Magnetoelastic contribution to the thermal expansion of the rare-earth phosphates TbPO4 and TmPO4

The thermal expansion of the rare-earth phosphates TbPO₄ and TmPO₄ having zircon structure has been investigated experimentally and theoretically. Significant magnetoelastic anomalies of the thermal expansion have been identified and the magnetoelastic contributions have been isolated allowing for corrections to the variation of the phonon contribution along the rare-earth ion series. It is shown that the magnetoelastic contribution to the thermal expansion of terbium and thulium phosphate is well described by the temperature dependence of the quadrupole moments of the rare-earth ions. The fully symmetric magnetoelastic coefficients for Tb³⁺ and Tm³⁺ are determined and a comparison is made of the magnetoelastic anomalies of the thermal expansion and the magnetoelastic coefficients of rare-earth phosphates and vanadates allowing for the differences in the crystal fields of the two isomorphic groups of zircons. Fiz. Tverd. Tela (St. Petersburg) 39, 106–111 (January 1997)     

Crystal field effects in rare-earth ferroborates RFe3(BO3)4 with R = Nd, Tb, Dy, or Er

Crystal field effects in rare-earth ferroborates RFe₃(BO₃)₄ with various rare-earth elements are studied theoretically. The rare-earth magnetoelastic interaction Hamiltonian is written in a multipole approximation. The field and temperature dependences of the multipole moments and strain susceptibilities of rare-earth ions in the ferroborate structure are calculated. A comparative analysis of anomalies in the thermal expansion and elastic constants of rare-earth ferroborates with Tb and Dy ions having identical magnetic structure but differing in the degree of anisotropy of the rare-earth ion is performed.     

Anomalies in thermal expansion of DyVO4 induced by quadrupolar ordering

The thermal expansion of the DyVO₄ crystal has been experimentally and theoretically investigated in the range of the Jahn-Teller structural phase transition. The manifestation of totally symmetric magnetoelastic interactions upon this transition has been studied for the first time. It is found that the temperature dependences of the unit-cell and thermal expansion parameters along the nonactive Jahn-Teller direction in the basal plane for the DyVO₄ crystal exhibit characteristic magnetoelastic anomalies at T<T _c due to the ordering of quadrupole moments of Dy³⁺ ions. The magnetoelastic contributions of the totally symmetric ε^α1 and ε^α2 and symmetry-lowering ε^γ modes to the thermal expansion are calculated within the general crystal-field formalism. The total quadrupolar coefficient G ^γ and magnetoelastic coefficient B ^γ are determined from the spectroscopic and spontaneous deformation data. It is demonstrated that the thermal expansion of the DyVO₄ crystal in the tetragonal and orthorhombic phases is well described in the framework of the unified model using a common set of interaction parameters for both phases.     

Magnetoelastic effects in rare-earth vanadates YbVO4 and HoVO4

Magnetoelastic anomalies in the thermal expansion and Young modulus, as well as the ΔE-effect in rare-earth vanadates RVO₄ (R = Ho, Yb), are investigated experimentally and theoretically. A considerable softening of the Young modulus is observed for HoVO₄ and YbVO₄ at T < 70 K and T < 150 K, respectively; this effect is adequately described in the framework of the generalized susceptibility formalism. It is shown that the field dependences of the ΔE-effect and their temperature variation in YbVO₄ can also be described using this approach. To compare with experiment, the magnetoelastic contributions to the Young modulus of an isotropic polycrystal from various elastic modes have been averaged. For the Yb vanadate, considerable magnetoelastic anomalies in the thermal expansion along the tetragonal a and c axes have been discovered. The magnetoelastic contributions are used for determining completely symmetric magnetoelastic coefficients; the role of the completely symmetric quadrupole constant for magnetoelastic effects is analyzed.     

