On the structural phase transitions in the incommensurate Cs2CdBr4

Abstract

In the series of incommensurate A₂BX₄ halides with the β-K₂SO₄ type structure, Cs₂CdBr₄ exhibits an unusual behaviour since the “lock-in” phase transition occurs at the centre of the Brillouin zone. The observed phase sequence is the following: Pnma (Z = 4)?INC(k₀ ≈ 1/6a*)?P2_1/n(Z = 4)?P1 (Z = 4). These phase transitions have been studied by means of Raman scattering and ultrasonic measurements. It is shown that the Pnma?INC?P2_1/n sequence is governed by order-disorder processes due to CdB2-₄ tetrahedra reorientations coupled with translations of the Cs⁺ cations, and that the low-temperature P2_1/n?P1 transition is of a displacive nature, governed by a soft optical mode. The “pseudo-proper” ferroelastic character of these transformations is clearly established. A model potential developed in the framework of Landau theory is proposed; this model is able to reproduce the general trends observed in the temperature dependence of the soft-modes and of the elastic constants in the different phases.     

A comparative study of the modulated structures of some A2BX4 compounds

The structures of the modulated phases of K₂SeO₄, Rb₂ZnCl₄, Rb₂ZnCl₄ and Cs₂CdBr₄ are compared. Both commensurate and incommensurate modulations are considered. Clear common features can be derived between the polarization vectors of their primary harmonic modulations. Even distortions with very different modulation wavevectors present a clear correlation.     

Comparative study of ESR spectra in incommensurate antiferromagnets

The electron spin resonance is studied for noncollinear low-dimensional antiferromagnets RbMnBr₃ and RbFe(MoO₄)₂ in a wide range of frequencies and fields. Both compounds have incommensurate spin structures appearing due to a low-symmetry distortion of an ideal hexagonal crystal lattice. Magnetic field applied in the spin plane induces a first-order transition into the commensurate phase. The low-energy resonance branch corresponding to a uniform oscillation of the spin system in the easy plane is observed in the two compounds in both incommensurate and commensurate phases, with a dramatic change of the spectra taking place near the transition field. The resonance spectrum of a nearly commensurate spin structure with long-wave modulations is analyzed in clean and dirty limits in the framework of a hydrodynamic approach. The resonance branch with steep field dependence in the incommensurate state is attributed to the acoustic mode with the gap resulted from pinning of local domain walls (discommensurations) on defects of the crystal structure.     

A priori theory of incommensurate behavior in Rb2ZnCl4

We have performed a study of the potential energy, normal modes, static relaxation, and molecular dynamics of Rb₂ZnCl₄ using ab initio Gordon-Kim interionic potentials for intermolecular and interionic potentials. We find that the Pnam–Pna2₁ transition in this, and almost certainly many isomorphous systems, is entropy driven and shows no soft mode behavior. This is shown to arise from the presence in this system of a large equipotential volume of phase space between the Pnam and the tripled Pna2₁ low temperature structure. This region arises from a major lattice instability involving large rotations and displacements and having approximately six-fold screw symmetry along the a axis. This concealed imperfect symmetry which we call latent symmetry is the basic cause of the existence of a near-tripled incommensurate phase over a range of 113 K (302 K–189 K) between the Pnam and Pna2₁ phases. In this region the helicity is incommensurate with the lattice, being largely determined by the relief of intrahelical stresses. In addition, we have demonstrated by molecular dynamics that the ZnCl₄ ^2- tetrahedra are orientationally disorderd, but, despite this, the helical instability remains. These findings are also related to anomalies in the observed Raman spectra and to X-ray data which confirm the presence of dynamically correlated disorder.     

Light-scattering study of the non-zero wave vector incommensurate soft mode in K2SeO4

Observations are reported of inelastic light scattering from the non-zero wave vector soft phonon that drives the incommensurate structural phase transition in K₂SeO₄. They are shown to correlate with neutron scattering measurements of phonon frequency shifts on cooling to the incommensurate transition temperature. The observed light scattering is suggested to arise from intrinsic disorder.     

Nonlinear phenomena in A2MX4 type crystals with incommensurate phases

Investigations of the nonlinear phenomena in A₂MX₄ type crystals (A, organic cation or alkaline metal ion; M, metal ion; X, halogen ion) with incommensurate phases are very interesting from both a scientific and a practical point of view. In the crystals many interesting nonlinear phenomena are observed, e.g., thermal hysteresis of birefringence and absorption coefficient, piezooptic effect, electrooptic effect. Different anomalies (e.g., a discontinuity or change of sign of the briefringence coefficient, a distinct increase of the value of piezooptic and electrooptic coefficients) exist in the phase transition regions. They are especially distinct for a transition from the incommensurate phase to the commensurate phase. Some possibilities of detection and recognition of the existence of incommensurate phases by optical methods are suggested.     

