Possible path to a new class of ferromagnetic and half-metallic ferromagnetic materials

We introduce a path to a possibly new class of magnetic materials whose properties are determined entirely by the presence of a low concentration of specific point defects. Using model Hamiltonian and ab initio band structure methods we demonstrate that even large band gap nonmagnetic materials as simple as CaO with a small concentration of Ca vacancies can exhibit extraordinary properties. We show that such defects will initially bind the introduced charge carriers at neighboring sites and depending on the internal symmetry of the clusters so formed, will exhibit "local" magnetic moments which for concentrations as low as 3% transform this nonmagnetic insulator into a half-metallic ferromagnet.     

Probing the out-of-plane distortion of single point defects in atomically thin hexagonal boron nitride at the picometer scale

Crystalline systems often lower their energy by atom displacements from regular high-symmetry lattice sites. We demonstrate that such symmetry lowering distortions can be visualized by ultrahigh resolution transmission electron microscopy even at single point defects. Experimental investigation of structural distortions at the monovacancy defects in suspended bilayers of hexagonal boron nitride (h-BN) accompanied by first-principles calculations reveals a characteristic charge-induced pm symmetry configuration of boron vacancies. This symmetry breaking is caused by interlayer bond reconstruction across the bilayer h-BN at the negatively charged boron vacancy defects and results in local membrane bending at the defect site. This study confirms that boron vacancies are dominantly present in the h-BN membrane.     

Reversal-field memory in the hysteresis of spin glasses

We report a novel singularity in the hysteresis of spin glasses, the reversal-field memory effect, which creates a nonanalyticity in the magnetization curves at a particular point related to the history of the sample. The origin of the effect is due to the existence of a macroscopic number of "symmetric clusters" of spins associated with a local spin-reversal symmetry of the Hamiltonian. We use first order reversal curve (FORC) diagrams to characterize the effect and compare to experimental results on thin magnetic films. We contrast our results on spin glasses to random magnets and show that the FORC technique is an effective "magnetic fingerprinting" tool.     

Controlled nucleation of point defects on a disclination line near a free surface during smectic-A-to-nematic directional melting

A disclination line populated with point defects that break the translational symmetry forms near a free nematic (N) interface in a confined geometry. The disclination line is, however, absent in the smectic-A phase (SmA). We use this fact to control the formation of point defect distributions on a disclination line by directional melting of the SmA phase in a temperature gradient. A threshold velocity ( v _th) exists below which a defect-free disclination line is formed. The frequency of nucleation of point defects increases steadily for v > v _th and exhibits a remarkable regularity. We derive an empirical scaling for v _th in terms of the experimental tuning parameters. We propose a simple model that allows to understand the formation of the point defects. Received 1 October 2002 / Published online: 15 April 2003 RID="a" ID="a"Permanent address: Departament de Quımica Fısica, Universitat de Barcelona, Martı i Franquès 1, Barcelona 08028, Spain; e-mail: jignes@qf.ub.es     

Equilibrium configurations and energetics of point defects in two-dimensional colloidal crystals

We demonstrate a novel method of introducing point defects (mono- and divacancies) in a confined monolayer colloidal crystal by manipulating individual particles with optical tweezers. Digital video microscopy is used to study defect dynamics in real space and time. We verify the numerical predictions that the stable configurations of the defects have reduced symmetry compared to the triangular lattice and discover that in addition they are characterized by distinct topological arrangements of the particles in the defect core. Surprisingly, point defects are thermally excited into separated dislocations, from which we extract the dislocation pair potential.     

Erratum to: Allowable irreducible representations of the point groups with five-fold rotational axes†

Allowable irreducible representations of the point groups with five-fold rotations – that represent the symmetry of the quasicrystals in two and three dimensions – are derived by employing the little group technique in conjunction with the solvability property. The point groups D $_{5h} ({\overline {10}}{m}2)$ and ${I}_h \left(\frac{2}{m}\overline {3} \,\overline {5}\right)$ are taken to illustrate the method.     

Nonlinear optics and the defect solid state

Abstract

The condition for the generation of second harmonics in the dipole approximation is that the nonlinear crystal medium lack a center of inversion. Conversely, a center of inversion precludes optical second harmonic generation. It is well known, however, that lattice defects introduced into a crystal may alter the local point symmetry in the medium, and in fact may convert local inversion symmetry to that which corresponds to a noncentrosymmetric point group. It is thus clear that selected defects in nonlinear media may be of interest for studying nonlinear optical processes which depend on the square of the electric field strength. The specific case of second harmonic generation employing spatially ordered FA-centers in alkali halide crystals is considered.     

