The effect of clamped and free boundaries on long range strain coupling in structural phase transitions

In ferroelastic structural phase transitions, the atomic ordering in one cell creates a local strain field which is propagated elastically throughout the material, resulting in an effective or indirect coupling J(R _ij ) between the ordering in cells i and j. With free boundaries on the sample, the J(R _ij ) contains a Zener-Eshelby term J _Z of infinite range, which largely determines the transition temperature T _c. The present paper shows what happens when the boundaries are clamped. On cooling from a high temperature an anomaly takes place at more or less the same temperature as the phase transition for free boundaries. Cooling results in an irregular pattern of domains with positive and negative order parameter whose long range strains cancel. Two cases are distinguished. In the “tweed” case coherent domain boundaries form easily and result in fine lamellar domains. When coherent domain boundaries are not possible (the “non-Sapriel”) case, larger less regular domains are formed. In either case the macroscopic net strain adds up to zero.     

Influence of induced uniaxial anisotropy on the domain structure and phase transitions of yttrium-iron garnet films

The effect of induced uniaxial anisotropy on the properties and parameters of the domain structure and phase transitions in yttrium-iron garnet (YIG) films is investigated. Based on the measurements and the derived formulas we determine the difference between the magnetization and the uniaxial anisotropy field for each of the films. We have also measured the parameters of the domain structures and phase transitions of the films for the magnetization parallel and perpendicular to the projections of the [111] crystallographic axes onto the plane of the film. We find that films of pure YIG films grown in (111) are characterized by the existence of some critical value of the uniaxial anisotropy field. It is found that for films in which the uniaxial anisotropy field is larger than this critical value and films in which it is less than this critical value, such parameters of the domain structures as the ratio of the width of the domains to the film thickness, the orientation of the magnetization of the domains, the orientation of the domain boundaries, and the magnitudes of the phase transition fields differ substantially. Fiz. Tverd. Tela (St. Petersburg) 41, 2034–2041 (November 1999)     

极性相变的介电谱研究

用时域和频域方法研究了(Ba_1-xSr_x)TiO₃陶瓷的极性相变.类似于单晶的铁电相变所观察到的晶格软化,屏蔽电荷激发和畴运动讯号外,在陶瓷中还出现空间电荷运动的强讯号.空间电荷和电畴属于凝聚态物质的高级结构,它提供慢极化效应.慢效应使频域测量结果不能得到确定值.从统计观点给出高级结构的历史记忆效应对频域测量结果的影响;解释了频域介电常量的倒数在一级结构的转变中发生线性软化,而在高级结构的转变中发生抛物型软化. 关键词：     

Ginzburg-Landau-type theory of antiphase boundaries in polytwinned structures

The conventional Ginzburg-Landau theory of interphase boundaries is generalized to values of order parameters that are not small, with application to polytwinned structures characteristic of cubic-tetragonal-type phase transitions. Explicit expressions for the structure and energy of antiphase boundaries via the functions entering the free-energy functional are given. A peculiar dependence of equilibrium orientations of antiphase boundaries on the interaction type is predicted, and it qualitatively agrees with the available experimental data.     

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.     

Magnetic states of small cubic particles with uniaxial anisotropy

The lowest energy states in small cubic particles with uniaxial anisotropy are explored as a function of anisotropy strength and particle size. The investigations result in a phase diagram which contains the boundaries between the regions of one, two and three domains (flower, vortex and double vortex states). While the general features of the phase diagram are derived from energy estimates based on domain theory, the details are obtained using numerical micromagnetics. The two-domain and the three-domain phase can be subdivided into subphases. The comparison between different configurations revealed that a twisted vortex configuration with an S-shaped domain wall replaces the symmetric vortex with a straight wall at larger sizes. The three-domain phase contains two subphases which are symmetric with respect to (1 0 0) and (1 1 0) mirror planes, respectively. The transition from two to three domains occurs into the (1 1 0)-three-domain-state (diagonal state). This structure can be described as a configuration with two (quarter-) circular domain walls in two opposing corners. However, this configuration is energetically favored only in a small region within the phase diagram relative to the (1 0 0)-symmetry three-domain state with straight walls (sandwich state).     

