Features of the low-frequency polarization response in the region of the ferroelectric phase transition in multiferroic TbMnO<Subscript>3</Subscript>

The unusual behavior of the low-frequency (10 Hz–1 MHz) permittivity in single crystals of ferroelectric multiferroic TbMnO₃ has been experimentally and theoretically studied in detail in the region of the narrow temperature peak of the permittivity, associated with the ferroelectric phase transition (T_C ~ 27.4 K). It has been found that the ε_c^′(ω, T) maximum sharply decreases with increasing measured field frequency, while the temperature position of the maximum is independent of frequency. It has been shown that the observed features of the polarization response can be satisfactorily described within the Landau–Khalatnikov polarization relaxation theory.     

Dielectric relaxations,magnetodielectric and magnetoelectric interactions in Bi0.6La0.4MnO3 ceramics

Complex permittivity ε*/ε₀ = ε′/ε₀–iε″/ε₀ of the bismuth–lanthanum manganite Bi_0.6La_0.4MnO₃ ceramics has been measured in the temperature range of 10–220 K at frequencies f = 20–10⁶ Hz and magnetic inductions B = 0–0.846 T. At a temperature of 80 K, the spectra ε′/ε₀(t) and ε″/ε₀(t) demonstrate the dielectric relaxation that is a superposition of contributions of several relaxation processes, each of which is dominant in its frequency range: I (f < 10³ Hz, II (10³ < f < 10⁵ Hz), and III (10⁵ < f < 10⁶ Hz). In the range of 10–120 K, anomalous behavior of ε′/ε₀(T) and ε″/ε₀(T) is observed near the temperature of the transition from the paramagnetic to ferromagnetic phase and is due to the Anderson localization of charge carrier on a spin disorder.     

Dielectric constant anomalies of an improper Hg<Subscript>2</Subscript>Cl<Subscript>2</Subscript> ferroelastic near the phase-transition temperature

The temperature dependence of the permittivity of a Hg₂Cl₂ crystal has been investigated within the Landau phenomenological theory. At T < T _C, the linear permittivity has a singularity in the form ～(T _C?T)^1/2; however, this anomaly may disappear in a multidomain sample. The nonlinear permittivity also has an anomaly near T _C but of stronger type: ～(T _C ? T)^?1/2.     

Heat capacity of the Pb<Subscript>5</Subscript>(Ge<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>x</Subscript>)<Subscript>3</Subscript>O<Subscript>11</Subscript> ferroelectric system

The temperature dependences of the molar heat capacity at constant pressure, C_p, of Pb₅(Ge_1?xSi_x)₃O₁₁ crystals with x=0, 0.39, and 0.45 in the range 5–300 K, as well as of their permittivity, dielectric losses, and the pyroelectric effect, have been measured. Experimental data on the temperature behavior of the heat capacity are presented in the form of a sum of two Debye and one Einstein terms, C_p(T)=0.405C_D1(Θ_D1=160 K, T)+0.53C_D2(Θ_D2=750 K, T)+0.046C_E(Θ_E=47 K, T). Besides a peak in the region of the ferroelectric Curie point T_c=450 K for crystals with x=0, the temperature dependences of the heat capacity did not reveal any other pronounced anomalies.     

Dielectric properties of betaine phosphite-betaine phosphate solid-solution crystals in the improper ferroelastic phase

Temperature dependences of dielectric permittivity in the improper ferroelastic phase, including the region of the improper ferroelastic phase transition occurring at T=T_c1, were studied in the betaine phosphite-betaine phosphate solid-solution crystals. At a betaine phosphate (BP) concentration of 10%, the phase transition temperature T_c1 was found to shift toward higher temperatures by about 5 K compared to betaine phosphite (BPI) crystals, where T_c1=355 K. The phase transition remains in the vicinity of the tricritical point. As the BP concentration in BPI is increased, the dielectric anomaly at T=T_c1 weakens substantially compared to pure BPI. The nonlinear temperature dependence of reciprocal dielectric permittivity in the improper ferroelastic phase of BPI_xBP_1?x crystals is described in the concentration region 0.9≤x≤1 in terms of a thermodynamic model taking into account the biquadratic relation of the nonpolar order parameter of the improper ferroelastic phase transition to polarization. The decrease in the ferroelectric phase transition temperature T_c1 (or in the temperature of loss of improper ferroelastic phase stability) with increasing BP concentration in the above limits is due to the decreasing effect of the nonpolar mode on the polar instability, which is accompanied by a weakening of the dielectric anomaly at T=T_c1     

