A novel type of incommensurate phase in quartz: The elongated-triangle phase

We present evidence for a thermodynamically stable incommensurate elongated-triangle (ELT) phase in quartz, observed by transmission electron microscopy at the α-β structural transition. The phase sequence on cooling is: incommensurate equilateral-triangle (EQT) phase (ferroelectric)—incommensurate ELT (ferroelectric and ferroelastic)— uniform α phase. The ELT blocks could be responsible for the large light scattering in the vicinity of the α-gb transition. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 376–381 (10 September 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Interaction of acoustic and optical branches via a Lifshitz-type invariant

It is shown that the interaction of the acoustic and soft optical branches of the spectrum of normal vibrations of a crystal via a gradient invariant of the Lifshitz-invariant type explains the characteristic temperature dependences of these branches as the point of a transition from the initial phase into an incommensurate phase is approached. A comparison is made with the experimental data for betaine calcium chloride dihydrate — BCCD. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 9, 707–710 (10 May 1997)     

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)     

Effect of γ irradiation on the low-temperature electrical conductivity and dielectric properties of TlGaSe2 crystals

Electrical conductivity and dielectric properties of single-crystal TlGaSe₂ have been studied as a function of γ irradiation dose in the 100–280 K range including the existence of an incommensurate phase. Anomalies in the form of maxima have been observed in the σ=f(T), tan δ=f(T), and ɛ=f(T) curves at the points of transition from the paraphase to incommensurate (IC) phase, T _i, and from the IC to commensurate phase, T _c. The increase in the quantities σ, tan δ, and ɛ observed initially with increasing irradiation dose is followed by their strong decrease and disappearance of the anomalies. It has been established that γ irradiation does not affect the phase transition temperatures T _i and T _c. Fiz. Tverd. Tela (St. Petersburg) 40, 1328–1331 (July 1998)     

The invar effect and phase transitions in Cs2ZnI4 crystals

An in situ x-ray diffraction study of Cs₂ZnI₄ crystals performed in the 4.2–300 K temperature range is reported. The lattice parameter measurements have revealed three anomalies corresponding to phase transitions. The thermal expansion coefficient along the c axis was found to vanish in the region of incommensurate and commensurate modulated phases, 120–96 K (the invar effect). A possible crystallographic model relating modulated atomic displacements to the invar effect is discussed. Fiz. Tverd. Tela (St. Petersburg) 41, 137–142 (January 1999)     

Incommensurate phase in the layered hexagonal crystal Cs3Bi2I9

An incommensurate phase is observed in a Cs₃Bi₂I₉ crystal, which belongs to the family of layered A₃B₂X₉ structures. Data from ¹²⁷I NQR and x-ray powder diffraction patterns show that the second-order normal phase—incommensurate phase transition at T _i=220 K is accompanied by a P6₃/mmc↔P2₁/m symmetry change and takes place at the center of the Brillouin zone. The nature of the instability leading to the appearance of this little-studied form of incommensurability is discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 1105–1108 (June 1997)     

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)     

Dynamic properties of an incommensurate charge density wave in monoclinic TaS3 at low temperatures

The permittivity of monoclinic TaS₃, a quasi-one-dimensional conductor with an incommensurate charge density wave (CDW), as a function of frequency and temperature has been studied. At low temperatures and at frequencies below 1 MHz, the temperature dependence of the real part of the permittivity shows a maximum shift to lower temperatures with decreasing frequency. The temperature dependence of the relaxation time consists of two branches corresponding to macroscopic regions of CDWs with long and short relaxation times τ on the microscopic scale. With decreasing temperature, the growth of τ for large CDW regions is faster than thermal activation and shows a tendency to diverge at a finite temperature while the growth of τ due to the relaxation on the microscopic scale is slower than the activation rate. Our results show that with decreasing temperature the m-TaS₃ quasi-one-dimensional conductor goes over to a glasslike state due to the strong pinning of CDWs by randomly distributed impurities and the formation of mutually interacting solitary CDW collective excitations. Zh. éksp. Teor. Fiz. 111, 988–1000 (March 1997)     

μ+SR study of heavy-fermion magnetism in Ce(Cu1-xNix)2Ge2

We report muon spin relaxation (μ⁺SR) studies on the magnetic phase diagram of Ce(Cu_1-xNi_x)₂Ge₂ polycrystals for 0.5≤ x ≤ 0.8. A sharp magnetic transition, evidenced by the appearance of a fast Gaussian relaxation component σ, has been observed in the x = 0.5 alloy at 4.0 K in zero applied field. The average local field < B_μ> at the stopping sites of the muons, extracted from σ, exhibits a linear temperature dependence. We associate these features with an incommensurate spin density wave (SDW) ordering. Magnetic ordering, either long range or short range, and signatures of non-Fermi liquid behaviour have not been observed down to 2.0 K at x = 0.8. This revised version was published online in August 2006 with corrections to the Cover Date.     

