Soliton density and intensity of commensurate magnetic resonance lines in incommensurate systems

The intensity of the “commensurate” lines appearing in the magnetic resonance spectra of incommensurate systems in the presence of a multisoliton lattice is evaluated as a function of the soliton density. It is shown that the apparent soliton density obtained from a comparison of the intensities of the commensurate lines in the incommensurate and commensurate phases is different from the soliton density obtained by a comparison of the theoretical and experimental lineshapes and defined as the volume fraction of the incommensurate domain walls.     

Investigation into the domain structure dynamics in ferroelectrics with an incommensurate phase

The domain structure dynamics in ferroelectrics with an incommensurate phase is studied. Sodium nitrite is considered to be a prominent representative of the above ferroelectrics. The polarization properties of these ferroelectrics are described using pseudospin formalism. A kinetic equation for describing polarization of ferroelectrics is derived using the Hamiltonian. This equation is numerically solved simultaneously with the sound-vibration equation. The results are analyzed for various crystal parameters and initial conditions. The crystal domain structure is shown to be localized for reasonably long times. This circumstance makes it possible to conclude that these domain-structure states are long-lived states of a soliton type. The importance of finding and describing these states is emphasized. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 66–70, August, 2006.     

EPR lineshape study of the incommensurate phase in γ-irradiated K2SeO4

The temperature dependence of the SeO^4-₄ EPR frequencies and the asymmetric broadening of the EPR lines in the incommensurate phase of K₂SeO₄ can be explained by an incommensurate spatial modulation of the g tensors which corresponds to the “broad” phase soliton limit. A comparison between the experimental and calculated lineshape shows a ≈1% volume fraction of commensurate regions in the middle of the incommensurate phase at 110 K.     

Structural order and chaos in a one-dimensional quantum atomic chain

The spatial structure of a quantum chain of atoms interacting with a space-periodic field is analysed. Discrete maps for the average atomic positions in coherent states are obtained. Conditions for the existence of commensurate, incommensurate structures and “quantum structural chaos” are determined at zero temperature.     

Magnetic resonance and relaxation in structurally incommensurate systems

The present state of theoretical and experimental magnetic resonance investigations of structurally incommensurate systems is reviewed. The magnetic resonance lineshapes and the temperature and frequency dependences of the spin-lattice relaxation rates are evaluated in the plane wave and multisoliton limits. In contrast to translationally periodic systems, the spin-lattice relaxation rate is shown to vary over the incommensurate resonance line and is determined by phason and amplitudon fluctuations. The variation of the relaxation rate over the incommensurate line allows for a separate determination of the amplitudon and phason contributions as well as a discrimination between direct and Raman processes. The results further demonstrate that the soliton width is large as compared to the intersoliton spacing over most of the incommensurate phase.     

X-ray diffraction of incommensurate structures in the soliton regime

In order to elucidate the sensitivity of X-ray diffraction to the structural differences in an incommensurate structure between the sinusoidal and soliton regimes, a general expression for the structure factor of a displacive incommensurate structure in an ideal soliton regime is obtained in terms of the so called “atomic scattering modulation factors”, which reduce the expression to a form analogous to that of a commensurate structure. Consequently an approximate relationship between the intensities of particular sets of satellites is determined and compared with that expected in the sinusoidal regime. It is also shown that an ideal soliton regime gives place to a particular extinction rule, and the corresponding average structure has the atomic positions splitted like a disordered structure. These results allow to explain some recently reported measurements in Rb₂ZnCl₄.     

Magnetic domains and stripes in a spin-fermion model for cuprates

Monte Carlo simulations applied to a model of interacting fermions and classical spins show the existence of antiferromagnetic spin domains and charge stripes upon hole doping. The stripes have a filling of approximately 1/2 hole per site, and they separate spin domains with a pi phase shift among them. The observed stripes run either along the x or y axes. No particular boundary conditions or external fields are needed to stabilize these structures. When magnetic incommensurate peaks are observed at momentum pi(1,1-delta), charge incommensurate peaks appear at (0,2delta). The charge fluctuations responsible for the stripe formation also induce a pseudogap in the density of states.     

Neutron scattering study of the field-induced soliton lattice in CuGeO3

CuGeO3 undergoes a transition from a spin-Peierls phase to an incommensurate phase at a critical field of H(c) approximately 12.5 T. In the high-field phase a lattice of solitons forms, with both structural and magnetic components, and these have been studied using neutron scattering techniques. Our results provide direct evidence for a long-ranged magnetic soliton structure which has both staggered and uniform magnetizations with amplitudes that are broadly in accord with theoretical estimates. The magnetic soliton width gamma(m) and the field dependence of the incommensurability deltak(SP) are found to agree well with theoretical predictions.     