Metric-Space Approach for Distinguishing Quantum Phase Transitions in Spin-Imbalanced Systems

Metric spaces are characterized by distances between pairs of elements. Systems that are physically similar are expected to present smaller distances (between their densities, wave functions, and potentials) than systems that present different physical behaviors. For this reason, metric spaces are good candidates for probing quantum phase transitions, since they could identify regimes of distinct phases. Here, we apply metric space analysis to explore the transitions between the several phases in spin-imbalanced systems. In particular, we investigate the so-called FFLO (Fulde-Ferrel-Larkin-Ovchinnikov) phase, which is an intriguing phenomenon in which superconductivity and magnetism coexist in the same material. This is expected to appear for example in attractive fermionic systems with spin-imbalanced populations, due to the internal polarization produced by the imbalance. The transition between FFLO phase (superconducting phase) and the normal phase (non-superconducting) and their boundaries have been subject of discussion in recent years. We consider the Hubbard model in the attractive regime for which density matrix renormalization group calculations allow us to obtain the exact density function of the system. We then analyze the exact density distances as a function of the polarization. We find that our distances display signatures of the distinct quantum phases in spin-imbalanced fermionic systems: with respect to a central reference polarization, systems without FFLO present a very symmetric behavior, while systems with phase transitions are asymmetric.     

Reorientation,multidomain states and domain walls in diluted magnetic semiconductors

The competition between surface/interface and intrinsic anisotropies yields a number of specific reorientation effects and strongly influences magnetization processes in diluted magnetic semiconductors as (Ga,Mn)As and (In,Mn)As. We develop a phenomenological theory to describe reorientation transitions and the accompanying multidomain states applicable to layers of these magnetic semiconductors. It is shown that the magnetic phase diagrams of such systems include a region of four-phase domain structure with four adjoining areas of two-phase domains as well as several regions with coexisting metastable states. We demonstrate that the parameters of isolated domain walls in (Ga,Mn)As nanolayers are extremely sensitive to applied magnetic field and can vary in a broad range. This can be used in microdevices of magnetic semiconductors with pinned domain walls. For (Ga,Mn)As epilayers with perpendicular anisotropy the geometrical parameters of domains have been calculated.     

Phase transitions, stability, and dielectric response of the domain structure in ferroelectric-ferroelastic thin films

The first analytical study of phase transitions and domain structure in ferroelastic-ferroelectric epitaxial thin films is presented for an exactly solvable model. The emerging domain structure with domains of equal width (which may be exponentially large) remains stable irrespective of the film thickness. Shifts of the domain walls, unexpectedly, contribute nothing (or insignificantly) to the dielectric response of the film. Generally, the motion of the domain walls results in about the same contribution to the response as the one that comes from a standard bulk term. Therefore, no particular softening of the dielectric response is expected to occur due to the motion of domain walls.     

Exomorphic types of equitranslational phase transitions

A group theoretical classification of phase transitions based on their abstract similarity (exomorphism) is suggested. Exomorphic phase transitions have the same potentials (in absence of external fields) and the same domain structure. The existing 44 exomorphic types of equitranslational phase transitions are listed.     

Theory of switching of multiaxial ferroelectrics (Initial stage)

The classical theory of nucleation and growth is used to study the thermodynamics and kinetics of switching of multiaxial ferroelectrics. The initial stage of 180°-and 90°-domain switching is studied in the tetragonal, orthorhombic, and trigonal phases. The multidimensional kinetic theory of first-order phase transitions is applied to describe the initial stage of switching of ferroelectric crystals in the general case where three-dimensional growth (along the radius and height) of repolarized domains occurs. The energy of nucleus formation is calculated in the vicinity of the saddle point of an activation barrier in the space of sizes and shapes, and the dependence of the critical domain size on the switching field is found. The two-dimensional Fokker-Planck kinetic equation is reduced to a one-dimensional Zel’dovich equation, and a stationary solution to the Zel’dovich equation is obtained. The diffusion coefficients are derived in the size space for the normal and layer-by-layer mechanisms of domain growth. The main characteristic of the initial switching stage, namely, the steadystate flux of repolarized domains, is found as a function of the applied field.

     

Order—disorder phase transitions in domain structures of ferrite—garnet films

Order—order and order—disorder phase transitions in the domain structure of ferrite—garnet films upon a change in temperature or magnetic field were studied. It was shown that the structure of the domain boundaries affects the type of the phase transitions.     

Group analysis of domains and domain pairs

Basic symmetry properties of transformation twins and of ferroelectric or ferromagnetic domains are examined in terms of the abstract group theory. It is shown that the crystallographical relations between domains (twin components) and between domain pairs can be deduced from the decomposition of the symmetry group of the high symmetry phase into the left and double cosets of the group of the low symmetry phase. Expressions are derived for the numbers of proper and improper domains, for the number of crystallographically equivalent low symmetry phases, and for the number of crystallographically non-equivalent domain pairs. A classification of domain pairs according to their symmetry is proposed. The domain structure of the monoclinic phase in WO₃ and the Dauphiné twinning in quartz are analysed as illustrative examples.     