On the magnetism of Ln<Subscript>2/3</Subscript>Cu<Subscript>3</Subscript>Ti<Subscript>4</Subscript>O<Subscript>12</Subscript> (Ln = lanthanide)

The magnetic and thermodynamic properties of the complete Ln_2/3Cu₃Ti₄O₁₂ series were investigated. Here Ln stands for the lanthanides La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb. All the samples investigated crystallize in the space group Im[`3]Im\bar{3} with lattice constants that follow the lanthanide contraction. The lattice constant of the Ce compound reveals the presence of Ce⁴⁺ leading to the composition Ce_1/2Cu₃Ti₄O₁₂. From magnetic susceptibility and electron-spin resonance experiments it can be concluded that the copper ions always carry a spin S = 1/2 and order antiferromagnetically close to 25 K. The Curie-Weiss temperatures can approximately be calculated assuming a two-sublattice model corresponding to the copper and lanthanide ions, respectively. It seems that the magnetic moments of the heavy rare earths are weakly coupled to the copper spins, while for the light lanthanides no such coupling was found. The 4f moments remain paramagnetic down to the lowest temperatures, with the exception of the Tm compound, which indicates enhanced Van-Vleck magnetism due to a non-magnetic singlet ground state of the crystal-field split 4f manifold. From specific-heat measurements we accurately determined the antiferromagnetic ordering temperature and obtained information on the crystal-field states of the rare-earth ions.     

Vibrational spectrum and elastic properties of KPb<Subscript>2</Subscript>Cl<Subscript>5</Subscript> crystals

The Raman spectra and elastic moduli of KPb₂Cl₅ crystals were studied experimentally. The results are interpreted using a parameter-free model of the crystal lattice dynamics with inclusion of the multipole moments of the electron shells of ions. The calculated and experimental results are in good agreement. It is shown that not only the halogen ions but also the heavy cations make a significant contribution to the eigenvectors of high-frequency lattice vibration modes, which accounts for the relatively low frequencies of these modes.     

Effect of defects in the rare-earth sublattice of the Kondo insulator YbB<Subscript>12</Subscript> on its spectral characteristics and magnetic susceptibility

The results of measuring the static and dynamic magnetic susceptibilities of several series of samples, which are based on the YbB₁₂ Kondo insulator and are substituted in the rare-earth sublattice, are analyzed. Substitution is performed by nonmagnetic isoelectronic Lu ions; magnetic isoelectronic Tm ions; and nonisoelectronic nonmagnetic Y, Sc, and Zr ions. The static susceptibility is measured by a SQUID magnetometer in weak fields, and the dynamic susceptibility is determined from inelastic neutron scattering data. The magnetic properties are simulated using the spectral function found from neutron experimental data. A one-to-one correspondence is established between the influence of an impurity on the initial neutron spectrum and the temperature dependence of the static susceptibility. The results obtained allow one to analyze the relation between the magnetic properties and the electronic structure of the compounds of the given class.     

Jahn-Teller transitions in Yb<Emphasis Type="Italic">X</Emphasis>O<Subscript>4</Subscript> (<Emphasis Type="Italic">X</Emphasis>=V,P) stimulated by a strong magnetic field

The effect of an external magnetic field directed along various symmetry axes of a crystal on Jahn-Teller-type structural phase transitions (quadrupole ordering) is studied in YbPO₄ and YbVO₄ crystals with zircon structure. In the absence of a magnetic field, the crystals are in a precritical state and do not exhibit a spontaneous quadrupole ordering. It is shown that, in a field H ∥ [110], the strain susceptibility χ_γ increases with the field and, at a sufficiently high field strength, an orthorhombic lattice deformation along the [100] axis arises in the crystals under study; i.e., a stimulated Jahn-Teller phase transition of γ symmetry occurs. Using interaction constants determined from independent experiments, we calculated phase diagrams and anomalies in the magnetic and magnetoelastic properties of the YbPO₄ and YbVO₄ crystals near the stimulated phase transitions, investigated the effect of various pairwise interactions on them, and analyzed possible experimental observations of the predicted effects.     

Spin transition and thermal expansion in the layered cobaltite GdBaCo<Subscript>2</Subscript>O<Subscript>5.5</Subscript>

The electrical conductivity and thermal expansion coefficient of GdBaCo₂O_5.5 samples have been measured in order to reveal the mechanism of the metal-insulator transition in cation-ordered cobaltites RBaCo₂O_5.5 (where R is a rare-earth element) and its relation to the change in the spin state of cobalt ions. It has been established that the unit cell volume considerably increases upon the transition to the metallic state at T _MI ≈ 360–365 K and that the thermal expansion exhibits anomalies (which are two orders of magnitude weaker) due to the ferromagnetic and antiferromagnetic orderings. The data obtained confirm that the spin transition in Co³⁺ ions actually proceeds simultaneously with the metal-insulator transition and excludes the possibility of stepwise spin transitions occurring at lower temperatures.     

