The two models give different

The two models give different patterns of the ionic displacements in the phonon branches. In the case of the rigid-ion model the fit indicates that the TA branch in the (q, q, 0) direction, for q >0.1, corresponds mainly to the motion of lead and hafnium with the lead displacements about 2 times larger than the hafnium ones. In the case of the shell model the displacements in this branch are mostly due to Pb with a small addition of the oxygen displacement (about 15 percent of that of Pb). The result of the shell model appears to be more logical. The hafnium ret pathway has a large ionic radius and, thus, is not expected to participate intensively in the phonon modes with small energy. On the other hand, the lead ion is expected to move intensively in the low-energy modes because of its small ionic radius as compared to the available space in the large unit cell of PbHfO3. The parameters of the fits using the rigid-ion model and the shell model are listed in Tables 1 and 2. Similar to the data on SrTiO3, the short-range force constants are generally larger in magnitude for the shell model. In the case of the shell model the dielectric constant corresponding to the fit is 527, which is reasonably close to the experimental value of about 575 at high temperatures. Like other perovskites, the SM fit for PbHfO3 gives a strongly negative oxygen shell charge: about –2.7 electrons. By analogy with the analysis performed by Cowley for SrTiO3[9], we have analyzed the anisotropy of the oxygen polarizability. In the directions parallel to the corresponding PbO planes the polarizability is 4.4Å3, while in the direction towards hafnium it is only 1.8Å3. This anisotropy of oxygen polarizability may be important for further understanding of the microscopic reason for the flattened TA branch.
Conclusion We have performed the analysis of the phonon dispersion curves of PbHfO3 crystals in the paraelectric phase using two lattice-dynamical models. Both models provide an adequate description of the available data. The shell model, in addition to the actual dispersion curves, provides a reasonable value for the dielectric constant confirming the reliability of the ionic displacement patterns provided by this model.
Acknowledgments R. Burkovsky acknowledges the support by the Grant of the President of the Russian Federation for state support of Russian young scientists MK-5685.2016.2. D. Andronikova and Yu. Bronwald acknowledge the support of RFBR (Grant 16-02-01162). The work of Yu. Bronwald and A. Filimonov was performed under the government order of the Ministry of Education and Science of RF.
Introduction A very interesting correlation between doping-induced conductivity and ferromagnetism was discovered at the end of the 20th century for the initially dielectric manganese-containing perovskites LaMnO3, the so-called manganites, in which the rare-earth metal was replaced by the alkaline-earth one. Initial ternary composites LaMnO3 and AMnO3, where A=Ca, Sr or Ba, are antiferromagnetics whose magnetic moments are located at the sites occupied by manganese ions. In the case of quaternary stoichiometry of the La1–AMnO3 type with intermediate compositions (with different values of x), the composite not only becomes a strong ferromagnetic, but also exhibits metallic-type conductivity observed below the Curie temperature [1]. Additionally, this compound is a material with extremely high values of dielectric permittivity (up to 107) and magnetocapacitance effect (up to 105%) even at room temperature [2]. The structure of the cubic perovskite LaMnO3 is a three-dimensional lattice consisting of regular MnO3 octahedra connected by oxygen vertices [3,4]. In this structure, La3+, which is the larger cation, is located in the center of the cube formed by the oxygen octahedra, and Mn3+, which is smaller, is in the center of the octahedron. On the other hand, the structure of La1–SrMnO3 changes from orthorhombic to rhombohedral [5] at increasing of strontium cation concentration, and an unusual polaron-ordered state is observed in the intermediate range of concentrations (for x=0.10–0.15). According to the neutron diffraction data [6], this condition is associated with the ordered arrangement of aliovalent Mn3+/Mn4+ ions in alternating (001) planes and the emergence of the corresponding superstructure.