Dynamics of relaxor ferroelectrics

We study a dynamic model of relaxor ferroelectrics based on the spherical random-bond---random-field model and the Langevin equations of motion. The solution to these equations is obtained in the long-time limit where the system reaches an equilibrium state in the presence of random local electric fields. The complex dynamic linear and third-order nonlinear susceptibilities $\chi_1(\omega)$ and $\chi_3(\omega)$, respectively, are calculated as functions of frequency and temperature. In analogy with the static case, the dynamic model predicts a narrow frequency dependent peak in $\chi_3(T,\omega)$, which mimics a transition into a glass-like state.Comment: 15 pages, Revtex plus 5 eps figure

Coexistence of the Critical Slowing Down and Glassy Freezing in Relaxor Ferroelectrics

We have developed a dynamical model for the dielectric response in relaxor ferroelectrics which explicitly takes into account the coexistence of the critical slowing down and glassy freezing. The application of the model to the experiment in PMN allowed for the reconstruction of the nonequilibrium spin glass state order parameter and its comparison with the results of recent NMR experiment (Blinc et al., Phys. Rev. Lett. 83, No. 2 (1999)). It is shown that the degree of the local freezing is rather small even at temperatures where the field-cooled permittivity exceeds the frequency dependent permittivity by an order of magnitude. This observation indicates the significant role of the critical slowing down (accompanying the glass freezing) in the system dynamics. Also the theory predicts an important interrelationship between the frequency dependent permittivity and the zero-field-cooled permittivity, which proved to be consistent with the experiment in PMN (A. Levstik et. al., Phys. Rev. B 57, 11204 (1998))

Fanny Copeland and the geographical imagination

Raised in Scotland, married and divorced in the English south, an adopted Slovene, Fanny Copeland (1872 – 1970) occupied the intersection of a number of complex spatial and temporal conjunctures. A Slavophile, she played a part in the formation of what subsequently became the Kingdom of Yugoslavia that emerged from the First World War. Living in Ljubljana, she facilitated the first ‘foreign visit’ (in 1932) of the newly formed Le Play Society (a precursor of the Institute of British Geographers) and guided its studies of Solčava (a then ‘remote’ Alpine valley system) which, led by Dudley Stamp and commended by Halford Mackinder, were subsequently hailed as a model for regional studies elsewhere. Arrested by the Gestapo and interned in Italy during the Second World War, she eventually returned to a socialist Yugoslavia, a celebrated figure. An accomplished musician, linguist, and mountaineer, she became an authority on (and populist for) the Julian Alps and was instrumental in the establishment of the Triglav National Park. Copeland’s role as participant observer (and protagonist) enriches our understanding of the particularities of her time and place and illuminates some inter-war relationships within G/geography, inside and outside the academy, suggesting their relative autonomy in the production of geographical knowledge

Tricritical Points in the Sherrington-Kirkpatrick Model in the Presence of Discrete Random Fields

The infinite-range-interaction Ising spin glass is considered in the presence of an external random magnetic field following a trimodal (three-peak) distribution. The model is studied through the replica method and phase diagrams are obtained within the replica-symmetry approximation. It is shown that the border of the ferromagnetic phase may present first-order phase transitions, as well as tricritical points at finite temperatures. Analogous to what happens for the Ising ferromagnet under a trimodal random field, it is verified that the first-order phase transitions are directly related to the dilution in the fields (represented by $p_{0}$). The ferromagnetic boundary at zero temperature also exhibits an interesting behavior: for $0<p_{0}<p_{0}^{*} \approx 0.30856$, a single tricritical point occurs, whereas if $p_{0}>p_{0}^{*}$ the critical frontier is completely continuous; however, for $p_{0}=p_{0}^{*}$, a fourth-order critical point appears. The stability analysis of the replica-symmetric solution is performed and the regions of validity of such a solution are identified; in particular, the Almeida-Thouless line in the plane field versus temperature is shown to depend on the weight $p_{0}$.Comment: 23pages, 7 ps figure

Random Electric Field Instabilities of Relaxor Ferroelectrics

Relaxor ferroelectrics are complex oxide materials which are rather unique to study the effects of compositional disorder on phase transitions. Here, we study the effects of quenched cubic random electric fields on the lattice instabilities that lead to a ferroelectric transition and show that, within a microscopic model and a statistical mechanical solution, even weak compositional disorder can prohibit the development of long-range order and that a random field state with anisotropic and power-law correlations of polarization emerges from the combined effect of their characteristic dipole forces and their inherent charge disorder. We compare and reproduce several key experimental observations in the well-studied relaxor PbMg1/3Nb2/3O3–PbTiO3.Universidad de Costa Rica/[816-B7-601]/UCR/Costa RicaBasic Energy Sciences, Department of Energy/[contract no. DE-AC02-06CH11357]//Estados UnidosUCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigación en Ciencia e Ingeniería de Materiales (CICIMA

Nonlinear contributions to the quasistatic and the first-harmonic dielectric response in relaxor systems

Nonlinear dielectric response in relaxor systems was studied as a function of the ac and dc electric field. Significant frequency dependence was found in the nonlinearity a3. The crossover temperature dependence of a3 -a fingerprint of the spherical glass freezing-was confirmed to exist even in the static limit. Beside the expected reflection of the third harmonic component $\varepsilon_3(3\omega)$ additional nonlinear contribution was found in the nonlinear dependence of the first harmonic response $\varepsilon_1(\omega)$. It is shown that this second contribution to the field dependence of $\varepsilon_1(\omega)$ and also the quasistatic measurements of the nonlinear dielectric response throughout the glassy-to-ferroelectric crossover region can be described by the spherical random-bond-random-field model of relaxor ferroelectrics

Relaxor freezing and electric-field–induced ferroelectric transition in a lanthanum lead zirconate titanate ceramics

Transition lines between various phases in the electric-field–temperature phase diagram of 9/65/35 lanthanum lead zirconate titanate ceramics were determined by measurements of the temperature and electric-field–dependent dielectric constant. Above the critical field (EC) the dc bias electric field induces a transition from the relaxor to the ferroelectric phase, while below EC the system exhibits a freezing transition between the ergodic and nonergodic relaxor state. Transition lines are discussed in terms of the spherical random-bond–random-field model of relaxor ferroelectrics. Measurements in the quasistatic temperature regime confirm the prediction of the model that the nonlinear dielectric response shows a sharp peak at the freezing transition temperature

Polarons in magnetoelectric K

The ac electrical conductivity of magnetoelectric K3Fe5F15 was investigated as a function of frequency and temperature. While at higher temperatures charge transport is governed by a thermally activated process, at lower temperatures the real part of the complex ac electric conductivity was found to follow the universal dielectric response $\sigma^\prime\propto\nu^{s}$, being typical for hopping or tunnelling of localized charge carriers. A detailed analysis of the temperature dependence of the UDR parameter s in terms of the theoretical model for tunnelling of small polarons revealed that, below 80 K, this mechanism governs the charge transport in the K3Fe5F15 magnetoelectric fluoride system