Thermal expansion and thermal conductivity of single-crystal Cu<Subscript>x</Subscript>Ag<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>InS<Subscript>2</Subscript> solid solutions grown by the moving solvent method

Single crystals of Cu_xAg_1−x InS₂ solid solutions are grown by the moving solvent method. The compositions and structures of the single crystals are determined. The thermal expansion coefficients of these crystals are determined with a dilatometer. The thermal expansion coefficients are found to vary linearly with concentration x. The thermal conductivity of the crystals is measured by the absolute method, and the concentration dependence of the thermal conductivity is constructed. This dependence is shown to have a minimum near the equimolar composition.     

Hyperfine structure of the energy levels of the 2<Emphasis Type="Italic">p</Emphasis><Subscript>3/2</Subscript> state of the Li-, B-, and N-like <Stack><Subscript>83</Subscript><Superscript>209</Superscript></Stack>Bi ions

The lowest order corrections, considering the electron-electron interaction, to the hyperfine structure of the energy levels of the Li-, B-, and N-like ₈₃ ²⁰⁹ BI ions in the 2p _3/2 state are calculated. The contributions of the magnetic dipole moment, electric quadrupole moment, and magnetic octupole moment are taken into account. The dynamic proton model is used, in which an electron interacts with a valence proton of a nucleus via photon exchange. In this model, the distribution of the electric and magnetic moments in a nucleus is taken into account automatically.     

Magnetic properties of DyNi<Subscript>2</Subscript>B<Subscript>2</Subscript>C studied with a two-ion model for antiferromagnets

In a rare-earth antiferromagnet, two neighboring magnetic ions order spontaneously in opposite directions below the Néel temperature. Especially when it is placed in an external magnetic field, the two magnetic ions react to the field in different ways, so that they usually have different magnitudes and orientations below the magnetic transition temperature. Therefore, to describe the magnetic structure of an antiferromagnet, the single-ion ferromagnetic-like model is inadequate. To solve this problem, a two-ion model for rare-earth antiferromagnets is proposed and used in this work to investigate the magnetic properties of DyNi₂B₂C. The magnetic susceptibility curves obtained with this model show good agreements with experimental data.     

Untangling electronic,elastic and bonding properties of the ThGeO<Subscript>4</Subscript> host material from first principles calculation

We investigate the electronic, thermodynamic and bonding properties of the ThGeO₄ host material by means of pseudo-potential method within the framework of density functional theory. Zircon-type ThGeO₄ is found to undergo a pressure-driven phase transition to tetragonal scheelite structure, and beyond to monoclinic fergusonite ones. Emphasis is placed on the trends of the dynamical stability and anisotropic behavior related to structural phase transition. Linear as well as cubic thermal expansion component show a different directional dependence as a function of temperature for the investigated polymorphs of the compound. The origin of the difference in the unit cell expansion is found to be related to the distortion of the ThO₈ dodecahedra. The analysis of the non-covalent dispersion of the zircon and scheelite structures reveals a counter-balance between destabilizing interactions due to steric crowding and the current attractive and repulsive ones.     

Leading and higher twists in proton,neutron and deuteron unpolarized structure functions F<Subscript>2</Subscript>

We summarize the results of a recent global analysis of proton and deuteron F₂ structure function world data performed over a large range of kinematics, including recent measurements done at JLab with the CLAS detector. From these data the lowest moments (n≤10) of the unpolarized structure functions are determined with good statistics and systematics. The Q² evolution of the extracted moments is analyzed in terms of an OPE-based twist expansion, taking into account soft-gluon effects at large x. A clean separation among the leading- and higher-twist terms is achieved. By combining proton and deuteron measurements the lowest moments of the neutron F₂ structure function are determined and its leading-twist term is extracted. Particular attention is paid to nuclear effects in the deuteron, which become increasingly important for the higher moments. Our results for the non-singlet, isovector (p-n) combination of the leading-twist moments are used to test recent lattice simulations. We also determine the lowest few moments of the higher-twist contributions, and find these to be approximately isospin independent, suggesting the possible dominance of ud correlations over uu and dd in the nucleon.     