Slow stage in the evolution of an incommensurate ferroelectric superlattice

The nature of the slow evolution of a soliton system in an incommensurate phase of a ferroelectric is investigated experimentally. It is shown that the duration of the time interval in which the anomalous permittivity and the corresponding soliton spacings are governed by a logarithmic law increases from a few minutes to several hours as the ferroelectric phase transition is approached. Fiz. Tverd. Tela (St. Petersburg) 40, 2101–2102 (November 1998)     

Applications of optical activity to studies of phase transitions

This article reviews at an introductory level the physics of optical activity and its recent applications to studies of phase transitions of ferroelectrics. Optical activity is a kind of internal perturbation of the refractive index, and accordingly induces a resonating effect on the eigenstates of the susceptibility. This is the reason why optical activity provides us with unreplaceable information concerning the chirality of the structure and specific bonding nature of constituent atoms. The principles of our high accuracy universal polarimeter (defined as HAUP) method are described, which realized for the first time simultaneous measurements of birefringence, optical activity, and rotation angles of the indicatrices of any crystals, even those belonging to monoclinic and triclinic systems. The utility of the HAUP method is exemplified by our recent experiments. The origin of the occurrence of incommensurate states in some A₂BX₄ crystals was theoretically explained from the fact that they showed optical activity. It is of particular interest that the origin is also resonance of eigenstates of the dynamical matrix. The merits of the HAUP method have been extended to the evaluation of the soliton density in the incommensurate phase, discrimination of the twin mechanism of the ferroelectric domains, and search for the origin of ferroelectricity of Rochelle salt.     

Pseudospin soliton in the nu=1 bilayer quantum Hall state

We investigate a domain structure of pseudospins, a soliton lattice in the bilayer quantum Hall state at total Landau level filling factor nu = 1, in a tilted magnetic field, where the pseudospin represents the layer degree of freedom. An anomalous peak in the magnetoresistance Rxx appears at the transition point between the commensurate and incommensurate phases. The Rxx at the peak is highly anisotropic for the angle between the in-plain magnetic field B parallel and the current, and indicates a formation of the soliton lattice aligned parallel to B parallel. The temperature dependence of the Rxx peak reveals that the dissipation is caused by thermal fluctuations of pseudospin solitons. We also study a phase diagram of the bilayer nu = 1 system, and the effects of density imbalance between the two layers.     

Phase diagram of the ground state of a classical anisotropic frustrated ferromagnet

The phase diagram of the ground state is obtained for the one-dimensional easy-axis model of classical spins coupled by ferromagnetic and antiferromagnetic exchanges between nearest and next-nearest neighbors, respectively. The parameters of the incommensurate magnetic structure with a variable step (soliton lattice) are calculated in the mean field approximation from the condition of the collinearity of spins to the effective exchange fields in the continuous approximation. The ground state of the soliton lattice and interfaces between soliton and collinear (ferromagnetic and “up–up–down–down”) phases are determined by the numerical minimization of the average energy over the initial angular velocity of spins.     

Methods of nonlinear dynamics and equilibrium structures of magnetoelastic chains

To study equilibrium structures of magnetoelastic chains we have introduced an equivalent system and examined the whole class of its solutions. Appearance of various structures of the chain is due to the choice of an appropriate minimizing solution of the equivalent dynamic system. Commensurate and incommensurate structures, transitions from ferromagnetic to antiferromagnetic states, and transitions to the states with alternating clusters of ordered spins are obtained. Conditions for appearance of chaotic structures and amorphous magnetic states of the chain are discussed.     

Hybridization wave as the "hidden order" in URu2Si2

A phenomenological model for the "hidden order" transition in the heavy-Fermion material URu(2)Si(2) is introduced. The hidden order is identified as an incommensurate, momentum-carrying hybridization between the light hole band and the heavy electron band. This modulated hybridization appears after a Fano hybridization at higher temperatures takes place. We focus on the hybridization wave as the order parameter in URu(2)Si(2) and possibly other materials with similar band structures. The model is qualitatively consistent with numerous experimental results obtained from, e.g., neutron scattering and scanning tunneling microscopy. Specifically, we find a gaplike feature in the density of states and the appearance of features at an incommensurate vector Q(*)～0.6π/a(0). Finally, the model allows us to make various predictions which are amenable to current experiments.     

