoscopic clusters occurs in two stages: at lower temperatures, there is orientation melting, from the frozen phase into a phase with rotational reorientation of “crystalline” shells with respect to each other; subsequently, a transition occurs in which the radial order disappears. Melting in dipole macroclusters occurs in a single stage. However, in Coulomb and logarithmic macroclusters, orientation melting occurs only for the outer pairs of shells. Orientation melting is also detected in three-dimensional Coulomb clusters. A connection is established between the character of the melting and the ratio of the energy barriers that describe the breakdown of the orientational and radial structure of a cluster. Zh. éksp. Teor. Fiz. 116, 2012–2037 (December 1999)     

Two-dimensional mesoscopic vortex clusters in a superconducting ring: Shell structure and melting

The structure and phase transitions in the mesoscopic system of vortices in a quasi-two-dimensional superconducting ring are investigated. The shell structure of the mesoscopic system of vortices is studied, and its variation with the number of vortices and the parameters of the superconducting ring is analyzed. Two mechanisms of formation of new shells in vortex clusters with an increasing number of vortices in an increasing magnetic field are discovered: the generation of a new shell in a cluster and the splitting of the internal shell into two shells. The melting of vortex clusters and their thermodynamic parameters are analyzed using the Monte Carlo method. It is found that the melting of shell-type clusters occurs in two stages, orientation melting taking place at the lower temperature (during which nearly crystalline adjacent shells start rotating relative to each other) and blurring of the vortex structure occurring at the higher temperature. The shells obtained by splitting upon an increase in the number of vortices do not participate in orientational melting. The two-stage form of melting is associated with the smaller height of potential barriers being surmounted during the rotation of shells relative to one another as compared to the barrier for vortices jumping from one shell to another.     

Structure and melting of dipole clusters

Two-dimensional microclusters made up of particles repelled by the dipole law and confined by an external quadratic potential are considered. The model describes a number of physical systems, in particular, electrons in semiconductor structures near a metallic electrode, indirect excitons in coupled semiconductor dots etc. Two competing types of particle ordering in clusters have been revealed: formation of a triangular lattice and of a shell structure. Equilibrium configurations of clusters with N=1–40 particles are calculated. Temperature dependences of the structure, potential energy, and mean-square radial and angular displacements are studied. These characteristics are used to investigate cluster melting. Melting occurs in one or two stages, depending on N. Melting of a two-shell microcluster takes place in two stages: at low temperatures—from the frozen phase to a state with rotationally reoriented “crystalline” shells with respect to one another, followed by a transition involving breakdown of radial order. Melting in a cluster made up of a larger number of shells occurs in one stage. This is due to the fact that the potential barrier to intershell rotation is substantially lower than that to particle jumping from one shell to another for small N, and of the same order of magnitude for large N. A method is proposed for predicting the character of melting in shell clusters by comparing the potential barriers for shell rotation and intershell particle jumping. Fiz. Tverd. Tela (St. Petersburg) 40, 1379–1386 (July 1998)     

Magnetic properties of Lu2Co17−xSix single crystals

The Co-sublattice anisotropy in Lu₂Co₁₇ consists of four competitive contributions from Co atoms at crystallographically different sites in the Th₂Ni₁₇-type of crystal structure, which result in the appearance of a spontaneous spin-reorientation transition (SRT) from the easy plane to the easy axis at elevated temperatures. In order to investigate this SRT in detail and to study the influence of Si substitution for Co on the magnetic anisotropy, magnetization measurements were performed on single crystals of Lu₂Co_17−xSi_x (x=0−3.4) grown by the Czochralski method. The SRT in Lu₂Co₁₇ was found to consist of two second-order spin reorientations, “easy-plane”–“easy-cone” at T_SR1≈680 K and “easy-cone”–“easy-axis” at T_SR2≈730 K. Upon Si substitution for Co, both SRTs shift toward the lower temperatures in Lu₂Co₁₆Si (T_SR1≈75 K and T_SR2≈130 K) with the further onset of the uniaxial type of magnetic anisotropy in the whole range of magnetic ordering for Lu₂Co_17−xSi_x compounds with x>1 due to a weakening of the easy-plane contribution from the Co atoms at the 6g and 12k sites to the total anisotropy.     