Dielectric properties of CuInP<Subscript>2</Subscript>(Se<Subscript>x</Subscript>S<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>6</Subscript> solid solutions

The dielectric properties of layered crystals of CuInP₂(Se_xS_1?x)₆ solid solutions are studied at x = 0.02, 0.05, 0.20, and 0.40. At a low selenium content (x ≤ 0.05), the solid solutions undergo a transition to the phase with short-range polar order. This transition manifests itself as a diffuse maximum in the temperature dependence of the permittivity ε′(T). Ferroelectric ordering in the solid solutions under investigation is suppressed at x > 1. It is assumed that the structural disordering initiated by the substitution of atoms in the anion sublattice of the solid solutions at 0.1 < x < 0.75 leads to the formation of the state of structured glass. The dielectric relaxation dispersion observed in the radio-frequency range at temperatures of 80–140 K is associated with the freezing of the relaxation dynamics of individual copper atoms.     

Optical and dielectric studies of phase transitions in single crystals of NaNbO<Subscript>3</Subscript>-Gd<Subscript>1/3</Subscript>NbO<Subscript>3</Subscript> solid solutions

The temperature dependences of the permittivity ? and the false-color image patterns obtained by the rotating polarizer method for single crystals of (1 ? x)NaNbO_3?x Gd_1/3NbO₃ (x = 0.003, 0.090) solid solutions with different degrees of diffuseness of the phase transition are investigated. A multifractal analysis of the false-color images has revealed anomalies in the temperature dependences of the parameter ?_∞ of the multifractal spectrum. For a sample with a sharp phase transition (x ≈ 0.003), the temperature of this anomaly is in good agreement with the temperature of the jumps in the permittivity ?(T) and birefringence. For an NNG crystal with x ≈ 0.09, which exhibits a diffuse maximum of ?(T), the temperatures of the anomalies of ?_∞(T) differ in the central and peripheral regions, which correlates with the distribution of Gd over the crystal.     

Specific heat of the [NH<Subscript>2</Subscript>(CH<Subscript>3</Subscript>)<Subscript>2</Subscript>]<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> crystal in the temperature region 80–300 K

The specific heat of [NH₂(CH₃)₂]₂ZnCl₄ was measured calorimetrically in the temperature region 80–300 K. As the temperature T decreases, the C _p (T) dependence indicates a phase transition sequence, with the phase transition at T₆=151 K observed for the first time. The thermodynamic characteristics of the crystal were refined. The transformation occurring at T₂=298.3 K is shown to be an incommensurate-commensurate phase transition.     

Electrical conductivity and dielectric properties of β-BaB<Subscript>2</Subscript>O<Subscript>4</Subscript> crystal in the temperature range 90–300 K

The electrical conductivity σ and dielectric properties (?, tanδ) of β-BaB₂O₄ were studied in the temperature range 90–300 K. The quantities σ, ?, and tanδ were measured at frequencies of 0.1, 1, and 10 kHz and 1 MHz. The dielectric permittivity and electrical conductivity were found to grow with increasing temperature at all frequencies. The permittivity decreases and the electrical conductivity increases (by several orders of magnitude) with increasing frequency. Maxima were observed in the σ=f(T) and tanδ=f(T) curves for all frequencies; the maxima shift toward higher temperatures with increasing frequency.     

