Coulomb interaction and ferroelectric instability of BaTiO3

Using first-principles calculations, the phonon frequencies at the $\Gamma$ point and the dielectric tensor are determined and analysed for the cubic and rhombohedral phases of BaTiO$_{3}$. The dipole-dipole interaction is then separated \`a la Cochran from the remaining short-range forces, in order to investigate their respective influence on lattice dynamics. This analysis highlights the delicate balance of forces leading to an unstable phonon in the cubic phase and demonstrates the extreme sensitivity of this close compensation to minute effective charge changes. Within our decomposition, the stabilization of the unstable mode in the rhombohedral phase or under isotropic pressure has a different origin.Comment: 9 pages, 4 tables, 1 figur

Ab initio phonon dispersion curves and interatomic force constants of barium titanate

The phonon dispersion curves of cubic BaTiO_3 have been computed within a first-principles approach and the results compared to the experimental data. The curves obtained are very similar to those reported for KNbO_3 by Yu and Krakauer [Phys. Rev. Lett. 74, 4067 (1995)]. They reveal that correlated atomic displacements along chains are at the origin of the ferroelectric instability. A simplified model illustrates that spontaneous collective displacements will occur when a dozen of aligned atoms are coupled. The longitudinal interatomic force constant between nearest neighbour Ti and O atoms is relatively weak in comparison to that between Ti atoms in adjacent cells. The small coupling between Ti and O displacements seems however necessary to reproduce a ferroelectric instability.Comment: 12 pages, 4 figure

Applications of the generalized gradient approximation to ferroelectric perovskites

The Perdew-Burke-Ernzerhof generalized gradient approximation to the density functional theory is tested with respect to sensitivity to the choice of the value of the parameter $\kappa$, which is associated to the degree of localization of the exchange-correlation hole. A study of structural and dynamical properties of four selected ferroelectric perovskites is presented. The originally proposed value of $\kappa$=0.804 %(best suited for atoms and molecules) works well for some solids, whereas for the ABO$_3$ perovskites it must be decreased in order to predict equilibrium lattice parameters in good agreement with experiments. The effects on the structural instabilities and zone center phonon modes are examined. The need of varying $\kappa$ from one system to another reflects the fact that the localization of the exchange-correlation hole is system dependent, and the sensitivity of the structural properties to its actual value illustrates the necessity of finding a universal function for $\kappa$.Comment: 15 pages, 2 figures, PRB in pres

Effet Brillouin du molybdate de gadolinium au voisinage du point de transition

The velocities of longitudinal acoustic phonons propagating perpendicularly to the fourfold axis of the high temperature phase, show discontinuities at 159°C. The broadening of the Brillouin lines is attributed to an anharmonic coupling with soft modes whose frequencies vanish at 155 and 161°C.Les vitesses des phonons acoustiques longitudinaux qui se propagent perpendiculairement à l'axe quaternaire de la phase haute température subissent des discontinuités à 159°C. L'élargissement des raies Brillouin est attribué à un couplage anharmonique avec des modes mous dont les fréquences s'annulent à 155 et 161°C

Brillouin Spectroscopy Investigation of the Superionic Transition in CsH2_{\bf 2}AsO4_{\bf 4}

A Brillouin scattering investigation in CsH$_2$AsO$_4$ has been performed over a temperature range 20–200 °C which includes the superionic transition at $T_{\rm S} \sim 167 ^{\circ}$C. At $T_{\rm S}$, large discontinuities are observed for elastic constants $C_{11},\, C_{33}$ and $C^{*}=(C_{11}+C_{12}+2C^{E}_{66})/2$ and above $T_{\rm S}$, a broadening of the corresponding lines takes place. In the conducting phase above $T_{\rm S}$, the spectra reveal a domain structure. The results are discussed by comparison with compounds of CsHSeO$_4$ type. It is shown that a linear coupling between strains and mobile protons in the conducting phase can neither contribute to modification of elastic constants nor to broadening of lines. The experimental results reflect a strong general anharmonicity of the lattice dynamics in the conducting phase.Une étude par diffusion Brillouin de CsH$_2$AsO$_4$ a été faite sur l'intervalle de température 20–200 °C qui contient la transition superionique à $T_{\rm S} \sim 167 ^{\circ}$C. À $T_{\rm S}$, d'importantes discontinuités sont observées pour les constantes $C_{11},\, C_{33}$ et $C^{*}=(C_{11}+C_{12}+2C^{E}_{66})/2$ et, au-dessus de $T_{\rm S}$, un élargissement des raies correspondantes apparaît. Dans la phase conductrice au-dessus de $T_{\rm S}$, les spectres révèlent une structure en domaines. Les résultats sont discutés par comparaison avec les composés du type CsHSeO$_4$. On montre qu'un couplage linéaire entre une déformation et les protons mobiles dans la phase conductrice ne peut pas contribuer à la modification des constantes élastiques ni à l'élargissement des raies. Les résultats expérimentaux révèlent plutôt une forte anharmonicité générale pour la dynamique de réseau dans la phase conductrice

Discontinuities in Elastic Properties of CsH2\mathsf{_2}PO4\mathsf{_4} at the Superionic Transition

