Study of ferroelectric phase transitions in disordered PbSc<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> and PbSc<Subscript>1/2</Subscript>Ta<Subscript>1/2</Subscript>O<Subscript>3</Subscript> solid solutions

Ferroelectric phase transitions and thermodynamic properties of disordered PbSc_1/2Ta_1/2O₃ and PbSc_1/2Nb_1/2O₃ solid solutions have been investigated by the Monte Carlo method. The parameters of the effective Hamiltonian were calculated within the generalized Gordon-Kim model. The obtained values of the phase-transition temperatures and spontaneous polarization are in satisfactory agreement with the experimental data.     

Lattice dynamics and ferroelectric instability in ordered and disordered PbSc<Subscript>1/2</Subscript>Ta<Subscript>1/2</Subscript>O<Subscript>3</Subscript> and PbSc<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> solid solutions

The dynamic Born charges and the frequency spectra of lattice oscillations in the crystals of ordered and disordered PbSc_1/2Ta_1/2O₃ (PST) and PbSc_1/2Nb_1/2O₃ (PSN) solid solutions have been calculated within the framework of the generalized Gordon-Kim model with allowance for the dipole and quadrupole polarizabilities. The phonon spectra of both compounds contain ferroelectric soft modes. The influence of various interactions on the magnitude of dynamic charges and ferroelectric instability in PSN and PST solid solutions has been studied and it is shown that both these charges and the ferroelectric instability are determined by the competition between long-range dipole-dipole interactions and short-range dipole-charge interactions, the determining role played by the interaction of Nb (Ta) cations and oxygen anions in the Nb-O (Ta-O) bond direction.     

Heat capacity study of relaxor PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript> in a wide temperature range

Heat capacity of the PbMg_1/3Nb_2/3O₃ compound is measured using the methods of adiabatic and differential scanning calorimetry in the temperature range 80–750 K. Two blurred anomalies on the C _p (T) dependence are observed in wide temperature intervals of 200–400 K and 500–700 K. The results of studies are discussed together with data on the structure and phonon spectrum in the framework of spherical random bond-random field model.     

Acoustic emission and thermal expansion of Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> and Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript>-PbTiO<Subscript>3</Subscript> crystals

The temperature dependence of the elongation per unit length for Pb(Mg_1/3Nb_2/3)O₃ crystals unannealed after growth and mechanical treatment is investigated in the course of thermocycling. It is revealed that this dependence deviates from linear behavior at temperatures below 350°C. The observed deviation is characteristic of relaxors, is very small in the first cycle, increases with increasing number n of thermocycles, and reaches saturation at n≥3. In the first cycle, a narrow maximum of the acoustic emission activity is observed in the vicinity of 350°C. In the course of thermocycling, the intensity of this maximum decreases and becomes zero at n>3. For (1?x)Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃ crystals, the dependence of the temperature of this acoustic emission maximum on x exhibits a minimum. It is assumed that the phenomena observed are associated with the phase strain hardening due to local phase transitions occurring in compositionally ordered and polar nanoregions.     

Simulation of the magnetic properties of manganese oxide Pb<Subscript>3</Subscript>Mn<Subscript>7</Subscript>O<Subscript>15</Subscript>

The magnetic susceptibility, heat capacity, and spin-spin correlation functions of manganese oxide Pb₃Mn₇O₁₅ are calculated by the Monte Carlo method. Two critical temperatures are determined: T ₁ ≈ 20 K, above which a modulated structure along the hexagonal axis is formed, and T ₂ ≈ 70 K, at which the long-range magnetic order disappears. The antiferromagnetic exchange interaction constant in a hexagonal plane is estimated to be J ₁ ～ 7 K, and the antiferromagnetic and ferromagnetic exchange interaction constants between hexagonal planes are calculated to be J ₂ ～ 3 K and K ～ 50 K, respectively.     