Phase transitions and magnetoelectric coupling in BiFe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Zn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript>3</Subscript> multiferroics

Multiferroic BiFe_1?xZn _x O₃ ceramics were prepared by solution combustion method. Their structure, magnetoelectric, dielectric, magnetic, thermal characteristics were studied. The magnetic M(T) and heat capacity C _p (T) measurements demonstrate an antiferromagnetic to paramagnetic phase transition (T _N ) around 635 K. The anomaly on the temperature dependence of the dielectric constant near T _N was observed, which could be induced by the magnetoelectric coupling between electric and magnetic ordering. The magnetoelectric behavior was also confirmed by the linear relation between Δε and M², which is in the agreement of the Ginzburg-Landau theory for the second-order phase transition.     

Possibility of inducing superparaelectricity in strontium bismuth titanate ceramics SrTiO<Subscript>3</Subscript>: Bi

Dielectric strontium bismuth titanate ceramics SrTiO₃: Bi is a complex solid solution consisting of the Sr_1?uBi_2u/3□_u/3TiO₃ perovskite matrix and small planar inclusions related to Aurivillius-type layered ferroelectric compounds with a high Curie temperature T_C (700–950 K). The matrix is characterized by a smeared ferroelectric phase transition in the temperature range 150–200 K and exhibits relaxation dielectric polarization. At temperatures below but close to the Curie temperature T_C, the state of the ceramics can be treated as superparaelectric. The concentration dependence of the temperature corresponding to the maximum of the permittivity is explained.     

Low-temperature anomalies in the specific heat and thermal conductivity of MgB<Subscript>2</Subscript>

The temperature dependences of the specific heat C(T) and thermal conductivity K(T) of MgB₂ were measured at low temperatures and in the neighborhood of T _c . In addition to the well-known superconducting transition at T _c ≈40 K, this compound was found to exhibit anomalous behavior of both the specific heat and thermal conductivity at lower temperatures, T≈10–12 K. Note that the anomalous behavior of C(T) and K(T) is observed in the same temperature region where MgB₂ was found to undergo negative thermal expansion. All the observed low-temperature anomalies are assigned to the existence in MgB₂ of a second group of carriers and its transition to the superconducting state at T_c2≈10?12 K.     

Specific features of dielectric anomalies in Pb<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Te(Ga) near a ferroelectric phase transition

The dielectric properties of Pb_{1 ? x} Ge _x Te(Ga) (x = 0.02, 0.03, 0.05) were studied in the temperature range 77–150 K at frequencies of 10⁴–10⁶ Hz. It is revealed that the ferroelectric phase transition temperature T _c and the permittivity ? of Pb_{1 ? x} Ge _x Te(Ga) increase substantially with the Ge content. The temperature dependence of the permittivity of Pb_{1 ? x} Ge _x Te shows two peaks; the main peak is at the ferroelectric phase transition temperature T _c , and an additional peak is at T ₁ > T _c .     

Heat capacity of the [N(C<Subscript>2</Subscript>H<Subscript>5</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>CdBr<Subscript>4</Subscript> crystal in the temperature range 80–300 K

The heat capacity of the [[N(C₂H₅)₄]₂CdBr₄ crystal is measured by the calorimetric method in the temperature range from 80 to 300 K. It is revealed for the first time that the temperature dependence of the heat capacity C _p (T) exhibits an anomaly associated with the first-order phase transition occurring at the temperature T ₁ = 226.5 K. A long relaxation of the temperature of the crystal is observed in the temperature range 150–165 K.     

Adiabatic calorimetric study of the intense magnetocaloric effect and the heat capacity of (La<Subscript>0.4</Subscript>Eu<Subscript>0.6</Subscript>)<Subscript>0.7</Subscript>Pb<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript>

The temperature dependences of the intense magnetocaloric effect ΔT _AD(T, H) and the heat capacity C _p (T) of the (La_0.4Eu_0.6)_0.7Pb_0.3MnO₃ manganite are directly measured using adiabatic calorimetry. The experimental dependences ΔT _AD(T) are in satisfactory agreement with those calculated from the data on the behavior of the magnetization. The factors responsible for the absence of an anomaly in the experimental temperature dependence of the heat capacity C _p (T) in the range of the magnetic phase transition are discussed.     

