Lattice dynamics and hydrostatic-pressure-induced phase transitions in ScF3

New phase transitions induced by hydrostatic pressure in a cubic (under standard conditions) ScF₃ crystal are discovered by the methods of polarization microscopy and Raman scattering. The space groups $R\bar 3c$ for Z=2 and Pnma for Z=4 are proposed for the high-pressure phases. A nonempirical computation of the lattice dynamics of the crystal is carried out. It is shown that, under normal pressure, the cubic phase is stable down to T=0 K, while the application of a hydrostatic pressure gives rise to a phonon branch in the vibrational spectrum (between points R and M of the Brillouin zone) with negative values of squares of frequencies. The condensation of soft mode R₅ at the boundary point of the Brillouin zone leads to rhombohedral distortion of the cubic structure with the unit cell volume doubling. The calculated frequencies at q=0 of the ScF₃ lattice in the distorted rhombohedral phase are real-valued; the number and position of frequencies active in Raman scattering are in accord with the experimental values.     

Lattice dynamics of a Rb2KScF6 crystal in unstable cubic and tetragonal phases and in a stable monoclinic phase

The results of a nonempirical calculation of the static and dynamic properties of a Rb₂KScF₆ crystal with elpasolite structure in cubic, tetragonal, and monoclinic phases are presented. The calculation is performed on the basis of a microscopic model of an ionic crystal that takes account of the deformability and polarizability of the ions. The deformability parameters of the ions are determined from the condition that the total energy of the crystal is minimum. The computational results for the equilibrium lattice parameters are in satisfactory agreement with experimental data. Unstable vibrational modes are found in the vibrational spectrum of the lattice in the cubic and tetragonal phases. These modes occupy the phase space throughout the entire Brillouin zone. The characteristic vectors of the most unstable mode at the center of the Brillouin zone of the cubic phase are related to the displacements of the fluorine ions and correspond to rotation of ScF₆ octahedra. Condensation of this mode leads to a tetragonal distortion of the structure. In the tetragonal phase the most unstable mode belongs to the boundary point of the Brillouin zone and condensation of this mode leads to monoclinic distortion with doubling of the unit-cell volume. In the monoclinic phase unstable modes are absent in the vibrational spectrum of the lattice. Fiz. Tverd. Tela (St. Petersburg) 41, 1297–1305 (July 1999)     

Lattice dynamics and Raman scattering spectrum of elpasolite Rb<Subscript>2</Subscript>KScF<Subscript>6</Subscript>: Comparative analysis

Raman scattering spectra of elpasolite Rb₂KScF₆ are studied in a wide temperature range including two phase transitions: from the cubic to the tetragonal phase and then to the monoclinic phase. The experimental Raman scattering spectrum is compared with the lattice vibration spectra of these phases calculated using an ab initio approach. A number of anomalies (caused by structural rearrangement during the phase transitions) are revealed and quantitatively analyzed in the ranges of both the intramolecular vibrations of the octahedron molecular ScF₆ ions and low-frequency intermolecular lattice vibrations. The interaction between low-frequency intramolecular vibrations and the intermolecular modes is found to be significant, and strong resonance interaction of the rotational soft modes (which are recovered below the phase transition points) with hard low-frequency vibrations of the rubidium ion sublattice is detected. These interactions are shown to substantially complicate the spectra.     

Lattice dynamics of BiFeO<Subscript>3</Subscript> under hydrostatic pressure

The vibrational frequencies of the BiFeO₃ crystal lattice in the cubic phase (Pm3m) and the rhombohedral paraelectric phase (R3c) are calculated in terms of the ab initio model of an ionic crystal with the inclusion of the dipole and quadrupole polarizabilities. In the ferroelectric phase with the symmetry R3c, the calculated spontaneous polarization of 136 μC cm^?2 agrees well with the experimental data. The dependences of the unit cell volume, the elastic modulus, and the vibrational frequencies on the pressure are calculated. It is found that the frequency of an unstable ferroelectric mode in both the cubic (Pm3m) and rhombohedral (R3c) phases are almost independent of the applied pressure, in contrast to classical ferroelectrics with a perovskite structure, where the ferroelectric instability is very sensitive to a variation in the pressure.     