The ground-state phase diagram of the spinless 1D falicov-kimball model: Numerical studies

Extrapolation of small-cluster exact-diagonalization calculations is used to study the ground state phase diagram of the spinless one-dimensional Falicov-Kimball model at half filling. Our results show that the phase diagram has an extremely simple structure for the Coulomb interactionsU≥2. Here the ground states are the most homogeneous configurations (mhc) with the smallest periods. Valence transitions are discontinuous and only of the type insulator-insulator. In this region the finite size effects are negligible and thus the picture of valence transitions is definitive. ForU<2 the phase diagram exhibits a more complicated structure. Here we have specified a domain where the ground states are the mhc and a metallic domain where the ground states are mixtures of configurations with the empty configuration. The boundary between these two domains is the boundary of discontinuous insulator-metal transitions. Unlike the caseU≥2 the valence transitions are gradual in the weak coupling limit. This work was supported by the Slovak scientific grant agency VEGA, contract No. 4177/97.     

Wetting phenomena in the (3 × 1) phase of a model for H on Fe(110)

Interfaces between the three physically distinct, but equivalent domains in the (3 × 1) phase of a lattice gas model for the adsorbate system H/Fe(110) and its Ising analog are studied. In the ground state two types of wetting transitions are found where a light or a heavy domain wall decomposes into two heavy or two light walls separated by the third domain. These transitions give rise to wetting lines in the phase diagram which are located using Monte Carlo techniques.     

Diamagnetic length scales of the Condon domain phase in Lifschitz–Kosevich–Shoenberg approximation

Equilibrium properties of the non-uniform diamagnetic phase in normal metals (Condon domains) are studied theoretically in the framework of Lifschitz–Kosevich–Shoenberg (LKS) approximation. It is found that characteristic diamagnetic lengths of the phase, e.g. a period of the domain structure and width of interface boundary between domains, as well as specific surface energy of domain wall, are strongly affected by electron correlations and depend on temperature, magnetic field and purity of the sample. The developed theory is in a good agreement with existent experiment data.     

Phase transformations of the magnetic structure in film nanobridges

The magnetic structure of a plane nanobridge consisting of two ferromagnetic film electrodes connected by a nanosized crossbar of the same material is studied. Due to their magnetoresistive properties, such bridges are of considerable interest for microelectronics. Using a numerical micromagnetics method, it is shown that a domain wall is displaced from the center of the bridge crossbar as the anisotropy constant of the system decreases and reaches a critical value. A phase diagram is constructed, which makes it possible to determine the possible magnetic states of real nanobridges. The mechanism of the phase transformation is described in terms of an analytical model. This model explains the shape of the phase diagram of the nanobridge. Formally, the transformations of the magnetic structure of the nanocontact can be described in terms of the Landau theory of phase transitions in a certain range of parameters of the system.     

Phenomenological theory of pressure-induced equilibrium phase transitions: The mott model

A theory is constructed for the pressure-induced phase transitions caused by a strong nonlinear dependence of nonequilibrium potential on the mean deformation of a crystal’s unit cell. Four distinctions are revealed between such phase transitions and the transitions described by a Fermi model (i.e., those related to the inversion of lower energy levels in elements of the structure). Examples of the pressure4nduced phase transitions described by the Mott model are given.     

Elastic phase transitions in plutonium

The rich phase diagram of plutonium with a large number of different transitions in a narrow temperature interval has been puzzling scientists for decades. We offer a theoretical proof that most of the structural transformations in plutonium at temperatures exceeding the Debye temperature are the elastic phase transitions. The proof is given in the framework of the Landau theory of phase transitions and space group theory taking into account the anomalously small value of the elastic shear constants related to tetragonal and orthorhombic lattice deformations.     

Ferroelastic domain structure of (CH3)4N CdCl3 (TMCC) crystal

The ferroelastic domain structure and the phase boundaries of TMCC have been studied in the temperature range 114-90 K by direct observation under polarised light. By applying an external, compressive and unidirectional mechanical stress the ferroelastic character of the domain structure has been confirmed. The orientation of the domain walls and phase boundaries are analysed. To characterise quantitatively the observed domain wall distribution the classical symmetry approach, based on the criterion of spontaneous strain compatibility, has to be extended to allow small rotations of the domain walls with respect to their ideal orientation. The observed switching process among the different domains can be understood as a mechanism that minimises the elastic energy. Received 21 July 2000