Existence of an incommensurate phase in a Li2B4O7 crystal

The x-ray diffraction spectra of Li₂B₄O₇ single crystals are investigated in the temperature range 80–300 K, and the lattice parameter c is determined in the same temperature range in the presence of a periodically varying temperature field. An incommensurate phase is not observed anywhere in the temperature range investigated, regardless of whether the crystals are subjected to a periodic temperature field. Fiz. Tverd. Tela (St. Petersburg) 39, 1461–1463 (August 1997)     

Fluctuation-induced broadening of Mn2+ EPR lines in the incommensurate phase of Rb2ZnCl4 crystals

The EPR spectra of Mn²⁺ ions in Rb₂ZnCl₄ crystals is investigated in the vicinity of the transition from the paraelectric phase to an incommensurate modulated phase. When these crystals are cooled below the transition temperature T _i =304 K, a splitting of the resonance lines is observed in the singular spectrum. A one-harmonic model is used to discuss the contributions that fluctuations in the amplitude and phase of the incommensurate displacement wave make to the local width of the singular spectra. It is shown that anomalies in the local width of the low-temperature singular peaks observed in the vicinity of T _i are caused by amplitude fluctuations. Fiz. Tverd. Tela (St. Petersburg) 41, 1668–1674 (September 1999)     

Phase transitions in the ferroelectrics (Sn1−x In(2/3)x )2P2S6 at high pressures

New ferroelectric solid solutions (Sn_1−x In_(2/3)x )₂P₂S₆ were investigated at high hydrostatic pressures. The range in which the incommensurate structure exists was determined. A dynamic shift of the incommensurate-ferroelectric phase transition temperature with increasing rate of change of temperature and the appearance of “reverse hysteresis” were observed. The characteristic features in the appearance of the latter effect in these crystals are investigated. Fiz. Tverd. Telsa (St. Petersburg) 41, 1276–1278 (July 1999)     

Vibronic charge-transfer excitons: Possible nature of the unusual properties of virtual perovskitelike ferroelectrics

A vibronic charge-transfer exciton, which is a pair of Jahn-Teller electron and hole polarons, is considered as a possible cause of the appearance of the Müller phase in the virtual ferroelectric SrTiO₃ and the “green” luminescence in the virtual ferroelectric KTaO₃. The two “green” luminescence bands can be associated with emission from two states of a typical intrinsic defect, viz., a vibronic charge-transfer exciton trapped by an oxygen vacancy and an isolated vibronic charge-transfer exciton. In both cases the “green” luminescence corresponds to the recombination of the electron and the hole in the vibronic charge-transfer exciton, which is accompanied by the emission of light. The properties of the Müller phase can be attributed to mixing of the normal state and states of the vibronic charge-transfer exciton phase when they interact with polarization in the soft SrTiO₃ matrix under the conditions of a pseudo-Jahn-Teller (pseudo-JT) effect on a soft TO mode of the displacement type. In this case the vibronic charge-transfer exciton phase forming the low-lying excited states has “order-disorder” degrees of freedom and exists at temperatures significantly below the point of the order-disorder ferroelectric transition in SrTiO₃ at T=T Q≈37 K. The corresponding lowering of the symmetry of the vibronic charge-transfer exciton phase to polar symmetry leads to the possibility of a long-period incommensurate phase in such excited states, which arises as a result of the appearance of a Lifshitz invariant. The valence-band state making the largest contribution of the pseudo-JT effect corresponds to a wave vector equal to the critical wave vector of the incommensurate vibronic charge-transfer exciton phase. When the temperature is lowered, the pseudo-JT distortion increases down to ∼T _Q and subsequently saturates in accordance with the saturation of the dielectric constant. The basic assumption in the model is that the temperature T=T _Q corresponds to the narrow temperature range for the transition from an intermediate to a strong pseudo-JT effect under the conditions for the realization of polarization tunneling states. The appearance of a significant admixture of states of the modulated ferroelectric vibronic charge-transfer exciton phase to the ground state under the conditions for the realization of polarization tunneling states at low temperatures provides an explanation for the principal properties of the Müller phase. Fiz. Tverd. Tela (St. Petersburg) 40, 907–909 (May 1998)     

Magnetic phases in Mn<Subscript>1</Subscript>_<Subscript>x</Subscript>Fe<Subscript>x</Subscript>WO<Subscript>4</Subscript> studied by neutron powder diffraction

The magnetic structures of Mn_1-xFe_xWO₄ with x = 0.0, 0.16, 0.21, 0.225, 0.232, 0.24, 0.27, 0.29, and 1.0 were refined from neutron powder diffraction data. The magnetic phase diagram could be completed in the coexistence range of different magnetic structures up to x = 0.29. For the magnetic state at 1.5 K a commensurate antiferromagnetic structure with a propagation vector = (±1/4, 1/2, 1/2) was found for x ⩽ 0.22 while the magnetic spins order with = (1/2, 0, 0) for x ≥ 0.22. In the latter phase, additionally, weak magnetic reflections indexed to an incommensurate ordering with = (- 0.214, 1/2, 0.457) occur in the diffraction pattern up to x = 0.29 indicating the occurence of a reentrant phase. For 0.12 ⩽ x ⩽ 0.29 the low temperature phases are separated from a magnetic high temperature phase showing only magnetic reflections indexed to a spin arrangement with = (1/2, 0, 0). The magnetic phase diagram is discussed qualitatively considering random superexchange between the statistically distributed Mn²⁺- and Fe²⁺-ions in the coexistence range 0.12 ⩽ x ⩽ 0.29 of different magnetic structures related to those of pure MnWO₄ and FeWO₄. Received 9 October 2002 Published online 14 March 2003     

