Harmonic analysis of coefficients of free energy decomposition in the polarization of a Rb<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> crystal

Landau–Devonshire decomposition coefficients W_C in a series with respect to P_C are determined via harmonic analysis of experimental free energy coordinates W_C of a Rb₂ZnCl₄ crystal, depending on its polarization P_C. The number of terms needed in W_C decomposition is determined for quantitative evaluation of the measured data.     

Using Harmonic Analysis to Determine the Coefficients of Expansion in the Electrical Energy of a Rb<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> Crystal from Its Polarization

Values of the expansion coefficients of electrical energy W_c in a series with respect to even powers of polarization P_c are determined using the Landau–Devonshire theory by studying the repolarization dynamics of an Rb₂ZnCl₄ crystal. Experimental results obtained from the dynamics are compared to theoretical representations of the Landau–Devonshire theory that describe the dependences of W_c(P_c) in statics.     

X-ray study of [N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> at low temperatures

The unit cell parameters a, b, and c of [N(CH₃)₄]₂ZnCl₄ have been measured by x-ray diffraction in the temperature range 80–293 K. Temperature dependences of the thermal expansion coefficients α_a, α_b, and α_c along the principal crystallographic axes and of the unit cell thermal expansion coefficient α_V were determined. It is shown that the a=f(T), b=f(T), and c=f(T) curves exhibit anomalies in the form of jumps at phase transition temperatures T₁=161 K and T₂=181 K and that the phase transition occurring at T₃=276 K manifests itself in the a=f(T) and b=f(T) curves as a break. A slight anisotropy in the coefficient of thermal expansion of the crystal was revealed. The phase transitions occurring at T₁=161 K and T₂=181 K in [N(CH₃)₄]₂ZnCl₄ were established to be first-order.     

Refractometry of mechanically compressed (NH<Subscript>4</Subscript>)<Subscript>2</Subscript>SO<Subscript>4</Subscript> crystals

The effect of uniaxial mechanical pressure σ _m ≤ 150 bar on the spectral (300–800 nm) dependence of the birefringerence Δn _i and refractive indices n _i of (NH₄)₂SO₄ crystals has been investigated. It is shown that the dispersion of n _i (λ) and Δn _i (λ) is normal and sharply increases with approach to the absorption edge. It is established that uniaxial pressure does not change the character of the dispersions dn _i /dλ and dΔn _i /dλ and only affects their magnitudes. It is shown that the increase in the refractive indices under uniaxial stress is mainly due to the increase in the refraction caused by the increase in the band gap and long-wavelength shift of the UV absorption band maximum.     

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.

     

Crystallographic characteristics and phase transitions in the [N(C<Subscript>2</Subscript>H<Subscript>5</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>CdBr<Subscript>4</Subscript> crystal in the low-temperature range

The results of x-ray structural studies of the [N(C₂H₅)₄]₂CdBr₄ crystal at low temperatures are presented. The unit cell parameters and the thermal expansion coefficients along the main crystallographic directions are measured at temperatures in the range from 90 to 320 K. The integrated intensities of the diffraction reflections are investigated as a function of the temperature. It is shown that the curves a = f(T), c = f(T), I ₅₀₀ = f(T), and I ₀₀₆ = f(T) at temperatures T ₁ ≈ 174 K and T ₂ ≈ 226 K exhibit anomalies in the form of abrupt changes in the lattice parameters and the diffraction reflection intensities. This indicates that the [N(C₂H₅)₄]₂CdBr₄ crystal undergo phase transitions at these temperatures. Moreover, there is an anomaly in the form of a small maximum at the temperature T ₃ = 293 K.     

Multiphonon mechanism of the ionization of traps in Al<Subscript>2</Subscript>O<Subscript>3</Subscript>: Experiment and numerical simulation

Charge transfer in Al₂O₃ has been investigated experimentally and theoretically. The experimental results are in qualitative agreement with the theory of the multiphonon ionization of deep centers. The thermal (W _T = 1.5 eV) and optical (W _opt = 3.0 eV) energies of the deep centers have been determined. It has been found that the experimental data are unsatisfactorily described by the Pool-Frenkel mechanism, which provides a non-physically small frequency factor and anomalously large effective tunneling mass.     