Allowable irreducible representations of the point groups with five-fold rotational axes

Allowable irreducible representations of the point groups with five-fold rotations – that represent the symmetry of the quasicrystals in two and three dimensions – are derived by employing the little group technique in conjunction with the solvability property. The point groups D $_{5h} ({\overline {10} {\text{{\emph m}}}2})$ and ${\text{{\emph I}}}_h (\frac{2}{\text{{\emph m}}}\overline 3 \,\overline 5)$ are taken to illustrate the method.     

Residual Symmetry Reduction and Consistent Riccati Expansion of the Generalized Kaup-Kupershmidt Equation

The residual symmetry of the generalized Kaup-Kupershmidt(gKK) equation is obtained from the truncated Painlevé expansion and localized to a Lie point symmetry in a prolonged system. New symmetry reduction solutions of the prolonged system are given by using the standard Lie symmetry method. Furthermore, the g KK equation is proved to integrable in the sense of owning consistent Riccati expansion and some new B¨acklund transformations are given based on this property, from which interaction solutions between soliton and periodic waves are given.     

Anelasticity and stress-induced ordering of point defects in crystals

Point defects may exist in a crystal on a set of crystallographically equivalent orientations or sites. The response of a crystal containing point defects to an externally applied stress takes the form of ‘stress-induced ordering’, or preferential alignment of the defects. Recent experiments have used optical and spin resonance techniques to observe this stress-induced ordering directly. This same process also gives rise to anelasticity, e.g. to an internal friction peak. In describing such behaviour, the concept of a point defect as an ‘elastic dipole’, introduced by Kröner and others, is very useful. The elastic dipole is here defined as a second-rank tensor, the ‘λ-tensor’, equal to the average strain per mole fraction of defects all aligned in a particular orientation. This definition is then used to develop a thermodynamic theory of stress-induced ordering, which includes the interaction among defects and the possibility of a ‘reaction’ or interconversion between two species of defects. Applications of the theory are made to defects of various point symmetries in cubic crystals, and a number of specific examples are discussed to illustrate each type of defect symmetry. The usefulness of the theory is that it enables one to calculate the values of the components of the λ-tensor from experimental information and the defect symmetry. Typical values of these λ-parameters range from 10^-2 unity.     

Dislocations as linear topological defects

Dislocations and dislocation plasticity are considered and compared with such dissimilar physical phenomena as superfluidity of liquid helium and type II superconductivity. These phenomena share the common property that the dislocations, as well as quantum vortices in superconductors and superfluid helium, are topological defects. They arise during a phase transformation which is accompanied by spontaneous symmetry breaking caused by Bose condensation of acoustic phonons. The general problems of the evolution of ensembles of linear topological defects and the character of the spatial structures formed by them are discussed.     

Dynamics of surface dislocation ensembles in silicon under conditions of mechanical and magnetic perturbations

This paper reports on the results of investigations into the dynamics of surface dislocation ensembles in silicon under conditions of mechanical and magnetic perturbations. The motion of defects is described with due regard for barriers of three types, including magnetically sensitive point defects and dislocations. Within the concept of spin-dependent reactions between structural defects, a kinetic model is proposed for the magnetic-field-stimulated changes observed in the dislocation mobility due to the formation of long-lived complexes involving paramagnetic impurities. It is experimentally proved that the preliminary treatment of dislocation-containing crystals in a magnetic field (B=1 T) for 5–45 min leads to an increase in the velocity of dislocations in n-Si and p-Si samples by factors of two and three, respectively. The magnetic memory effect is observed in dislocation-containing silicon crystals. Consideration is given to the decay kinetics of the magnetic memory during storage of the silicon samples under natural conditions after magnetic treatment. The basic quantitative characteristics of the motion of linear defects in a magnetic field (for example, the partial velocities of dislocations, the dynamics of dislocation segments at stoppers of different types, and the expectation times for the appearance of the appropriate stoppers) are determined by fitting the experimental data to the theoretical results.     

