Critical changes in vibrational modes in a magnetic debye crystal with a magnon-phonon coupling

Using the Green function technique we calculate the mean square of the vibrational amplitude of an ion (or equivalently the Debye Waller factor W, or the Mössbauer recoil free fraction ?) in a magnetic Debye crystal near the magnetic phase transition temperature T_c. We find that the magnon-phonon coupling which leads to the phonon spectrum broadening and frequency shift leads to sharp changes in W near T_c. The frequency shift leads to an increase in W, the broadening leads to a decrease in W. These results can explain the anisotropic critical changes in W near T_c observed recently in the magnetostrictive materials RFe₂ and RCo₂ (R = rare earth). In addition we calculate the expected changes in the second order Doppler shift near T_c. We find that when T approaches T_c from above a positive discontinuity and decrease in absolute value of slope of the thermal shift should occur.     

On the s-type superconductivity in heavy-fermion compounds

The amplitude of scattering of f electrons has been calculated for the periodic Anderson model in the strong-correlation limit (U = ∞) in the Cooper channel. From the condition of the existence of a pole of this amplitude, an equation is derived for determining the critical temperature (T _c) of the transition to the superconducting phase with the s symmetry of the order parameter. The temperature T _c as a function of the electron density and hybridization parameter has been calculated by self-consistently solving the system of equations. The region of the existence of the superconducting phase is found to adjoin the region of the existence of the unsaturated ferromagnetic state and does not overlap it. The results can be used to describe the transition to the superconducting phase with the s symmetry of the order parameter in heavy-fermion skutterudite LaFe₄P₁₂. In this case, the inclusion of the scattering of fermions by spin fluctuations turns out to be substantial enough to obtain T _c values close to the experimental data.     

Anomalous behavior of the surface tension at the interface of the metallic and insulating phases in the vicinity of the metal-insulator phase transition in a magnetic field

Mean-field equations describing the metal-insulator (MI) transition are formulated. They involve two coupled order parameters characterizing this transition: (i) a scalar order parameter describing the density change accompanying the transition from the insulating state to the metallic one and (ii) an order parameter (a two-component vector) describing the electron density in the metallic or semimetallic phase affected by the applied magnetic field. Two components of this vector correspond to different possible spin states of electrons in the applied magnetic field. The transition in the density of metallic and insulating phases being a first order phase transition is treated in terms of the Cahn-Hilliard-type gradient expansion. The transition in the electron density is a second order phase described by the Ginzburg-Landau-type functional. The coupling of these two parameters is described by the term linearly dependent on the electron density n in the metal with the proportionality factor being a function of the density of the metallic phase. The derived equations are solved in the case of the MI interface in the presence of both parallel and perpendicular uniform magnetic fields. The calculated surface tension Σ_mi between the metallic and insulating phases has a singular behavior. In the limit of zero electron density n ? 0, Σ_mi ～ n ^3/2. Near the MI transition point T _c(h) in the applied magnetic field, Σ_mi ～ [T - T _c(h)]^3/2. The singular behavior of the surface tension at the MI interface results in the clearly pronounced hysteresis accompanying the transition from the insulating to metallic state and vice versa.     

Central peak in the strontium titanate crystal near the tetragonal-to-cubic phase transition

Raman spectra of the SrTiO3 crystal have been measured in wide temperature (22?C316 K) and frequency (2?C1020 cm^?1) ranges. It has been shown that a central peak appears in low-frequency Raman spectra at temperatures above 70 K. In the spectral geometry with polarization rotation near the temperature T _c = 106 K of the cubic-to-tetragonal phase transition, the central peak exhibits properties of the order-disorder phase transition. Such a behavior of the central peak has been explained by the interaction of the low-frequency soft mode E _g with the relaxation mode near T _c .     

Dynamic critical behaviour at the structural phase transition in SrTiO3

The soft mode frequency involved in the structural phase transition in SrTiO₃ is measured with high accuracy. Two regimes are observed: a Landau regime remote from T_c and a critical regime near T_c with exponents of 0.5 and 0.33, respectively. This gives evidence for a proportionality of this dynamic quantity with the static order parameter also in the critical regime. The results for the soft mode linewidth are close to the theoretical expectations.     