Characteristic features of the melting of two-dimensional mesoscopic Wigner clusters

Two-dimensional Wigner microclusters in a semiconductor dot are studied. Their melting is investigated in detail and it is shown that, for typical mesoscopic clusters possessing a shell structure, melting occurs in two stages: orientational melting (rotation of the shells relative to one another) and total melting, where the shells start to overlap with one another and exchange particles. An example of a “magic” microstructure which has a triangular structure and melts in a single stage is presented. For this, the temperature dependences of various quantities characterizing cluster structure are investigated. The change in the distribution of cluster configurations over local minima of the potential energy with increasing temperature is investigated. At temperatures below the temperature of total melting, a cluster is always located near the configuration of a global minimum and, at temperatures above the temperature of complete melting, a cluster can be located with finite probability near configurations corresponding to various local minima of the potential energy. Fiz. Tverd. Tela (St. Petersburg) 41, 1499–1504 (August 1999)     

Two-dimensional microclusters of vortices: Shell structure and melting

The melting of two-dimensional microclusters of “particles” which repel one another according to a logarithmic law and are confined by an external quadratic potential is investigated. The model describes Abrikosov vortices in a superconducting island of vortices in a rotating superfluid liquid and electrons in a semiconductor nanostructure surrounded by a low-permittivity medium. The structure of clusters and its dependence on temperature and melting are investigated. The melting of microclusters of vortices proceeds in two stages: 1. A transition from a frozen phase into a state corresponding to rotational reorientation of crystal shells relative to one another. 2. At a higher temperature, the radial order vanishes. This is connected with the fact that the barrier for rotation of the shells is much lower than the barrier for radial breakup of the shells. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 3, 268–273 (10 February 1997)     

Molecular dynamics study of orientational melting and thermodynamic properties of C<Subscript>60</Subscript>@C<Subscript>240</Subscript> nanoparticles

The barriers to relative shell rotation and other energy characteristics of C₆₀@C₂₄₀ two-shell carbon nanoparticles (“onions”) with outer shells of different shapes are calculated. The disturbance of the orientational order in the mutual arrangement of shells with an increase in temperature (orientational melting) is studied by the molecular dynamics method. The intershell orientational diffusion is represented by the Arrhenius relationship, and the Arrhenius parameters are calculated numerically. A definition is proposed for the temperature of short-range order disturbance in systems that undergo melting without structural change. The calculated temperature of orientational melting of the C₆₀@C₂₄₀ nanoparticle is approximately equal to 60 K.     

On long-range order in low-dimensional lattice-gas models of nematic liquid crystals

The problem of the orientational ordering transition for lattice-gas models of liquid crystals is discussed in the low-dimensional case d = 1, 2. For isotropic short-range interactions, orientational long-range order at finite temperature is excluded for any packing of molecules on the lattice Z^d; on the other hand, for reflection-positive long-range isotropic interactions, we prove the existence of an orientational ordering transition for high packing (μ > μ₀) and low temperatures (β > β_c(μ)).     

Mesoscopic and macroscopic dipole clusters: Structure and phase transitions

A two dimensional (2D) classical system of dipole particles confined by a quadratic potential is studied. This system can be used as a model for rare electrons in semiconductor structures near a metal electrode, indirect excitons in coupled quantum dots etc. For clusters of N ≤ 80 particles ground state configurations and appropriate eigenfrequencies and eigenvectors for the normal modes are found. Monte-Carlo and molecular dynamic methods are used to study the order-disorder transition (the “melting” of clusters). In mesoscopic clusters (N < 37) there is a hierarchy of transitions: at lower temperatures an intershell orientational disordering of pairs of shells takes place; at higher temperatures the intershell diffusion sets in and the shell structure disappears. In “macroscopic” clusters (N > 37) an orientational “melting” of only the outer shell is possible. The most stable clusters (having both maximal lowest nonzero eigenfrequencies and maximal temperatures of total melting) are those of completed crystal shells which are concentric groups of nodes of 2D hexagonal lattice with a number of nodes placed in the center of them. The picture of disordering in clusters is compared with that in an infinite 2D dipole system. The study of the radial diffusion constant, the structure factor, the local minima distribution and other quantities shows that the melting temperature is a nonmonotonic function of the number of particles in the system. The dynamical equilibrium between “solid-like” and “orientationally disordered” forms of clusters is considered.     