Convergence analysis of stochastic hybrid bidirectional associative memory neural networks with delays

The stability property of stochastic hybrid bidirectional associate memory (BAM) neural networks with discrete delays is considered. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the delay-independent sufficient conditions to guarantee the exponential stability of the equilibrium solution for such networks are given by using the nonnegative semimartingale convergence theorem.     

Modeling abnormal strain states in ferroelastic systems: the role of point defects

Recent experiments have revealed a rich variety of strain states in doped ferroelastic systems. We study the origin of two abnormal strain states; precursory tweed and strain glass, and their relationship with the well-known austenite and martensite (the para- and ferroelastic states). A Landau free energy model is proposed, which assumes that point defects alter the global thermodynamic stability of martensite and create local lattice distortions that interact with the strain order parameters and break the symmetry of the Landau potential. Phase field simulations based on the model have predicted all the important signatures of a strain glass found in experiment. Moreover, the generic "phase diagram" constructed from the simulation results shows clearly the relationships among all the strain states, which agrees well with experimental measurements.     

The differential geometry of elementary point and line defects in Bravais crystals

Since line defects (dislocations) and point defects (vacancies, self-interstitials, point stacking faults) in Bravais crystals can mutually convert, only theories which comprise these two sorts of defects can be closed in the sense of general field theory. Since the pioneering work of Kondo and of Bilby, Bullough, and Smith it is clear that differential geometry is the appropriate mathematical tool to formulate a field theory of defects in ordered structures. This is done here on the example of the Bravais crystal, where the above-mentioned defects are the only elementary point and line defects. It is shown that point defects can be described by a step-counting procedure which makes it possible to include also point stacking faults as elementary point defects. The results comprise two equations with the appropriate interpretation of the mathematical symbols. The point defects are step-counting defects and are essentially described by a metric tensorg, which supplements the torsion responsible for the dislocations. The proposed theory is meant to form a framework for defect phenomena, in a similar way that Maxwell's theory is a framework for the electromagnetic world.     

Self-organization processes and topological defects in nanolayers in a nematic liquid crystal

Atomic force microscopy is used to study the self-organization processes that occur during the formation of topological defects in nanomolecular layers in a nematic liquid crystal with the homeotropic orientation of its molecules with respect to the substrate. In this case, a smectic monolayer with a thickness of one molecule length (about 2.2 nm) forms on the substrate, and a nanomolecular layer of a nematic liquid crystal forms above this monolayer. In such virtually two-dimensional layers, numerous different nanoclusters, namely, hut structures, pyramids, raft structures with symmetry C _nm (where n = 2, 4, 5, 6, 7, …, ∞), cones, and nanopools, form [1]. They have a regular shape close to the geometry of solid crystals. Modulated linear structures and topological point defects appear spontaneously in the nanopools and raft structures.     

耦合Burgers系统的Painlevé性质分析，对称和对称约化

本文给出了耦合Burgers系统的Painlevé性质，逆强对称算子，无穷多对称和李对称约化。通过把强对称和逆强对称算子重复多次作用到耦合Burgers模型的一些平庸对称，如恒等变换，空间平移变换和标度变换上，我们得到了三族无穷多对称。这些对称构成了无穷维李代数。用其中的有限维子代数——点李代数对模型进行对称约化，得到了模型的群不变解。     

Stretched-exponential decay laws of general defect diffusion models

We calculate a correlation function of a dipole which flips upon contact with one of the defects making generally non-Gaussian diffusions. Other than the memory effect in the fractal random walk model, the non-Gaussian property can be an origin of the stretched-exponential law of the correlation function.     

Black Hole Thermodynamics and Lorentz Symmetry

Recent developments point to a breakdown in the generalized second law of thermodynamics for theories with Lorentz symmetry violation. It appears possible to construct a perpetual motion machine of the second kind in such theories, using a black hole to catalyze the conversion of heat to work. Here we describe and extend the arguments leading to that conclusion. We suggest the inference that local Lorentz symmetry may be an emergent property of the macroscopic world with origins in a microscopic second law of causal horizon thermodynamics.     

Invariant Lie-admissible formulation of quantum deformations

In this note we outline the history of q-deformations, indicate their physical shortcomings, suggest their apparent resolution via an invariant Lie-admissible formulation based on a new mathematics of genotopic type, and point out their expected physical significance. This paper is dedicated to the memory of Larry Biedenharn, my teacher of the rotational symmetry