Magnetotransport characteristics of strained La<Subscript>0.7</Subscript>Sr<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript> epitaxial manganite films

The electrical and magnetic characteristics of La_0.7Sr_0.3MnO₃ (LSMO) epitaxial manganite films are investigated by different methods under conditions when the crystal structure is strongly strained as a result of mismatch between the lattice parameters of the LSMO crystal and the substrate. Substrates with lattice parameters larger and smaller than the nominal lattice parameter of the LSMO crystal are used in experiments. It is shown that the behavior of the temperature dependence of the electrical resistance for the films in the low-temperature range does not depend on the strain of the film and agrees well with the results obtained from the calculations with allowance made for the interaction of electrons with magnetic excitations in the framework of the double-exchange model for systems with strongly correlated electronic states. Investigations of the magneto- optical Kerr effect have revealed that an insignificant (0.3%) orthorhombic distortion of the cubic lattice in the plane of the NdGaO₃(110) substrate leads to uniaxial anisotropy of the magnetization of the film, with the easy-magnetization axis lying in the substrate plane. However, LSMO films on substrates (((LaAlO₃)_0.3+(Sr₂AlTaO₆)_0.7)(001)) ensuring minimum strain of the films exhibit a biaxial anisotropy typical of cubic crystals. The study of the ferromagnetic resonance lines at a frequency of 9.76 GHz confirms the results of magnetooptical investigations and indicates that the ferromagnetic phase in the LSMO films is weakly inhomogeneous.     

Hydrostatic pressure-induced phase transitions in RbMnCl<Subscript>3</Subscript>: Raman spectra and lattice dynamics

Raman scattering spectra of RbMnCl₃ are measured at room temperature under high hydrostatic pressure. The results are interpreted based on first principles lattice dynamics calculations. The experimental data obtained correlate with the calculations in the low frequency domain but disagree slightly in the region of high-frequency vibrations. The transition from the hexagonal to the cubic perovskite phase observed earlier (near 0.7 GPa) was confirmed, and new transitions to lower symmetry distorted phases were discovered (at 1.1 and 5 GPa).     

X-ray studies of the (La,Sr)MnO<Subscript>3</Subscript> perovskite manganite structure

X-ray studies of perovskite manganites (La_0.9Sr_0.1)_0.9MnO₃ and La_1?xSr_xMnO₃ (x = 0.1, 0.15, 0.2, 0.25) are reported. The atom positions and interatomic distances and angles are calculated as a function of Sr doping at room temperature using the FullProf software. The temperature dependences of the crystal lattice parameters and unit cell volume are investigated. The effects of structural and magnetic phase transitions on the crystal lattice parameters are studied in detail. The bulk magnetoelastic contribution to thermal expansion is studied experimentally and calculated.     

Phase separation in a manganite La<Subscript>0.95</Subscript>Ba<Subscript>0.05</Subscript>MnO<Subscript>3</Subscript> crystal

The structure and magnetic states of a crystal of lightly doped manganite La_0.95Ba_0.05MnO₃ were studied using thermal-neutron diffraction, magnetic measurements, and electrical resistance data in a wide temperature range. It is shown that, in terms of its magnetic properties, the orthorhombic crystal is characterized by two order parameters, namely, antiferromagnetic (T _N = 123.6 K) and ferromagnetic (T _C = 136.7 K). The results obtained differ in detail from known information on the manganites La_0.95Ca_0.05MnO₃ and La_0.94Sr_0.06MnO₃. Two models of the magnetic state of the La_0.95Ba_0.05MnO₃ crystal are discussed, one of which is a model of a canted antiferromagnetic spin system and another is associated with the phase separation of the manganite. Arguments are advanced in favor of the coexistence in this crystal of the antiferromagnetic phase (about 87%) with a Mn⁴⁺ ion concentration of 0.048 and the 1/16-type charge-ordered ferromagnetic phase (about 13%) with a Mn⁴⁺ ion concentration of 0.0625. The specific features of the manganite studied are due to self-organization of the La_0.95Ba_0.05MnO₃ crystal lattice caused by the relatively large barium ion size.     

Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in Rb2KInF6

The static and dynamic properties of cubic Rb₂KInF₆ crystals with elpasolite structure are calculated using a nonempirical method. Calculations are performed within a microscopic ionic-crystal model taking into account the deformation and polarization of ions. The deformation parameters of ions are determined by minimizing the total energy of the crystal. The calculated equilibrium lattice parameters agree satisfactorily with the experimental data. It is found that in the cubic phase there are vibrational modes that are unstable everywhere in the Brillouin zone. The eigenvectors of the unstablest mode at the center of the Brillouin zone of the cubic phase are associated with the displacements of F ions and correspond to rotations of InF₆ octahedra. Condensation of this mode leads to a tetragonal distortion of the structure. In order to describe the Fm3m → I4/m phase transition, an effective Hamiltonian is constructed under the assumption that the soft mode whose eigenvector corresponds to octahedron rotation is local and coupled with homogeneous elastic strains. The parameters of the effective Hamiltonian are determined using the calculated crystal energy for the distorted structures due to soft-mode condensation. The thermodynamic properties of the system with this model Hamiltonian are investigated using the Monte Carlo method. The phase transition temperature is calculated to be 550 K, which is twice its experimental value (283 K). The tetragonal phase remains stable down to T=0 K; the effective Hamiltonian used in this paper thus fails to describe the second phase transition (to the monoclinic phase). Thus, the transition to the tetragonal phase occurs for the most part through octahedron rotations; however, additional degrees of freedom, first of all, the displacements of Rb ions, should be included into the effective Hamiltonian in order to describe the transition to the monoclinic phase.     

Phase transition in CdHfO<Subscript>3</Subscript>

The phase transition from an orthorhombic phase (space group Pnma) to a rhombohedral phase (space group R3m) of the CdHfO₃ hafnate is investigated using methods of structural analysis. It is shown that crystal lattices of both phases contain polar structural units (octahedra, cubooctahedra). On this basis, it is assumed that the orthorhombic and rhombohedral phases of the CdHfO₃ compound are the antiferroelectric and ferroelectric phases, respectively.     

Effect of high pressure on the crystal and magnetic structure and on the raman spectra in Pr<Subscript>0.7</Subscript>Ba<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript> manganite

The crystal and magnetic structure and the Raman spectra in Pr_0.7Ba_0.3MnO₃ manganite have been studied by the neutron diffraction technique at pressures up to 5 GPa as well as by the X-ray diffraction and Raman spectroscopy at pressures up to 30 GPa. The pressure dependence is determined for the lattice parameters, unit cell volume, Mn-O bond lengths in the orthorhombic structure of the Imma symmetry, and bending and stretching vibration modes for oxygen octahedra. In the low-temperature range at pressure P = 1.9 GPa, the magnetic transition from the initial ferromagnetic (FM) ground state (T _C = 197 K) to the A-type antiferromagnetic (AFM) state (T _N = 153 K) has been revealed. The FM and AFM phases coexist at pressures up to 5.1 GPa and exhibit negative and positive values of the pressure coefficient for the Curie and Néel temperature, respectively (dT _C/dP = −2.3 K/GPa and dT _N/dP = 8 K/GPa). The pressure dependence of the Curie temperature in Pr_0.7Ba_0.3MnO₃ differs drastically from that observed in other manganites of nearly the same composition with the orthorhombic Pnma and rhombohedral R[`3]cR\bar 3c structures, where the FM phase is characterized by the positive values of dT _C/dP. The structural mechanisms of these phenomena are discussed.     