Magnetic and thermal properties of single-crystal NdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The neodymium ferroborate NdFe₃(BO₃)₄ undergoes an antiferromagnetic transition at T _N = 30 K, which manifests itself as a λ-type anomaly in the temperature dependence of the specific heat C and as inflection points in the temperature dependences of the magnetic susceptibility χ measured at various directions of an applied magnetic field with respect to the crystallographic axes of the sample. Magnetic ordering occurs only in the subsystem of Fe³⁺ ions, whereas the subsystem of Nd³⁺ ions remains polarized by the magnetic field of the iron subsystem. A change in the population of the levels of the ground Kramers doublet of neodymium ions manifests itself as Schottky-type anomalies in the C(T) and χ(T) dependences at low temperatures. At low temperatures, the magnetic properties of single-crystal NdFe₃(BO₃)₄ are substantially anisotropic, which is determined by the anisotropic contribution of the rare-earth subsystem to the magnetization. The experimental data obtained are used to propose a model for the magnetic structure of NdFe₃(BO₃)₄.     

Specific features of the thermal,magnetic, and dielectric properties of multiferroics BiFeO<Subscript>3</Subscript> and Bi<Subscript>0.95</Subscript>La<Subscript>0.05</Subscript>FeO<Subscript>3</Subscript>

Thermophysical, magnetic, and dielectric properties of multiferroic BiFeO₃ and Bi_0.95La_0.05FeO₃ ceramic compounds were comprehensively studied. Anomalies of the permittivity near an antiferromagnetic phase transition related to the structural variations were detected. The temperature T _N was determined from the temperature dependences of the thermal expansion coefficient, heat capacity, and differential susceptibility. It is shown that the transition point is shifted to higher temperatures as the rare-earth La ion substitutes for Bi. It is established that an insignificant substitution of lanthanum for bismuth enhances the magnetic properties of bismuth ferrite and the magnetodielectric effect.     

Thermal expansion and thermal conductivity of CuGa<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>In<Subscript>x</Subscript>Te<Subscript>2</Subscript> solid solutions

The thermal expansion coefficients and the thermal conductivity of Bridgman-grown crystals of CuGa_1−x In_xTe₂ solid solutions are investigated. It is found that the thermal expansion coefficient varies with x linearly, while the thermal conductivity is minimal when x=0.5. The Debye temperature and the rms dynamic atomic displacements are calculated from experimental data. It is shown that the Debye temperature decreases and the rms displacements in the crystal lattice sharply increase as the In content in the solid solutions grows.     

Thermal expansion of nanocrystalline and coarse-crystalline silver sulfide Ag<Subscript>2</Subscript>S

In situ studies of the thermal expansion of polymorphic phases of coarse-crystalline and nanocrystalline silver sulfide, namely, monoclinic acanthite α-Ag₂S and cubic argentite β-Ag₂S, have been performed for the first time by high-temperature X-ray diffraction. The temperature dependences of the unit cell parameters of acanthite and argentite have been measured from temperatures in the range of 300–623 K, and the thermal expansion coefficients of acanthite and argentite have been determined. The observed difference between the thermal expansion coefficients of nano- and coarse-crystalline acanthite is shown to be due to a small size of nanocrystalline silver sulfide particles, which leads to an increase in the anharmonicity of atomic vibrations.     

Excitons and energy transfer in KPb<Subscript>2</Subscript>Cl<Subscript>5</Subscript> and RbPb<Subscript>2</Subscript>Br<Subscript>5</Subscript> laser crystals

Excitonic states, radiative relaxation of electronic excitations, and energy transfer to luminescence centers in both undoped and rare-earth activated (Pr, Er, Nd, Ho, Tb, Tm) KPb₂Cl₅ and RbPb₂Br₅ crystals were studied using low-temperature (8 K) time-resolved VUV spectroscopy under selective photoexcitation by synchrotron radiation.