Experimental Study and Analysis of Absorption Spectra of Ni<Superscript>2+</Superscript> Ions in Nickel Orthoborate Ni<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>2</Subscript>

The results of studies of the absorption spectra of nickel orthoborate Ni₃(BO₃)₂ in the range of electronic d–d-transitions are reported. The obtained data are analyzed in the framework of the crystal field theory. The Ni²⁺ ions are located in two crystallographically nonequivalent positions 2a and 4f with point symmetry groups C_2h and C₂, respectively, surrounded by six oxygen ions forming deformed octahedra. The absorption spectra exhibit three intense bands corresponding to spin-resolved transitions from the ground state of nickel ion ³A_2g (³F) to the sublevels of the ³T_2g (³F), ³T_1g (³F) and ³T_1g (³P) triplets split by the spinorbit interaction and the rhombic component of the crystal field. At temperatures below 100 K, the spectra exhibit a thin structure, in which phonon-free lines can be distinguished. Comparison of the calculated frequencies of the zero-phonon transitions with the experimental data allows estimating parameters of the crystal field acting on the nickel ions in the 2a- and 4f-positions, as well as the parameters of electrostatic interaction between the 3d electrons and spin-orbit interaction constants.     

Concentration quenching and migration of excitations in a bulk Cd<Subscript>0.5</Subscript>Mn<Subscript>0.5</Subscript>Te crystal

The curves of intracenter luminescence decay for Mn²⁺ ions in the Cd_0.5Mn_0.5Te semiconductor solid solution, obtained in a low-temperature experiment, have been simulated by the Monte Carlo method. The features of the kinetics of the 2-eV band in the time interval where significant nonexponentiality of relaxation at different points of the emission band profile manifests itself, as well the integral kinetics and energy relaxation, have been considered. Migration of ion excitations and concentration quenching (which was previously disregarded) are considered to be the main mechanisms determining the kinetic curve formation. It was established that excitation by 2.34-eV photons leads to both selective (intracenter) and band excitation of Mn²⁺ ions. Comparison of the results of numerical simulation and experiment showed that the characteristic values of the migration and quenching rates (W _m and W _q , respectively) are close in magnitude and W _{q, m} ≈ 0.1/τ, where τ is the lifetime at the long-wavelength band wing with the exponential kinetics. The estimated quantum yield (0.56) indicates significant influence of the concentration quenching on the 2-eV luminescence quantum yield in Cd_{1 ? x} Mn _x Te and Zn_{1 ? x} Mn _x S crystals with a high concentration of Mn²⁺ ions.     

Pressure-induced superconductivity and structural transitions in Ba(Fe<Subscript>0.9</Subscript>Ru<Subscript>0.1</Subscript>)<Subscript>2</Subscript>As<Subscript>2</Subscript>

Electrical transport and structural characterizations of isoelectronically substituted Ba(Fe_0.9Ru_0.1)₂As₂ have been performed as a function of pressure up to ～ 30 GPa and temperature down to ～ 10 K using designer diamond anvil cell. Similar to undoped members of the AFe₂As₂ (A = Ca, Sr, Ba) family, Ba(Fe_0.9Ru_0.1)₂As₂ shows anomalous a-lattice parameter expansion with increasing pressure and a concurrent ThCr₂Si₂ type isostructural (I4/mmm) phase transition from tetragonal (T) phase to a collapsed tetragonal (cT) phase occurring between 12 and 17 GPa where the a is maximum. Above 17 GPa, the material remains in the cT phase up to 30 GPa at 200 K. The resistance measurements show evidence of pressure-induced zero resistance that may be indicative of high-temperature superconductivity for pressures above 3.9 GPa. The onset of the resistive transition temperature decreases gradually with increasing pressure before completely disappearing for pressures above ～ 10.6 GPa near the T-cT transition. We have determined the crystal structure of the high-T _c phase of Ru-doped BaFe₂As₂ to remain as tetragonal (I4/mmm) by analyzing the X-ray diffraction pattern obtained at 10 K and 9.7 ± 0.7 GPa, as opposed to inferring the structural transition from electrical resistance measurement, as in a previous report [S.K. Kim, M.S. Torikachvili, E. Colombier, A. Thaler, S.L. Bud’ko, P.C. Canfield, Phys. Rev. B 84, 134525 (2011)].     

Electronic Structure,Optical Properties,and Pressure Behavior of the CdB<Subscript>4</Subscript>O<Subscript>7</Subscript> and HgB<Subscript>4</Subscript>O<Subscript>7</Subscript> Compounds

Ab initio calculations of the structural, electronic, and optical properties of the CdB₄O₇ and HgB₄O₇ tetraborate compounds in three structural modifications with the Pbca, Cmcm, and Pmn2₁ symmetry have been performed in the framework of the density functional theory using the VASP package. The calculations of the electronic band structure showed that these compounds in all the investigated modifications are dielectrics with a band gap of 2–4 eV. The calculation of the structural properties of the tetraborates under pressure showed that the phase transition between the Pbca and Pmn2₁ structures in cadmium and mercury tetraborates occurs under pressures of 4.8 and 4.7 GPa, respectively.     