Mobility and diffusion of oxygen isotopes in YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6+<Emphasis Type="Italic">x</Emphasis></Subscript>: Monte carlo simulation

The self-diffusion (D₀) and isotope diffusion (D*) coefficients of oxygen in YBa₂Cu₃O_6+x are calculated as functions of the temperature (600–1200 K) and the oxygen content (0<x<1). The Monte Carlo simulation is performed with due regard for both the interaction of oxygen ions at lattice sites in the basal planes of YBa₂Cu₃O_6+x and the interaction between a jumping ion at a saddle point and the environment. Equilibrium thermodynamic characteristics (including the phase diagram and the heat capacity) are calculated in terms of the Hamiltonian of interaction between oxygen ions at the lattice sites. It is found that an increase in the oxygen content leads to a decrease in the diffusion coefficients D₀ and D*, an increase in the effective activation energies for diffusion by 0.3–0.5 eV, and a decrease in the Haven ratio from 1 to ～0.5.     

Structural and magnetic phase transformations in the BiFeO<Subscript>3</Subscript>-CaFe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> system

The crystal structure and magnetic properties of the Bi_{1 ? x} Ca _x Fe_{1 ? x/2}Nb _x/2O₃ system were studied. It is shown that, at x ≤ 0.15, the unit-cell symmetry of solid solutions is rhombohedral (space group R3c). Solid solutions with x ≥ 0.3 have an orthorhombic unit cell (space group Pbnm). The rhombohedral compositions are antiferromagnetic, while the orthorhombic compositions exhibit a small spontaneous magnetization due to Dzyaloshinski?-Moriya interaction. In CaFe_0.5Nb_0.5O₃, the Fe³⁺ and Nb⁵⁺ ions are partially ordered and the unit cell is monoclinic (space group P2₁/n). In the concentration range 0.15 < x < 0.30, a two-phase state (R3c + Pbnm) is revealed.     

Manifestation of a ferroelectric-antiferroelectric phase transition in Li<Subscript>0.12</Subscript>Na<Subscript>0.88</Subscript>Ta<Subscript>0.4</Subscript>Nb<Subscript>0.6</Subscript>O<Subscript>3</Subscript> in its Raman scattering spectra

The ferroelectric-antiferroelectric phase transition in the Li_0.12Na_0.88Ta_0.4Nb_0.6O₃ ceramic solid solution has been studied by the Raman scattering technique. As the temperature approached the transition point from below, we observed an appreciable broadening of the lines associated with the vibrations of the cations occupying octahedral and cubooctahedral cavities of the structure and with the oxygen network vibrations (which implies a substantial increase in disorder on the cation sublattices), as well as a decrease to zero intensity of the 875-cm^?1 line corresponding to stretch vibrations of the bridging oxygen in the BO₆ octahedral anion in the vicinity of the transition. The temperature dependence of the 875-cm_?1 line intensity near the transition was used to study the behavior of the phase transition order parameter η. The behavior of η was found to disagree markedly with the Landau theory of second-order phase transitions. It is shown that discrepancies originate from the increase in disorder in the niobium and tantalum sublattices in the Li_0.12Na_0.88Ta _y Nb_1-y O₃ solid solution system with increasing y. The order of the transition is lowered.     

Ionic displacements and structure of disordered PbFe<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript>

A sequence of structural models of unit cells of complex oxides with perovskite-type structure has been constructed to refine the average structure of PbFe_1/2Nb_1/2O₃ (PFN) at temperatures above the ferroelectric Curie point (T _C ～ 110°C). Owing to the analysis of the probability theory considerations, each model is characterized by only two positional fitting parameters. With the use of the intensities of 95 symmetrically independent X-ray reflections from a PFN single crystal at 160°C, a model with the R factor below 3% (K = 2.44%) was chosen. The ravine method has been used to verify the existence of a single minimum for the R factor with respect to the fitting parameter.     