Low energy electron diffraction beam profiles and phase transition at Si(111)-7 X 7 surface

Angular profiles of low energy electron diffraction (LEED) beams from Si(111)-7 × 7 are measured for various crystal temperatures T near the phase transition with apparent critical temperature T_c ≈ 1140 K. From analyses of the profiles it is concluded that (1) long range superstructure order persists for T up to at least 50 K above T_c and (2) with increasing T the correlation length characterizing the short-range order peaks for T ≈ T_c ? 100 K and decreases rapidly for T >T_c. Conclusion (1) is discussed with reference to a dislocation network model of Si(111)-7 × 7 reconstruction.     

Critical behavior of dilute electrolyte solutions

A theory of the critical behavior of a dilute ionic solution is constructed. An expression for the susceptibility in a wide temperature range is obtained. It is shown that ionic solutions belong to the universality class of the Ising model. The Ginzburg parameter of the ionic solutions decreases with the increase of the solvent concentration. In the general case, the critical exponent of susceptibility nonmonotonically depends on the temperature in the crossover region from the Ising-like to the mean-field behavior. In the vicinity of the transition point, the Debye-Hückel screening radius is proportional to the correlation length. As T→T _c, the screening radius tends to infinity and the screening disappears. The voltage between the two phases of the ionic solution is proportional to the order parameter and changes as |T/T _c?1|^β in the vicinity of the phase transition point.     

Esr study of (SO4)2− dynamics in relation to the ferroelectric phase transition in ammonium sulfate

Ferroelectric phase transition in ammonium sulfate has been studied by ESR of CrO₄^3? radical substituting for SO₄^2? ion in (NH₄)₂SO₄. In addition to discontinuous changes at T_c, certain continuous changes are observed in ESR parameters of this probe below T_c, which reflect the role of the sulfate ion in the phase transition. A microscopic mechanism of the phase transition is proposed and discussed in terms of the change of orientation of the sulfate tetrahedron through a finite angle. The degree of the change of orientation below T_c is thought to be the possible order parameter of the phase transition.     

Width of the zero-field superconducting resistive transition in the vicinity of the localization threshold

Resistive superconducting zero-field transition in amorphous In-O films in the states in the vicinity of the insulator-superconductor transition is analyzed in terms of two characteristic temperatures: the upper T _c0 , where the finite amplitude of the order parameter is established, and the lower T _c , where the phase ordering takes place. It follows from the magnetoresistance measurements that the resistance in between, T _c <T< T _c0 , cannot be ascribed to the dissipation by thermally dissociated vortex pairs. So, it is not a Kosterlitz-Thouless-Berezinskii transition that occurs at T _c .     

Magnetic states of the surface and bulk of ferrites near a phase transition at the Curie temperature

Investigations of the magnetic state of a surface layer ~200 nm thick and of the bulk in macroscopic ferrite crystals of the type Ba-M (BaFe₁₂O₁₉) are performed in the phase transition region around the Curie temperature (T _c). The method of simultaneous gamma, x-ray, and electron Mössbauer spectroscopy, which made it possible to compare directly the phase states of the surface and bulk of the sample, is used for the measurements. It is observed experimentally that in BaFe₁₂O₁₉ the transition of a surface layer ~200 nm thick to the paramagnetic state occurs at temperatures below T _c. It is established that the transition temperature T _c(L) of a thin layer localized at depth L from the surface of the crystal increases with distance from the surface and reaches the value T _c at the lower boundary of the “critical” surface layer. Therefore, near T _c a nonuniform state in which the crystal is magnetically ordered in the bulk but disordered at the surface is observed. A phase diagram of the states of the surface and of the bulk of macroscopic magnets near the Curie (or Néel) point is proposed on the basis of all the experimental results obtained in the present work as well as previously published results.     

Fluctuations in superconductors belowT c

Thermal fluctuations of the order parameter in the superconducting state are investigated, particularly near the transition temperature, using the time dependent Ginzburg-Landau theory. These fluctuations give rise to a contribution of the dynamical conductivity, which strongly increases as the temperature is raised towardsT _c , in contrast to the temperature dependence of the electromagnetic response due to the static order parameter. At the transition temperature this contribution joins continuously to the extra response (conductivity, susceptibility) which has been calculated and observed in the temperature region aboveT _c , where it represents the onset of superconductivity in the normal state. Particularly the dynamical conductivity due to fluctuations is calculated and discussed for bulk material, thin films and thin wires belowT _c . The temperature and frequency dependence should be observable in microwave experiments.     

Ferroelectricity and phase transition from incommensurate phase into commensurate one in (NH4)2ZnCl4

Phase transition has been found in (NH₄)₂ZnCl₄ at T = 266 ± 0.5 K by NQR method. There is a ferroelectric phase below T_c with a space group P2₁cn and with the trebling of the elementary lattice parameter along the axis c. Above the phase transition temperature in the crystal (NH₄)₂ZnCl₄ an incommensurate phase is realized.     