Surface superconductivity and<Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">c3</Emphasis></Subscript> in UPt<Subscript>3</Subscript>

Ginzburg-Landau (GL) theory is used to study surface superconductivity for UPt₃ for various order parameter symmetries (OPS), andH _c3 is found for all principal directions of the surface normal\(\hat n\) and the field [1]. Assuming specular reflection, and allowing for reorientation of the antiferromagnetic symmetry breaking field in the models withE _1g ,E _2g ,E _1u , orE _2u symmetry, the experiments of Keller et al. [2] with\(\hat n = \hat a\) can be qualitatively explained for all OPS except possiblyA _1u ⊕B _1u . The implied GL parameters then predict qualitatively different and OPS dependent behavior for\(\hat n = \hat a^* \) and\(\hat n = \hat c\). Study ofH _c3 for these surfaces would give strong clues about the OPS of UPt₃.     

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.     

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.     

Optical and x-ray diffraction studies of the symmetry of distorted phases of the (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>ZrF<Subscript>7</Subscript> crystal

(NH₄)₃ZrF₇ single crystals were grown, and polarization-optical and x-ray diffraction studies were performed on powders and crystalline plates of various cuts over a wide temperature range. Phase transitions are revealed at temperatures T _1↑ = 280 K, T _2↑ = 279.6 K, T _3↑ = 260–265 K, and T _4↑ = 238 K on heating and at T _1↓ = 280 K, T _2↓ = 269–270 K, T _3↓ = 246 K, and T _4↓ = 235 K on cooling. The sequence of changes in symmetry is established to be as follows: O _h ⁵ (Z = 4) ? D _2h ²⁵ (Z = 2) ? C _2h ³ (Z = 2) ? C _i ¹ (Z = 108) ? monoclinic²(Z = 216).     

Thermophysical studies of the phase transitions in (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>NbOF<Subscript>6</Subscript> crystals

The thermophysical properties of oxyfluoride (NH₄)₃NbOF₆ were studied in detail over wide ranges of temperatures and pressures. At atmospheric pressure, a sequence of four structural phase transitions was established with the following changes in entropy: ΔS ₁ = Rln 2.7, δS ₂ = Rln38.3, ΔS ₃ = 0.08R, and ΔS ₄ = 0.17R. An external hydrostatic pressure was found to narrow the region of existence of the initial cubic phase. A triple point was detected in the p-T diagram; at a pressure above 0.07 GPa, the transition between the tetragonal and monoclinic phases occurs through a distorted high-pressure phase.     

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.     

Breit-Wigner parameters of the <Emphasis Type="Italic">S</Emphasis><Subscript>11</Subscript>(1535) nucleon resonance

The results of a partial-wave analysis of the angular distributions for the process γp → ηp over the energy range up to 2 GeV are presented. Reliable estimates of the Breit-Wigner parameters of the S₁₁(1535) resonance, as well as the energy dependence of the real and imaginary parts of the electric dipole amplitude E₀₊ and its phase, are derived from the energy dependence of the regression coefficient a₀(W).     

Structural transformations of K<Subscript>3</Subscript>H(SO<Subscript>4</Subscript>)<Subscript>2</Subscript> crystals with variations in temperature

Single crystals of the K₃H(SO₄)₂ compound are investigated using X-ray diffraction on Xcalibur S and Bruker diffractometers. The structure of the low-temperature monoclinic phase is refined (space group C2/c, z = 4, a = 14.698(1) Å, b = 5.683(1) Å, c = 9.783(1) Å, β = 103.01(1)°, T = 293 K, Bruker diffractometer), the structural phase transition is revealed, and the structure of the high-temperature trigonal phase is determined (space group R \(\bar 3\) m, z = 3, a = 5.73(1) Å,c = 21.51(1) Å,T = 458 K, Xcalibur diffractometer).     

Ferroelastic phase transition in crystalline K<Subscript>3</Subscript>Na(CrO<Subscript>4</Subscript>)<Subscript>2</Subscript>: Acoustic studies

Ultrasonic studies of the temperature behavior of the velocity and damping of sound for the xx and zz longitudinal and yx and zx transverse waves in K₃Na(CrO₄)₂ have been carried out in the temperature interval 185–295 K, which includes the region of the ferroelastic phase transition. The acoustic parameters for both shear and longitudinal waves were found to have anomalies in the region of the phase transition with a Curie temperature of 235.5 K. A theoretical analysis of the softening of the elastic moduli c₄₄ and c₆₆ was performed on the basis of the Landau expansion in terms of the strain tensor components ?₄ and (?₂-?₁)/2 considered as the linearly coupled primary and secondary order parameter, respectively. The absolute values of the elastic moduli c₁₁, c₃₃, c₄₄, c₆₆, c₁₂, and c₁₄ at 295 K were calculated.