An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of $^{4}\mathrm{He}$.

Theory of Dynamic Critical Phenomena

Scaling theory of percolation clusters

An overview of the state of art in ferroelectric thin films is presented. First, we review applications: microsystems' applications, applications in high frequency electronics, and memories based on ferroelectric materials. The second section deals with materials, structure (domains, in particular), and size effects. Properties of thin films that are important for applications are then addressed: polarization reversal and properties related to the reliability of ferroelectric memories, piezoelectric nonlinearity of ferroelectric films which is relevant to microsystems' applications, and permittivity and loss in ferroelectric films-important in all applications and essential in high frequency devices. In the context of properties we also discuss nanoscale probing of ferroelectrics. Finally, we comment on two important emerging topics: multiferroic materials and ferroelectric one-dimensional nanostructures. (c) 2006 American Institute of Physics.

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Ferroelectric thin films: Review of materials, properties, and applications

A review of the properties of ferroelectric materials that are relevant to microwave tunable devices is presented: we discuss the theory of dielectric response of tunable bulk materials and thin films; the experimental results from the literature and from own work are reviewed; the correspondence between the theoretical results and the measured properties of tunable materials is critically analyzed; nominally pure, real (defected), and composite bulk materials and thin films are addressed. In addition, techniques for characterization of tunable ferroelectrics and applications of these materials are briefly presented.

Ferroelectric materials for microwave tunable applications

Understanding the suppression of ferroelectricity in perovskite thin films is a fundamental issue that has remained unresolved for decades. We report a synchrotron x-ray study of lead titanate as a function of temperature and film thickness for films as thin as a single unit cell. At room temperature, the ferroelectric phase is stable for thicknesses down to 3 unit cells (1.2 nanometers). Our results imply that no thickness limit is imposed on practical devices by an intrinsic ferroelectric size effect.

https://science.sciencemag.org/content/sci/304/5677/1650.full.pdf

Ferroelectricity in ultrathin perovskite films.

A phenomenological theory is developed to describe the change of the local spontaneous polarization in the vicinity of a free surface of a ferroelectric thin film which is kept between metallic electrodes. It is shown that depolarizing field effects reduce the deviation of this local polarization from its bulk value, as compared to surface effects on phase transitions in other systems. In particular, the critical exponents describing the behavior of the local polarization in the vicinity of the Curie temperature ${T}_{C}$ are the same as the bulk exponents and only critical amplitudes are changed. This behavior contrasts to phase transitions in other systems (antiferroelectrics, ferro- and antiferromagnets, ordering alloys etc.) where different exponents are predicted. In order to improve upon this Landau-type theory by taking into account the effects of statistical fluctuations near ${T}_{C}$, recent results of renormalization-group theory are used to estimate logarithmic correction factors which should modify the critical behavior of the local polarization. Finally the experimental implications of our results are briefly discussed, and also a discussion of surface effects on the phase transition of dipolar magnets is given.

Surface effects on phase transitions in ferroelectrics and dipolar magnets

As a simple model of order-disorder ferroelectrics or dipolar magnets we consider a simple cubic Ising-system with nearest neighbor exchangeJ and dipolar interaction of strengthµ
2/a
3. ForJa
3/µ
2<−1.3384 the ground-state is antiferromagnetic, while for −1.3384<Ja
3/µ
2<0.1270 the ground state consists of ferromagnetic rows (in spin direction) arranged antiferromagnetically in the plane perpendicular to it. AtJa
3/µ
2=0.1279 the structure changes to a layered antiferromagnetic structure with a twocomponent order parameter, while forJa
3/µ
2>0.16429 the ferromagnetic phase becomes stable (with domain arrangements depending on the shape of the sample). For all critical values ofJa
3/µ
2 where the bulk energies of two phases become equal also the interface energy between these phases is found to be zero. The ordering at nonzero temperature is studied by means of mean-field approximations (MFA) and Monte Carlo (MC) calculations. It turns out that forJa
3/µ
2 of order unity the MFA overestimates ordering temperatures by about a factor of two, and predicts multicritical points (between the disordered and two ordered phases) at nonzero temperature, including two biaxial Lifshitz points which the MC work suggests to occur atT=0. In contrast to MFA the layered antiferromagnetic structure is found to be stable only at extremely lowT, because a metastable spin-glass phase (with random arrangement of ferromagnetic rows in the spin direction) has only slightly higher energy. The MFA also yields two regimes of helical phases which are “locked in” to the antiferromagnetic phases at uniaxial Lifshitz points occurring at the Brillouin zone boundary. In the MC-work various methods of treating the long-range interaction are investigated. While all kinds of truncations as well as compensating field methods are rather unsatisfactory in our case, Ewald summation techniques yield satisfactory results. Nevertheless strong fluctuations as well as strong finite size effects prevent us from making accurate exponent estimates, but arguments are given that there is no regime of broad visibility of Landaulike critical behavior. Finally the extension of our results to other lattices as well as experimental applications are briefly discussed.

Ordering and phase transitions in ising systems with competing short range and dipolar interactions

The critical slowing down of anisotropic magnets, binary mixtures, and systems undergoing structural transitions is interpreted in terms of suitable defined “clusters,” their growth, and their motions (cluster reactions, cluster diffusion, and cluster waves). Our previous studies of the Glauber model are extended considerably by numerical calculations, including the use of the cluster model of Reatto and Rastelli. The behavior of the relaxation function is very insensitive to the details of the models used. A scaling theory of nonlinear response is given, which is far more general than the cluster dynamics treatment. Two different cases occur:(i) at fixed “relative nonlinearity” the critical exponents agree with the corresponding exponents of linear response; (ii) if the initial state is held fixed, different exponents are found, however, which agree with predictions of Racz, and are consistent with Monte Carlo simulations of the nonlinear slowing down of the energy in kinetic Ising models.

R. Kretschmer

Papers

Surface effects on phase transitions in ferroelectrics and dipolar magnets

Ordering and phase transitions in ising systems with competing short range and dipolar interactions

Linear and nonlinear relaxation and cluster dynamics near critical points