Order-disorder transition in a system of magnetic holes

Polystyrene spheres of the same size (10–100μm) dispersed in ferrofluid produce voids, which have been denoted magnetic holes. A two-dimensional system of interacting magnetic holes confined between two glass plates and subject to rotating magnetic fields in the sample plane are studied in a light microscope. For low frequencies of the field rotation, the holes form pairs, which arrange themselves in a regular triangular lattice when stabilized with a weak constant field normal to the sample plane. By increasing the frequency of the rotating field, we observe that above a critical frequency, the steady forward rotation of the pairs is interrupted by backward rotations in short time intervals. Because the intervals of backward rotation occur at different times for each individual pair, disorder is introduced in the system, and the triangular lattice of pairs “melts” and forms a liquid-like structure at high rotation frequencies of the field. This “melting” transition is observed both directly and in light scattering experiments using a laser.     

The magnetic anisotropy of samarium-alnico pseudobinary alloys

The anisotropy properties of samarium-Alnico V pseudobinary alloys have been investigated. With alloys containing less than 12.0 mol% samarium, the K₁ values are negative at 77 K and increase with increasing temperature to approximately zero at room temperature. The K₂ values remain positive at all temperatures. We do not find the easy cone that has long been thought to be existed in those alloys with K₁ < 0 and K₂ #62; 0. In alloys with samarium contents between 13.3 and 19.0 mol%, the K₁ and K₂ values are positive at all temperatures. The anisotropy fields are not changed monotonically in the whole range of 10.1 to 19.0 mol% of samarium. It is concluded that the alloys are characteristics in thermodynamically of first-order transition. We have found that the “hard cone” exists in each of those alloys with samarium content more than 16.0 mol% and at temperatures above 77 K. The alloys with samarium less that 13.4 mol% also have “hard cone” under 77 K. However, the observed “hard cone” is different from the well known one in the first-order magnetization process, and it will collapse to the easy axis when the measuring field and temperature increase while under room temperature.     

Multivortex states in large pinning centers

We have studied the vortex pinning in the large centers, i.e. in the spatial regions with the characteristic size a comparable with the London lenght λ. It is shown that the type of configuration and the number of vortices in the cluster are dependent on the ration a/λ and change nonmonotonically with the temperature. The influence of such vortex clusters on the decay of magnetization and the current-voltage characteristics are discussed. The important role of the potential barrier for the penetration of vortices into the pinning center is shown. The new state of vortex cluster, “vortex polaron”, is predicted. The stability of the multivortex state is discussed.     

Factorization and the soft overlap contribution to heavy-to-light form factors

Using the formalism of soft-collinear effective theory, a complete separation of short- and long-distance contributions to heavy-to-light transition form factors at large recoil is performed. The universal functions ζ_M(E) parameterizing the “soft overlap” contributions to the form factors are defined in terms of matrix elements in the effective theory. Endpoint configurations corresponding to kinematic situations where one of the valence partons in the external mesons carries very small momentum are accounted for in terms of operators involving soft-collinear messenger fields. They contribute at leading order in Λ_QCD/E and spoil factorization. An analysis of operator mixing and renormalization-group evolution in the effective theory reveals that the intermediate scale is without significance to the soft functions ζ_M(E), and that the soft overlap contribution does not receive a significant perturbative (Sudakov) suppression.     

Anisotropic defect-mediated melting of two-dimensional colloidal crystals

The melting transition of anisotropic two-dimensional (2D) crystals is studied in a model system of superparamagnetic colloids. The anisotropy of the induced dipole-dipole interaction is varied by tilting the external magnetic field off the normal to the particle plane. By analyzing the time-dependent Lindemann parameter as well as translational and orientational order we observe a 2D smecticlike phase. The Kosterlitz-Thouless-Halperin-Nelson-Young scenario of isotropic melting is modified: dislocation pairs and dislocations appear with different probabilities depending on their orientation with respect to the in-plane field.     