On the phase transition in CsCN

X-ray diffraction and dielectric measurements have been performed on the molecular crystal CsCN as a function of temperature. The order parameter of the cubic to rhombohedral phase transition (T _c =186 K) was determined and interpreted by a coupling of the (CN)^? orientations to the shear strain. At lower temperatures the dielectric response is dominated by thermally activated relaxations processes rather than by electrical ordering of the CN dipoles.     

T c of disordered superconductors near the Anderson transition

According to the Anderson theorem, the critical temperature T _c of a disordered superconductor is determined by the average density of states and does not change at the localization threshold. This statement is valid under assumption of a self-averaging order parameter, which can be violated in the strong localization region. Stimulating by statements on the essential increase of T _c near the Anderson transition, we carried out the systematic investigation of possible violations of self-averaging. Strong deviations from the Anderson theorem are possible due to resonances at the quasi-discrete levels, resulting in localization of the order parameter at the atomic scale. This effect is determined by the properties of individual impurities and has no direct relation to the Anderson transition. In particular, we do not see any reasons to say on “fractal superconductivity” near the localization threshold.     

Effect of electric field on the dielectric permittivity of betaine phosphite crystals in the paraelectric phase

Temperature dependences of the dielectric permittivity of betaine phosphite crystals are studied both without and under application of an electric bias. It is shown that, in view of the fact that the high-temperature improper ferroelastic (antiferrodistorsive) phase transition at T _c1=355 K is nearly tricritical, the nonlinear temperature dependence of inverse dielectric permittivity in the paraelectric phase and the effect of the field on the dielectric permittivity can be described within a phenomenological model containing two coupled (polar and nonpolar) order parameters with a negative coupling coefficient. An analysis of the model revealed that, in the case where two phase transitions, a nonpolar and a ferroelectric one, can occur in the crystal, all of its dielectric properties, including the polarization response in a field, can be described by one dimensionless parameter a. For the crystal under study, we have a=?2.5. This value of the parameter corresponds to a second-order ferroelectric transition far from the tricritical point, at which a=?1. It is shown that the polarization response in the paraelectric phase in an electric field calculated within this model differs radically from that in the ferroelectric phase-transition model for which the Curie-Weiss law holds in the paraelectric phase.     

Phase transitions sequence in pyrochlore Cd2Nb2O7 studied by IR reflectivity

The infrared reflectivity of Cd₂Nb₂O₇ single crystal was studied in the temperature interval of 10-540 K, together with complementary dielectric measurements. A ferroelectric soft mode was revealed above the ferroelectric phase transition at T _c = 196 K coupled with a central-mode type dispersion in the near-millimetre range. This proves the mixed displacive and order-disorder nature of the transition. Below T _c many new modes were detected due to lowering of the symmetry, especially below the previously suggested incommensurate transition at 85 K. Discussion of the possible phase transitions based on symmetry considerations is presented with the conclusion that the ferroelectric transition is proper with the F_1u symmetry of the order parameter, whereas the intermediate ferroelastic transition is improper and triggered by the coupling with the ferroelectric order parameter. Received 17 July 2000     

The behaviour of an isolated impurity near a phase transition in a spherical-like model

The behaviour of an isolated impurity in a crystal undergoing a displacive phase transition is investigated in an exactly soluble spherical-like model. We find, depending on the parameter of the impurity, either a global phase transition at the bulkT _c or a freezing-out of local order at a temperatureT _c ^loc >T _c driven by a soft local mode. We furthermore discuss the dynamic autocorrelation function of the impurity by introducing a phenomenological damping.Work Supported by The Swiss National Science Foundation     

On the applicability of mode coupling theory to a ϕ 4-model with first order phase transition

A ? ⁴-model with symmetric double-well-like on-site potential and anharmonic, infinite range interactions is investigated. This model exhibits a first order phase transition at a temperature T _c. The time-dependent displacement correlation function is studied in the framework of the mode coupling theory (MCT). Depending on the choice of slow modes, MCT makes qualitatively different predictions which are compared with MD-results. These numerical results suggest that only the order parameter mode {ie1-1} should be considered as slow. In that case it is shown that MCT yields a dynamical transition in the supercooled high-temperature phase {ie1-2} at a temperature T* which coincides with the spinodal temperature T _s (T _s = 0 for our model) where the metastable supercooled phase becomes instable.