Influence of γ irradiation on the electrical conductivity and dielectric properties of β TlInS2 in the temperature range of the incommensurate phase

The influence of γ irradiation on the electrical conductivity σ, the dielectric permittivity ɛ, and the dielectric loss tangent tanδ of β-TlInS₂ crystals is investigated in the temperature range of the incommensurate phase. It is established that γ irradiation lowers the values of ɛ and tanδ over the entire investigated temperature range and decreases the maxima of the σ(T) and tanδ(T) curves in the vicinity of the transition temperature T _c, but does not alter the transition temperature. Fiz. Tverd. Tela (St. Petersburg) 39, 1088–1090 (May 1997)     

Metastable structures of Dy layers adsorbed on Mo(112) and their transformations

Ordering of dysprosium on Mo(112) up to 1.5 monolayers has been investigated by LEED and work function analysis after adsorption at 100 K and annealing between 200 and 1000 K. At low annealing temperatures (< 350-600 K) ordered structures are found, which are changed or even destroyed irreversibly by annealing steps to higher temperatures. At coverages, θ, up to 0.3 monolayer a (6×1) not strictly commensurate chain structure is seen, which coexists up to θ = 0.58 with a one-dimensionally incommensurate c( 1.56×2) structure. At higher coverages up to the physical monolayer at θ≈ 0.77, incommensurate ( n×2) followed by oblique ( n×1) structures are seen with n continuously variable with coverage. The second layer forms a p (1.33×1) structure. Annealing to higher temperatures causes irreversible structural transitions with strongly coverage dependent properties. Up to θ = 0.58, only a glass-like disordered phase is formed, which cannot be ordered again. In contrast, the rectangular incommensurate structures between 0.58 < θ < 0.68 remain unchanged upon annealing, whereas the structures at higher coverages and those of the second layer are transformed into commensurate (s×1) structures with integer s. Geometrical models are presented for the non-annealed structures and possible origins for the two-dimensional concentration dependent vitrification of the Dy layers are discussed. Received 15 June 2001     

Dielectric properties of Sn2P2S6 crystals as a function of their growth conditions

The behavior of the permittivity near a phase transition in Sn₂P₂S₆ crystals of different technological quality is studied. It is established that, in high-resistance crystals, where an internal electric field is formed by the screening of spontaneous polarization in the polar phase, long-time relaxation of ɛ is observed in a temperature range ∼2 K above T _max. This relaxation and change in the form of the maximum of ɛ′(T) at a phase transition are attributed to an internal electric field induced by the volume space charge formed in regions near the surface. It is established that the existing differences in the properties of Sn₂P₂S₆ crystals are due to deviations from stoichiometry, arising during growth and synthesis of the crystals. Fiz. Tverd. Tela (St. Petersburg) 41, 1456–1461 (August 1999)     

Superconductivity and magnetism in HoNi2B2C

The effect of magnetic ordering on superconductivity in HoNi₂B₂C is studied. It is concluded that the abrupt suppression of superconductivity in the region of incommensurate antiferromagnetic ordering is due to a modification of the wave functions of the conduction electrons by the long-range magnetic order. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 702–707 (10 May 1996)     

Long-range order and magnetic relaxation in a system of single-domain particles

The paramagnetic-ferromagnetic phase transition and distinctive characteristics of relaxation of the magnetization in a system of interacting single-domain ferromagnetic particles distributed randomly in a nonmagnetic matrix are investigated in the mean-field approximation. Fiz. Tverd. Tela (St. Petersburg) 41, 1822–1827 (October 1999)     

Magnetic structure of iron-doped UPd2Ge2

Neutron diffraction investigations have shown that a 2% substitution Fe atoms for Pd radically alters the magnetic structure of UPd²Ge². If the magnetic structure in the undoped compound at T>50 K consists of a longitudinal spin density wave (LSDW) with “square” modulation, then in polycrystalline U(Pd^0.98Fe^0.02)²Ge² a “simple” antiferromagnetic (AF) phase is observed below 65 K and a sinusoidally modulated LSDW-AF phase is observed between 65 K and the Neel temperature T ^N =135 K. In the interval 65> T>135 K the magnetic cell is incommensurate with the crystal cell, with the exception of the point T=93 K, where the wave vector of the magnetic structure passes through a “commensurate” value equal to 0.75. Below T ^N the magnetic moments of the uranium atoms are always parallel to the tetragonal axis c of the unit cell. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 9, 615–619 (10 November 1997)