Zero field μ spin relaxation in Cd1−xMnxTe diluted magnetic semiconductors

Zero field μSR measurements were carried out on samples of the typical diluted magnetic semiconductor Cd_1−xMn_xTe as a function of composition in the range 0.27x0.65, at temperatures in both the “spin glass’ regions of the magnetic phase diagram. The results show the onset of complex diffusion-trapping behaviour at temperatures T60 K for all concentrations. Below 50 K the exponential relaxation found for the main signal is consistent with the interactions of the muon spin with rapidly fluctuating and rather large local hyperfine fields in these concentrated random diluted magnetic systems. In spite of the loss of signal near and below the transition temperature, the present results show that rapid spin fluctuations persist below T_g.     

Properties of a local pairing model of high-Tc superconductivity

A simulation technique is used to study the properties of the “hole modulated hopping” model introduced by Hirsch. The superconducting order parameter, energy gap and pair size have been determined for a range of particle densities and temperatures in the neighbourhood of the superconducting phase transition. Results are consistent with the interpretation of the superconducting transition to be Bose-like at low hole densities and BCS-like at high hole densities, with a crossover near the T_c maximum in the T_c versus hole density curve. This behaviour is related to the existence of small non-overlapping pairs at low hole densities and large strongly interpenetrating pairs at hole densities above the T_c maximum.     

Melting properties of two-dimensional multi-species colloidal systems in a parabolic trap

The angular and radial melting properties of two-dimensional classical systems consisting of different types of particles confined in a parabolic trap are studied through modified Monte Carlo simulations. A universal behavior of the angular melting process is found, which occurs in multiple steps due to shell depended melting temperatures. The melting sequence of the different shells is determined by two major factors: (1) the confinement strength which each shell is subjected to, and (2) the specific structure of each shell. Further, a continuous radial disordering of the particle types forming a single circular shell is found and analyzed. This phenomenon has never been observed before in two-dimensional mono-dispersive systems. This continuous radial disordering results from the high energy barrier between different particle types in multi-species systems.     

Melting behavior of large disordered sodium clusters

The melting-like transition in disordered sodium clusters Na₉₂ and Na₁₄₂ is studied by performing density functional constant-energy molecular dynamics simulations. The orbital-free version of the density functional formalism is used. In Na₁₄₂ the atoms are distributed in two distinct shells (surface and inner shells) and this cluster melts in two steps: the first one, at ≈130 K, is characterized by the development of a high intrashell atomic mobility, and the second, homogeneous melting at ≈270 K, involves diffusive motion of all the atoms across the whole cluster volume. On the contrary, the melting of Na₉₂ proceeds smoothly over a very broad temperature interval, without any abrupt change in the thermal or structural indicators. The occurrence of two steps in the melting transition is suggested to be related to the existence of a grouping of the atoms in radial shells, even if those shells present a large degree of internal disorder. It then appears that a cluster can be considered fully amorphous (totally disordered) only when there are no radial regions of low atomic density separating shells. The isomer of Na₉₂ studied here fulfills this criterion and its thermal behavior can be considered as representative of that expected for fully amorphous clusters. Disordered Na₁₄₂, on the other hand, that has a discernible structure of an inner and a surface shell, should be considered as not fully disordered. The thermal behavior of these two clusters is also compared to that of icosahedral (totally ordered) sodium clusters of the same sizes. Received 5 February 2001 and Received in final form 21 May 2001     

High-resolution gamma-ray spectroscopy of ΛLi

We report on the first observation of hypernuclear γ transitions using germanium detectors. Using a large-acceptance Ge detector system, we observed two γ transitions in _Λ⁷Li, the spin-flip transition at 689±4keV and the transition at 2050±2 keV (preliminary). The strength of the ΛN spin-spin interaction is derived from the energy of the former transition. As for the latter transition, B(E2) was measured to be 3.9±0.6±0.4 e²fm⁴ (preliminary), which indicates a shrinkage of the nuclear size of _Λ⁷Li from ⁶Li and confirms “glue-like role” of Λ.