Dielectric and optical properties of Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)<Subscript>0.8</Subscript>Ti<Subscript>0.2</Subscript>O<Subscript>3</Subscript> (PMNT-0.2) ferroelectric relaxor single crystals

The dielectric and optical (optical transmission, small-angle light scattering, birefringence) properties of PMNT-0.2 single crystals and their variation induced by a dc electric field have been studied. The birefringence was found to increase anomalously at the transition from the rhombohedral ferroelectric to the inhomogeneous relaxor phase (the spontaneous ferroelectric transition temperature T_sp). Below T_sp, the dielectric and optical properties were observed to exhibit anomalies originating from reorientation and growth of domains in size. Unlike ferroelectric relaxors of the type of PbB′_1/3B′_2/3O₃ and PbB′_1/2B′_1/2O₃, in PMNT-0.2 neither induction of the ferroelectric phase by an electric field nor thermally stimulated destruction of the ferroelectric state occurs through the percolation mechanism (i.e., they are not accompanied by anomalously narrow maxima in small-angle light scattering). This is attributed to the inhomogeneous structure of the relaxor phase, as a result of which the phase transition does not take place simultaneously in various regions of the crystal.     

Optical studies of phase transitions in the (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>Ti(O<Subscript>2</Subscript>)F<Subscript>5</Subscript> crystal

Polarization-optical study of twinning and measurements of the Raman spectra and birefringence in oxyfluoride (NH₄)₃Ti(O₂)F₅ were carried out over the temperature range 90–350 K. Phase transitions were detected at temperatures T ₀₁ = 266 K (second-order transition) and T ₀₂ = 225 K (first order). It is assumed that the crystal symmetry is changed as follows: Fm3m ? I4/mmm ? I4/m. Anomalies of the spectral parameters are established in the frequency range of internal vibrations of ammonium ions and Ti(O₂)F₅ complexes. An analysis of the results shows that the transition at T ₀₁ is likely due to small shifts of the tetrahedral groups from their position on the triad axis and that the transition at T ₀₂ is due to fluorine-oxygen ordering of Ti(O₂)F₅ complexes.     

Peculiarities of the dielectric,elastic, and anelastic properties of the PbFe<Subscript>1/2</Subscript>Nb<Subscript>1/2</Subscript>O<Subscript>3</Subscript> ferroelectromagnet at the antiferromagnetic phase transition

Peculiarities in the behavior of the dielectric, elastic, and anelastic properties of the PbFe_1/2Nb_1/2O₃ ceramic ferroelectromagnet have been found and investigated near the antiferromagnetic phase transition (Néel temperature T _N = 160 K). It is established that the transition to the antiferromagnetic phase leads to a decrease in the permittivity and elastic compliance. The anomaly of permittivity found near T _N indicates the presence of magnetoelectric interaction in the magnetically ordered phase.     

Internal friction of Li<Subscript>2</Subscript>B<Subscript>4</Subscript>O<Subscript>7</Subscript> single crystals

This paper reports on the results of measurements of the internal friction Q^?1 and the shear modulus G of Li₂B₄O₇ single crystals along the crystallographic directions [100] and [001] in the temperature range 300–550 K for strain amplitudes of (2–10)×10^?5 at infralow frequencies. The anomalies observed in Q^?1 and G in the temperature range 390–410 K are due to thermal activation of the mobility of lithium cations and their migration from one energetically equivalent position to another. A jump in the internal friction background is revealed in the vicinity of the Q^?1 and G anomalies for the Li₂B₄O₇ crystal. The magnitude of this jump depends on the crystallographic direction.     