Soliton dynamics and nuclear spin-lattice relaxation in incommensurately modulated crystals

The nuclear spin-lattice relaxation rate in incommensurate systems is analysed for the the so-called soliton limit which often can be applied near the transition to a subsequent commensurate phase. Previous calculations are corrected by taking into account adequately the eigenfunctions of the relevant fluctuations. In contrast to previous conclusions, it is shown that for nuclei in the discommensurations the spin-lattice relaxation rate is expected to increase on approaching the phase transition. The theoretical predictions are confirmed by experimental data obtained from NMR measurements on the prototype incommensurate systems Rb₂ZnCl₄ and BCCD. b]References     

Incommensurate/commensurate charge-density-wave states as a source for plutonium metal behavior

Physical property behavior of plutonium (Pu) metal phases is like that of an incommensurate charge-density wave (ICDW) system where the CDW influenced distortion modulates the crystal. As incommensurates, the different Pu phases may have to be considered as superspace group structures where there is a one-dimensional modulation of the basic three-dimensional lattice. Certain Pu phases may then be classified into as many as three Bravais classes when considered in (3 + 1) dimensional space. The possible variants in Bravais class, crystals setting and bottom lines, as well as allowable differences in the number of atoms per unit cell, should permit incommensurate materials, as well as Pu phases, to appear in different variants of the basic space group structure on heating and cooling cycles. One should not expect the lower temperature phases, e.g., Pu, to return to their original distorted or modulated structures at constant rate cooling, after being distorted or modulated by CDWs in their higher temperature space group structures. This can explain the hysteresis in phase transitions noted with Pu metal and with incommensurate materials in general.

Chiral symmetry appears to be inherent to the incommensurability of a quasi-one dimensional system. All but one of the reported space group structures for Pu phases have at least a one-dimensional twofold screw axis with a center of symmetry, i.e., they show chiral symmetry. A theory suggests that chiral symmetry must permit the contraction in one or more dimensions noted with most incommensurate materials, as well as with Pu phases.

It is suggested that there is another ICDW Pu phase (αI) below ～ 60 K, and that the γ-Pu phase (Fddd) must be a composite structure. Other Pu phases appear to be composite structures also. There is evidence for a new phase, or phase mixture, which appears reproducibly between the δ and γ phases only on a cooling cycle. It is infered that this is a reappearance of the δ' phase.

Published dilatometry, internal friction and relative shear modulus results appear to confirm both incommensurate and commensurate CDW states in Pu metal phases. It is suggested that CDWs may be playing a role in f-bonding in Pu metal and that CDWs and valence fluctuations may be manifestations of the same electronic behavior.     

Bethe ansatz study of two-dimensional soliton lattice melting

We study the melting of incommensurate soliton lattice using the exact Bethe ansatz solution of one-dimensional quantum sine-Gordon Hamiltonian with U(1) coupling. The elastic moduli of soliton lattice are obtained and their asymptotic behaviors are explicitly calculated both at zero and finite temperature. We have obtained the thermodynamic phase boundaries of the soliton lattice and shown that the direct commensurate-incommensurate transitions are intervened by the fluid phase for T>0 as predicted by Coppersmith et al. [Coppersmith et al., Phys. Rev. Lett. 46 (1981) 549. [1]] for n≤2.     

Na掺杂反式聚乙炔中的孤子晶格的能谱与电子束缚态

从离散的ＳＳＨ模型出发，考虑了链内的电子相互作用，以及由杂质和周围链上的荷电孤子产生的库仑势的影响，探讨了各种掺杂浓度的反式聚乙炔中孤子晶格的能谱与电子束缚态。计算结果表明：在孤子晶格的能谱中，在价带底有两条定域能级，在导带顶存在着多个电子束缚态，随掺杂浓度的升高，束缚态的局域性减弱，禁带中的孤子能级形成孤子能带。当掺杂浓度高达１６．６７％时，所有的电子束缚态都消失，转变为扩展态。孤子晶格的禁带宽度随着掺杂浓度的增加而增大，最高占据态与导带底之间的能隙则随之逐渐减小。孤子能带底与价带顶之间的能隙在临界浓度附近有一极大值。还讨论了电子－电子相互作用对孤子晶格能谱的影响。 关键词：     

THEORY OF THE P=2 LOCK-IN PHASE TRANSITION IN SURFACE RECONSTRUCTION

The p=2 lock-in phase transition in surface reconstruction is studied within the soliton picture by a two-dimensional lattice effective Hamiltonian,which has the coupling of the semiinfinite crystal.An analytical form of the p=2 soliton is obtained.Having complicated structure and narrowed width,the Soliton solution is found to be different from the ordinary form.This behavior is due to the coupled extra dis-tortion of the incommensurate phase in the surface reconstruction,and is necessary for the p=2 lock-in phase transition.The theory is consistent with many known experimental results and is applicable to other physical systems.