Anisotropy of the incommensurate fluctuations in Sr2RuO4: a study with polarized neutrons

The anisotropy of the magnetic incommensurate fluctuations in Sr2RuO4 has been studied by inelastic neutron scattering with polarized neutrons. We find a sizable enhancement of the out-of-plane component by a factor of 2 for intermediate energy transfer, which appears to decrease for higher energies. Our results qualitatively confirm calculations of the spin-orbit coupling, but the experimental anisotropy and its energy dependence are weaker than predicted.     

Influence of domain structure on the nonlinear polarization properties of A 2 BX 4-group crystals

Harmonic analysis of repolarization in A ₂ BX ₄-group crystals in the ferroelectric phase near phase-transition temperature T _c is used to separate the contributions to the harmonic-component amplitudes in the output signal of a Sawyer-Tower circuit from charging the reference capacitor with capacitive and conductive current through such a crystal. Harmonic analysis of dielectric hysteresis loops obtained by placing a specimen in an electric field with harmonically changing strength reveals general regularities in the evolution of the domain walls of A ₂ BX ₄-group crystals. It is established that the domain structure affects the nonlinear polarization properties of our specimens. The dependence of the potential relief of ferroelectric ion motion in a harmonically changing electric field is plotted on the basis of the experimental results.     

Isomorphism among commensurate and incommensurate high-temperature phases of A2BO4 compounds

The incommensurate and commensurate superstructures of K₂MoO₄, Rb₂WO₄ and K₂WO₄ are shown to have orthorhombic symmetry rather than the hexagonal symmetry, reported earlier. The structures belong essentially to the β-K₂SO₄ type. The β-K₂SO₄ structure can be regarded as a commensurate superstructure of the α-K₂SO₄ structure by doubling of the unit cell. In this sense β-K₂SO₄ and K₂MoO₄ have the same average structures. Rb₂WO₄ displays a lock-in transition at 681 K where the incommensurate distortion wave vector jumps from an incommensurate value to the value 0.5 which results in the β-K₂SO₄ type. The distortion wave vectors of the other compounds range from 0.25 to 0.5.     

Large structural modulations in incommensurate Te-III and Se-IV

The high-pressure phase of tellurium, Te-III, is found to have an incommensurate monoclinic structure, superspace group I(')2/m(0q0)s0, of a type previously unknown in the elements. Te-III is stable from 4.5(2) to 29.2(7) GPa; the previously reported transition to a distinct Te-IV phase at 10.6 GPa is not observed. The incommensurate wave vector of Te-III is strongly pressure dependent and varies in a strongly nonlinear way. Se-IV is found to be isostructural with Te-III.     

Commensurate and incommensurate modulated structures of Rb2ZnCl4

The commensurate and incommensurate structures of Rb₂ZnCl₄ have been refined using the four-dimensional formalism for modulated structures. They are characterized by a rigid body modulated rotation of the ZnCl₄ tetrahedra and by a translation motion of the Rb atoms.     

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.     

Study of Mn2+ EPR spectra in the incommensurate phase of Rb2ZnCl4

An EPR study of Mn²⁺ centers in the incommensurate phase of rubidium tetrachlorozincate crystals is reported. It is shown that the temperature dependence of the high-field hyperfine line group M _S=3/2↔5/2 can be described in terms of a simple “local” model. The data obtained support the nonclassical type of critical behavior in Rb₂ZnCl₄ crystals corresponding to the three-dimensional Heisenberg model for a two-component order parameter. Fiz. Tverd. Tela (St. Petersburg) 41, 691–694 (April 1999)     

Stress dependence of Tc for the incommensurate phase transition in K2SeO4

We have measured the uniaxial stress dependence of the frequency of the zone center A₁ soft mode in the low temperature phase of K₂SeO₄. The frequency shows a strong decrease with stress. We infer from this a similar decrease of the incommensurate phase transition temperature T_c. This behavior is explained by detailed lattice dynamical calculations for K₂SeO₄ which reveal the unusual balance between Coulomb and short-range forces in this structure. Our calculations show that this balance is changed by stress in such a way that the quasi-harmonic normal mode frequencies harden drastically. T_c is reduced by this purely volume dependent effect. This unusual balance between Coulumb and short-range forces also provides a natural explanation for the occurence of an incommensurate phase transition in K₂SeO₄. We infer that similar transitions are likely in isomorphous structures.