High-frequency EPR of Cr<Superscript>2+</Superscript> ions in CdGa<Subscript>2</Subscript>S<Subscript>4</Subscript>

High-frequency broad-band (65–240 GHz) EPR is used to study impurity centers of bivalent chromium in a CdGa₂S₄ crystal. It is found that the EPR spectra correspond to tetragonal symmetry. The spin Hamiltonian H = βB · g · S + B ₂ ⁰ O ₂ ⁰ + B ₄ ⁰ O ₄ ⁰ + B ₄ ⁴ O ₄ ⁴ with the parameters B ₂ ⁰ =23659±2 MHz, B ₄ ⁰ =1.9±1 MHz, |B ₄ ⁴ |=54.2±2 MHz, g_‖=1.93±0.02, and g_⊥=1.99±0.02 is used to describe the observed spectra. It is concluded that chromium ions occupy one of the tetrahedrally coordinated cation positions.     

Ordered monoclinic vanadium suboxide V<Subscript>14</Subscript>O<Subscript>6</Subscript>

The monoclinic (space group C2/m) superstructure of the suboxide V₁₄O₆, which is formed as a result of the atomic and vacancy ordering of the tetragonal solid solution of oxygen in vanadium, is investigated using X-ray diffraction and symmetry analysis. The monoclinic suboxide V₁₄O₆ is observed in the vanadium oxide samples VO_0.57, VO_0.81, and VO_0.86 synthesized at 1770 K and the samples VO _y (0.87 ≤ y ≤ 0.98) additionally annealed at 1470 K after the synthesis. It is established that the channel of the disorder-order phase transition associated with the formation of the monoclinic suboxide V₁₄O₆ includes six superstructure vectors belonging to three non-Lifshitz stars of one type {k ₁}. The distribution function of the oxygen atoms in the monoclinic superstructure of the suboxide V₁₄O₆ is calculated. It is demonstrated that the displacements of vanadium atoms distort the body-centered tetragonal metal sublattice, thus preparing the formation of the facecentered cubic sublattice and the transition from the suboxide V₁₄O₆ to the cubic vanadium monoxide with the B1 structure.     

Spontaneous ferroelectricity in strained low-temperature monoclinic Fe<Subscript>3</Subscript>O<Subscript>4</Subscript>: A first-principles study

As a single-phase multiferroic material, Fe₃O₄ exhibits spontaneous ferroelectric polarization below 38 K. However, the nature of the ferroelectricity in Fe₃O₄ and effect of external disturbances such as strain on it remains ambiguous. Here, the spontaneous ferroelectric polarization of low-temperature monoclinic Fe₃O₄ was investigated by first-principles calculations. The pseudo-centrosymmetric FeB42–FeB43 pair has a different valence state. The noncentrosymmetric charge distribution results in ferroelectric polarization. The initial ferroelectric polarization direction is in the -x and -z directions. The ferroelectricity along the y axis is limited owing to the symmetry of the Cc space group. Both the ionic displacement and charge separation at the FeB42–FeB43 pair are affected by strain, which further influences the spontaneous ferroelectric polarization of monoclinic Fe₃O₄. The ferroelectric polarization along the z axis exhibits an increase of 45.3% as the strain changes from 6% to -6%.     

Heterophase states in 0.10PbTiO<Subscript>3</Subscript>-0.90Pb(Zn<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> crystals

A new model of the elastic matching of phases is proposed, and heterophase structures near the morphotropic phase boundary in 0.10PbTiO₃-0.90Pb(Zn_1/3Nb_2/3)O₃ crystals are studied. Unique behavior of the unit cell parameters is found to favor the elastic matching of the ferroelectric tetragonal and orthorhombic phases under the conditions of complete or partial relaxation of internal mechanical stresses at a volume concentration ratio of these phases of about 20/80% and temperatures of T=20–300 K. Interrelations between the volume concentrations of different domain (twin) types and of the coexisting phases are analyzed.     