Manganese doping effects on interband electronic transitions,lattice vibrations,and dielectric functions of perovskite-type Ba<Subscript>0.4</Subscript>Sr<Subscript>0.6</Subscript>TiO<Subscript>3</Subscript> ferroelectric ceramics

The Ba_0.4Sr_0.6−x Mn _x TiO₃ (BSMT) ceramics with different Mn composition (from 1% to 10%) have been prepared via the conventional solid-state reaction sintering. The X-ray diffraction analysis shows that the ceramics are polycrystalline with the single perovskite phase. The lattice vibrations and optical properties have been investigated using Raman scattering, spectroscopic ellipsometry (SE), and infrared reflectance spectra. It was found that the optical bandgap for the BSMT ceramics is varied between 3.40 and 3.65 eV. The three first-order Raman-active phonon modes can be observed, and the frequency of the A ₁(LO₃)/E(LO) mode shows a blue shift of 8 cm⁻¹ with the Mn composition, which can be attributed to the distortion of the TiO₆ octahedron. With increasing Mn composition, the frequency of the infrared-active TO₄ mode decreases from 532 to 520 cm⁻¹, owing to the local variation of the lattice constant induced by the Mn incorporation. Moreover, the optical functions of the ceramics from the far-infrared to ultraviolet region are obtained based on the SE and reflectance spectra, which is useful for the potential applications in ferroelectric-based optoelectronic devices.     

Electronic structure,lattice dynamics,and magnetoelectric properties of double perovskite La<Subscript>2</Subscript>CuTiO<Subscript>6</Subscript>

The results of ab initio calculations of the electronic structure, vibrational properties, and the magnetoelectric effect in the La₂CuTiO₆ crystal with double perovskite structure are presented. The lattice dynamics calculation shows the presence of unstable modes in the phonon spectrum of the high-symmetry cubic phase with space group \(Fm\overline 3 m\). Condensation of two most unstable modes belonging to the center and the boundary point X of the Brillouin zone leads to the formation of a nonpolar stable phase with space group P2₁/n. The calculation taking into account spin polarization shows that the magnetic ground state is E*-type antiferromagnetic with doubled magnetic cell and with the two spin-up and two spin-down configuration of magnetic moments of copper ions along the [010] crystallographic direction. Such ordering of magnetic moments leads to polar space group and polarization formation. The polarization magnitude is estimated as 71 μC/m².     

Lattice dynamics of BiFeO<Subscript>3</Subscript>: The untypical behavior of the ferroelectric instability under hydrostatic pressure

Within a nonempirical model of an ionic crystal with the inclusion of the dipole and quadrupole ion polarizations, the lattice vibrational frequencies, high-frequency dielectric constant, Born dynamic charges, and the elasticity moduli of the BiFeO₃ crystal have been calculated and their dependencies on the hydrostatic pressure in the cubic, rhombic, and rhombohedral phases have been determined. The results indicate the presence of the ferroelectric instability, which depends weakly on the pressure in all of the phases investigated. The dependence of the crystal lattice dynamics on the applied pressure for the cubic phases of BiAlO₃, BaTiO₃, and PbTiO₃ has been calculated for comparison.     

Structural disorder in the paraelectric phase of the Fe<Subscript>3</Subscript>B<Subscript>7</Subscript>O<Subscript>13</Subscript>Br boracite

A structural model of the cubic paraelectric phase of a Fe₃B₇O₁₃Br crystal belonging to the boracite family has been developed using the data obtained by single-crystal X-ray diffraction with due regard for the results of extended X-ray absorption fine structure (EXAFS) spectroscopy. It has been shown that the best agreement between the data obtained by these two methods is achieved within a model assuming a disorder in the arrangement of both the Fe and Br atoms and a high degree of correlation of their displacements. It has been found that, during the phase transition from the rhombohedral ferroelectric phase to the cubic paraelectric phase, no significant transformation of the structure is observed on a local level. In this case, a change in the macroscopic symmetry occurs predominantly as a result of the variation in the set of possible spatial orientations of stable structural fragments, which is characteristic of order-disorder phase transitions.     

Structural and magnetic phase transitions in Pr<Subscript>0.7</Subscript>Ca<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript> at high pressures

The crystal structure and Raman spectra of Pr_0.7Ca_0.3MnO₃ manganite at high pressures of up to 30 GPa and the magnetic structure at pressures of up to 1 GPa have been studied. A structural phase transition from the orthorhombic phase of the Pnma symmetry to the high-pressure orthorhombic phase of the Imma symmetry has been observed at P ∼ 15 GPa and room temperature. Anomalies of the pressure dependences of the bending and stretching vibrational modes have been observed in the region of the phase transition. A magnetic phase transition from the initial ferromagnetic ground state (T _C = 120 K) to the A-type antiferromagnetic state (T _N = 140 K) takes place at a relatively low pressure of P = 1 GPa in the low-temperature region. The structural mechanisms of the change of the character of the magnetic ordering have been discussed.     