Structure and dielectric properties of solid solutions Bi7Ti4 + x W x Ta1–2x O21 (x = 0–0.5)

A number of solid solutions Bi₇Ti_{4 + x} W _x Ta_1–2x O₂₁ (x = 0–0.5) have been synthesized from oxides by solid-phase reaction. The crystal structure, the electrophysical characteristics, and the microstructure of the prepared ceramic samples have been studied. According to X-ray powder diffraction, all the compounds are single-phase with the structure of mixed-layer Aurivillius phases (m = 2.5) with the orthorhombic crystal lattice (space group I2cm, Z = 2). Temperature dependences of the relative permittivity ε(T) of the compound have been measured, from which it has been found that the Curie temperature T _C of perovskite-like oxides Bi₇Ti_{4 + x} W _x Ta_1–2x O₂₁ (x = 0–0.5) decreases linearly as substitution parameter x decreases. The activation energies of charge carriers have been found in different temperature ranges.     

Phase transitions of SC(NH<Subscript>2</Subscript>)<Subscript>2</Subscript> ferroelectrics in Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-based nanoporous matrices

Temperature dependences of the linear permittivity ε' and the third harmonic amplitude γ_3ω of composites prepared by introducing ferroelectrics SC(NH₂)₂ into matrices of porous aluminum oxide Al₂O₃ with pore sizes 60 and 100 nm are determined. It is found that temperature T _c of the ferroelectric phase transition and the temperature T _i of the phase transition from incommensurable phase to the paraphrase increase significantly. The transition shifts increase as pore diameters decrease.     

(Pr–Ca) Manganites That Display Multiferroic Properties: High-Temperature Magnetic,Resistive, and Dielectric Measurements

Complex magnetic, resistive, and dielectric studies of Pr_1–xCa_xMnO₃ (х = 0.15–0.30) manganites reveal multiferroic properties at T?T_C in these solid solutions. States with local magnetization in the form of ferromagnetic clusters (nucleation temperature T* ≈ 700 K) and high dielectric constants coexist in the temperature window T_C ≤ T ≤ T*. There is a correlation between the temperature dependences of specific resistance and specific magnetization.     

Dielectric properties and specific heat of Bi<Subscript>1–<Emphasis Type="Italic">x</Emphasis> </Subscript>Sm<Subscript> <Emphasis Type="Italic">x</Emphasis> </Subscript>FeO<Subscript>3</Subscript> multiferroics

The specific heat and dielectric permittivity of Bi_1–xSm_xFeO₃ (x = 0–0.30) multiferroics have been studied in the temperature range of 300–800 K. A slight substitution of bismuth with samarium is established to cause a considerable shift in the antiferromagnetic phase transition temperature and to an increase in the specific heat over a wide temperature range. Other anomalies typical of phase transitions have been found in the temperature dependences of the specific heat and dielectric permittivity for the compounds with x = 0.10 and 0.15 at T ≈ 735 and 495 K, respectively. The results of the studies of the specific heat have been discussed together with the data of the structural investigations.     

Magnetic Resonance in Gadolinium Nanoparticles near the Curie Point

The Influence of temperature in the range from 275 to 320 K on ESR spectra and magnetization m of ensembles of spherical gadolinium nanoparticles with the diameter from 89 to 18 nm was studied. The particles with d = 18 nm had a cubic face centered structure and no magnetic transition. At T > T_C all particles were paramagnetic, and their g factors were g = 1.98 ± 0.02 irrespective of their size and structure. At T = T_C the particles having 28 to 89 nm in size experienced a magnetic and orientation transition; at T < T_C their m(H) dependences were described by the Langevin function, and the FMR lines broadened and shifted towards H = 0. FMR lines of the Gd particle ensembles showed a hysteresis behavior during magnetization reversal, which did not correlate with the coercivity of the particles. Dependences of the Gd nanoparticles FMR linewidth ΔH(T) changed proportionally to |T–T_C|.