The magnetization reversal in CoFe<Subscript>2</Subscript>O<Subscript>4</Subscript>/CoFe<Subscript>2</Subscript> granular systems

The temperature-dependent field cooling (FC) and zero-field cooling (ZFC) magnetizations, i.e., M _FC and M _ZFC, measured under different magnetic fields from 500 Oe to 20 kOe have been investigated on two exchange–spring CoFe₂O₄/CoFe₂ composites with different relative content of CoFe₂. Two samples exhibit different magnetization reversal behaviors. With decreasing temperature, a progressive freezing of the moments in two composites occurs at a field-dependent irreversible temperature T _irr. For the sample with less CoFe₂, the curves of ?d(M _FC ? M _ZFC)/dT versus temperature T exhibit a broad peak at an intermediate temperature T ₂ below T _irr , and the moments are suggested not to fully freeze till the lowest measuring temperature 10 K. However, for the ?d(M _FC ? M _ZFC)/dT curves of the sample with more CoFe₂, besides a broad peat at an intermediate temperature T ₂, a rapid rise around the low temperature T ₁~15 K is observed, below which the moments are suggested to fully freeze. Increase of magnetic field from 2 kOe leads to the shift of T ₂ and T _irr towards a lower temperature, and the shift of T ₂ is attributable to the moment reversal of CoFe₂O₄.

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Graphical abstract CoFe₂O₄/CoFe₂ composites with different relative content of CoFe₂ were prepared by reducing CoFe₂O₄ in H₂ for 4 h (S4H) and 8 h (S8H). The temperature-dependent FC and ZFC magnetizations, i.e., M _FC and M _ZFC, under different magnetic fields from 500 Oe to 20 kOe have been investigated. Two samples exhibit different magnetization reversal behaviors. With decreasing temperature, a progressive freezing of the moments in two composites occurs at field-dependent irreversible temperature T _irr. For the S4H sample, the curves of ?d(M _FC ? M _ZFC)/dT versus temperature T exhibit a broad and field-dependent relaxing peak at T ₂ below T _irr (figure a), and the moments were suggested not to fully freeze till the lowest measuring temperature 10 K. However, for the S8H sample, it exhibits the reentrant spin-glass state around 50 K, as evidenced by a peak in the M _FC curve (inset in figure b) and as a result of the cooperative effects of the random anisotropy of CoFe₂O₄, exchange–spring occurring at the interface of CoFe₂O₄ and CoFe₂ together with the inter-particle dipolar interaction (figure c); in ?d(M _FC ? M _ZFC)/dT curves, besides a broad relaxing peat at T ₂, a rapid rise around the low-temperature T ₁~15 K is observed, below which the moments are suggested to fully freeze. Increase of magnetic field from 2 kOe leads to the shift of T ₂ and T _irr towards a lower temperature, and the shift of T ₂ is attributable to the moment reversal of CoFe₂O₄.

     

Long-range and short-range magnetic order in new compound NaVGe<Subscript>2</Subscript>O<Subscript>6</Subscript>

New metal oxide pyroxene compound NaVGe₂O₆ containing isolated edge-sharing VO₆ (S=1) chains undergoes transition into a long-range antiferromagnetic state at T _N =16 K. The broad maximum in the temperature dependence of magnetic susceptibility at T _M =26 K indicates the low-dimensional character of the magnetic subsystem. Even though the antiferromagnetic ordering is accompanied by a sharp peak of specific heat, significant magnetic entropy is released above the Néel temperature.     

Magnetic properties of the Gd<Subscript>2</Subscript>V<Subscript>0.67</Subscript>Mo<Subscript>1.33</Subscript>O<Subscript>7</Subscript> and Y<Subscript>2</Subscript>VMoO<Subscript>7</Subscript> pyrochlore compounds

It is demonstrated that 50% substitution of vanadium for molybdenum in the pyrochlore lattice of the complex oxide Y₂(V _x Mo_{1 ? x} )₂O₇ results in a transition from the spin-glass ground state (at x = 0) to the ferromagnetic state in Y₂VMoO₇ (a = 10.1645(2) Å, T _C = 55 K). The Gd₂V_0.67Mo_1.33O₇ compound (a = 10.2862(3) Å) is a ferromagnet with T _C (84 K) exceeding that of undoped Gd₂MnO₂O₇.