Nuclear superstructure {1/2, 0, 1/2} of an La<Subscript>0.93</Subscript>Sr<Subscript>0.07</Subscript>MnO<Subscript>3</Subscript> manganite orthorhombic crystal

The {1/2, 0, 1/2} nuclear superstructure in an La_0.93Sr_0.07MnO₃ manganite orthorhombic crystal is revealed using thermal-neutron diffraction. It is demonstrated that this superlattice belongs to the class of distortion-type structures and is directly associated with a 1/16-type ordering of Mn⁴⁺ and Mn³⁺ ions in a collinear ferromagnetic phase of the La_0.93Sr_0.07MnO₃ manganite.     

Pressure-induced modifications of crystal and magnetic structure of oxygen deficient La<Subscript>0.7</Subscript>Sr<Subscript>0.3</Subscript>MnO<Subscript>3-d</Subscript> manganites

The crystal and magnetic structures of the oxygen deficient manganites La_0.7Sr_0.3MnO_3-d (d = 0.15, 0.20) have been studied by means of powder neutron diffraction over the 0–5.2 GPa pressure and 10–290 K temperature ranges. La_0.7Sr_0.3MnO_2.85 exhibits a coexistence of rhombohedral and tetragonal (I4/mcm) crystal structures and below T_g ~ 50 K a spin glass state is formed. La_0.7Sr_0.3MnO_2.80 exhibits a tetragonal (I4/mcm) crystal structure. Below T_g ~ 50 K a phase separated magnetic state is formed, involving coexistence of C-type AFM domains with spin glass domains. In both compounds the crystal structure and magnetic states remain stable upon compression. The factors leading to the formation of different magnetic states in La_0.7Sr_0.3MnO_3-d (d = 0.15, 0.20) and their specific high pressure behavior, contrasting with that of the stoichiometric A_0.5Ba_0.5MnO₃ (A = Nd, Sm) compounds showing pressure-induced suppression of the spin glass state and the appearance of the FM state, are analysed.     

Paramagnetic-ferromagnetic and insulator-metal phase transitions in La<Subscript>0.88</Subscript>MnO<Subscript>2.95</Subscript>

We present the results a study of structure by neutron diffraction and data on the magnetic properties (linear and nonlinear (second and third order) susceptibilities) of polycrystalline La_0.88MnO_2.95. This compound exhibits an insulator-metal (IM) phase transition at T _IM ≈ 253 K (above the Curie temperature, T _C ≈ 244 K) and reveals colossal magnetoresistance. The crystal structure is found to be rhombohedral, and the space group is R3c. Analysis of magnetic properties shows that at T* ≈ 258 K > T _C , isolated paramagnetic clusters occur in the paramagnetic matrix; their concentration increases upon cooling. We observed no noticeable differences between the temperature evolution of the clustered state of this manganite with its insulator-metal transition and in the insulator La_0.88MnO_2.91. Possible scenarios of the paramagnet-ferromagnet and I-M transitions in a self-organized clustered structure are discussed.     

Effect of Sr content on structure and electrical properties of La1−x Sr x MnO3 from ITSOFC cathode view point

The samples belonging to La_1−x Sr _x MnO₃ series, prepared by combustion route without using fuel, exhibit crystal structural phase transition with the change in Sr content. Less than 40 mol% Sr is partially substituted in the crystal structure of LaMnO₃. The structural phase transition from rhombohedral to cubic, cubic to tetragonal, and tetragonal to orthorhombic takes place on 40, 60, and 80 mol% addition of Sr. The highest electrical conductivity in La_0.4Sr_0.6MnO₃ is understood to be due to the maximum concentration of polaron. The polarons are formed due to the conversion of Mn³⁺ to Mn⁴⁺ so as to achieve electroneutrality after substitution of Sr²⁺ for La³⁺.