Defects as a reason of continuity of normal-incommensurate phase transitions

Almost all normal-incommensurate phase transitions observed experimentally are continuous. We show that there is not any theoretical reason for this general behaviour in perfect crystals. A normal-incommensurate phase transition that is not too far from the mean-field tricritical point should be discontinuous and it is highly improbable that so far reported normal-incommensurate phase transitions lie very far from this point. To understand this behaviour we study influence of defects on a hypothetical first-order normal-incommensurate phase transition in a pure material. We have found that this influence is strikingly different from that on other kinds of first-order phase transitions. The change of the discontinuity of the order parameter at the transition is negative and formally diverges within our approximate theory. At the same time the diminishing of the phase transition temperature remains finite. We interpret these results as an indication that at least some of the observed seemingly second-order normal-incommensurate transitions would be first-order transitions in defectless crystals.Comment: 17 pages, 1 figur

Effects of anisotropic elasticity in the problem of domain formation and stability of monodomain state in ferroelectric films

We study cubic ferroelectrics films that become uniaxial with a polar axis perpendicular to the film because of a misfit strain due to a substrate. The main present result is the analytical account for the elastic anisotropy as well as the anisotropy of the electrostriction. They define, in particular, an orientation of the domain boundaries and stabilizing or destabilizing effect of inhomogeneous elastic strains on the single domain state. We apply the general results to perovskite systems like BaTiO3/SrRuO3/SrTiO3 films and find that at least not far from the ferroelectric phase transition the equilibrium domain structure consists of the stripes along the cubic axes or at 45 degrees to them. We have also showed that in this system the inhomogeneous strains increase stability with regards to the small fluctuations of the metastable single domain state, which may exist not very close to the ferroelectric transition. The latter analytical result is in qualitative agreement with the numerical result by Pertsev and Kohlstedt [Phys. Rev. Lett. 98, 257603 (2007)], but we show that the effect is much smaller than those authors claim. We have found also that under certain conditions on the material constants, which are not satisfied in the perovskites but are not forbidden either, a checkerboard domain structure can be realized instead of the stripe-like one and that the polarization-strain coupling decreases stability of a single domain state instead of increasing it. The single domain state is metastable at certain large thicknesses and becomes suitable for memory applications at even larger thicknesses when the lifetime of the metastable state becomes sufficiently large.Comment: 20 pages, 6 figure

Phase transitions in ferroelectric-paraelectric superlattices

Within the phenomenological Landau–Ginzburg–Devonshire theory, we discuss the paraelectric-ferrolectric transition in superstructures consisting of ferroelectric and paraelectric layers of equal thickness. The polar axis of the ferroelectric is perpendicular to the layer plane as expected in fully strained BaTiO3/SrTiO3 superstructures on SrTiO3 substrates with pseudomorphic electrodes. We concentrate on the electrostatic effects and do not take into account the boundary conditions other than the electrostatic ones. We find that when the ferroelectric phase transition in the superstructures is into a multidomain state, both its temperature and its character, i. e., the profile of the polarization appearing at the phase transition is strongly influenced by the nature of the near-electrode region. This is also the case for the layer thickness separating the single-and multidomain regimes of the transition. Such a finding makes us question the idea that these superstructures can be thought of as infinite systems, i.e., periodic superstructures similar to a crystal. The irrelevance of this idea in certain conditions is demonstrated by comparing the phase transitions in two different superstructures consisting of ferroelectric and paraelectric layers of the same thickness. In one of them, the ferroelectric layer is in immediate contact with an ideal metallic electrode, whereas at the other boundary, it is the paraelectric layer that is in contact with the electrode. In another superstructure, one paraelectric layer is split in two equal parts which are placed as the first and last layer between the electrodes and the ferroelectric layers which are closest to the electrodes. We show (with some formal reservations) that the phase transition temperature in the first superstructure can be over 100 °C more than in the second one if the material parameters of BaTiO3/SrTiO3 are used for the estimations. Moreover, the profile of the polarization arising at the phase transition is inhomogeneous along the superstructure and has the maximum amplitude in the ferroelectric layer contacting the electrode. We argue that this situation is general and results in smearing of the phase transition anomalies for the layer thicknesses corresponding to multidomain transitions. The work is mainly analyical but numerical methods have been used to support some statements that have been put forward as hypotheses