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

Formation and rapid evolution of domain structure at phase transitions in slightly inhomogeneous ferroelectrics

We present the first analytical study of stability loss and evolution of domain structure in inhomogeneous ferroelectric samples for exactly solvable model. The model assumes a short-circuited capacitor with two regions with slightly different critical temperatures Tc1 > Tc2, where Tc1-Tc2 << Tc1, Tc2. Even a tiny inhomogeneity like 10-5 K may result in splitting the system into domains below the phase transition temperature. At T < Tc2 the domain width $a$ is proportional to (Tc1 - T)/(Tc1 - Tc2) and quickly increases with lowering temperature. The minute inhomogeneities in Tc may result from structural (growth) inhomogeneities which are always present in real samples and a similar role can be played by inevitable temperature gradients.Comment: 5 pages, 2 figures, discussion expanded and references added to experiments on graded ferroelectrics and ferroelectric superlattice