An investigation of the elastic properties of CsH$_2$PO$_4$ has been performed by Brillouin spectroscopy throughout a temperature range which includes the superionic transition at $T_{\rm S}\sim 233~^{\circ}$C. At $T_{\rm S}$, discontinuities have been observed for elastic constants $C_{11},~C_{22},~C_{33}$ and $C^* = (C_{11}+C_{22}+2C_{66})/4+[((C_{11}-C_{22})^2+4(C_{12}+C_{66})^2)^{1/2}]/4$. Above $T_{\rm S}$, the corresponding Brillouin lines show a broadening without pretransitional features. In the conducting phase, a domain structure is revealed by the spectra. The observed elastic anomalies are similar to those obtained in other hydrogen-bonded crystals, such MHSeO$_4$ (with M = NH$_4$, Rb, Cs) or CsH$_2$AsO$_4$. In the conducting phase, it has been shown that a bilinear coupling between strains and mobile protons neither contribute to a significant variation of the elastic constants nor can explain the values of the observed broadenings. It is concluded that the experimental results could reflect a strong general anharmonicity of the lattice dynamics in the conducting phase.Une étude des propriétés élastiques de CsH$_2$PO$_4$ a été faite par spectroscopie Brillouin sur un intervalle de température qui inclut la transition superionique à $T_{\rm S}\sim 233~^{\circ}$C. À $T_{\rm S}$, des discontinuités sont observées pour les constantes élastiques $C_{11},~C_{22},~C_{33}$ et $C^* = (C_{11}+C_{22}+2C_{66})/4+[((C_{11}-C_{22})^2+4(C_{12}+C_{66})^2)^{1/2}]/4$. Au dessus de $T_{\rm S}$, les raies Brillouin correspondantes présentent un élargissement sans effet prétransitionnel. Dans la phase conductrice, une structure en domaines est mise en évidence par les spectres. Ces anomalies élastiques ressemblent à celles qui ont été observées dans d'autres cristaux à liaisons hydrogène tels que MHSeO$_4$ (avec M = NH$_4$, Rb, Cs) ou CsH$_2$AsO$_4$. Dans la phase conductrice, nous avons montré qu'un couplage bilinéaire entre les déformations et les protons mobiles ne pouvait pas contribuer à une variation significative des constantes élastiques ni rendre compte des valeurs obtenues pour les élargissements. Il a été conclu que les résultats expérimentaux pourraient refléter une forte anharmonicité générale de la dynamique de réseau dans la phase conductrice

Brillouin scattering study of transverse elastic waves in the α, incommensurate and β phases of AlPO 4

PACS. 64.70.Rh Commensurate-incommensurate transitions - 62.20.-x Mechanical properties of solids - 78.35.+c Brillouin and Rayleigh scattering; other light scattering,

Investigation of AlPO4\mathsf{_4} by Brillouin Spectroscopy from 300 to 1100 K

The elastic constants of AlPO$_4$ (berlinite) have been measured at room temperature. The longitudinal and transverse acoustic waves related to $C^{\rm D}_{11}$, $C_{33}$ and $C^{\rm E}_{44}$ have been investigated over the temperature range 300-1100 K which includes the $\alpha\rightarrow$ inc. $\rightarrow \beta$ transitions near 860 K. Large anomalies of $C^{\rm D}_{11}$ and $C_{33}$, together with broadening of lines, are observed near the transitions, with a significant temperature range of pretransitionnal features. The $C^{\rm E}_{44}$ constant exhibits a discontinuous drop at the lock-in transition. The results concerning the longitudinal modes can be qualitatively interpreted in term of a third order anharmonic coupling between the acoustic modes and the soft modes. The range of the incommensurate phase is found to be $T_{\rm i}-T_{\rm c}\sim 3$ K, in agreement with previous data. The broadening of lines related to longitudinal modes allowed the determination of the constant $A$ of the relaxation time for the amplitudon $\tau_{\rm a}=A/(T_{\rm i}-T)$; we obtained $A=1.1\times 10^{-11}$ K s.Une étude par diffusion Brillouin nous a permis de mesurer les constantes élastiques de AlPO$_4$ (berlinite) à température ambiante. Les ondes acoustiques longitudinales et transverses correspondant aux constantes $C^{\rm D}_{11}$, $C_{33}$ et $C^{\rm E}_{44}$, ont été suivies sur un intervalle de température 300-1100 K qui inclut les transitions $\alpha\rightarrow$ inc. $\rightarrow \beta$ proches de 860 K. Près de ces transitions, des anomalies ont été observées pour les constantes $C^{\rm D}_{11}$, $C_{33}$, ainsi qu'un élargissement des raies Brillouin. La constante $C^{\rm E}_{44}$ montre une discontinuité à la transition de “lock-in”. Les résultats correspondant aux modes longitudinaux peuvent être interprétés qualitativement en termes de couplage du troisième ordre entre les modes acoustiques et les modes mous. Cette étude nous a également permis de vérifier que la phase incommensurable s'étend sur 3 K. Une étude plus approfondie des largeurs de raies Brillouin, correspondant aux ondes longitudinales, permet la détermination de la constante $A$ du temps de relaxation de l'amplitudon $\tau_{\rm a}=A/(T_{\rm i}-T)$ ; on obtient $A=1.1\times 10^{-11}$ K s