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It is known that ferroelectric single crystals can be turned from a polydomain to a monodomain state by the application of an electric field. Here we report an unexpected opposite effect: the formation of through-the-crystal polydomain pattern in a monodomain BaTiO3 crystal in response to the applied electric field favoring the initial orientation of the polarization. The effect is achieved for special electric field direction which equally selects two domain states, which are present in the polydomain pattern. At the formation of the pattern, the new wedge domains propagate from the sides of the sample in the direction transverse to the electric field. The observations are rationalized in terms of a simple analytical model treating energies of competing domain configurations as functions of the electric field. The results of the analytical treatment are supported by phase field modeling.

Highly reflecting mechanically compliant membranes based on photonic-crystal patterns have recently gained increasing attention within cavity optomechanics due to their prospects of reaching high coupling rates in membrane-in-the-middle experiments. Here we present an analysis and comparison of four different setups in which highly reflecting membranes can be employed for cavity optomechanics, and discuss optimal choices w.r.t. the figures of merit cooperativity and efficiency-weighted cooperativity. The analysis encompasses three different types of membrane-in-the-middle setups (membrane-at-the-edge, membrane-in-the-actual-middle, and membrane-at-the-back), as well as the simple Fabry-Perot cavity. Interestingly, we identify and propose the membrane-at-the-back setup as an optimal choice in the limit of negligible membrane parasitic loss, which can reach enormous enhancements of optomechanical cooperativity, and if implemented with a low-loss membrane would pave the way to nonlinear optomechanics in the quantum regime.

The recently identified possibility of ground-state cooling of a mechanical oscillator in the unresolved sideband regime by combination of the dissipative and dispersive optomechanical coupling under the red sideband excitation [Phys. Rev. A 88, 023850 (2013)], is currently viewed as a remarkable finding. We present a comprehensive analysis of this protocol, which reveals its very high sensitivity to small imperfections such as an additional dissipation, the inaccuracy of the optimized experimental settings, and the inaccuracy of the theoretical framework adopted. The impact of these imperfections on the cooling limit is quantitatively assessed. A very strong effect on the cooling limit is found from the internal cavity decay rate which even being small compared with the detection rate may drastically push that limit up, questioning the possibility of the ground state cooling. Specifically, the internal loss can only be neglected if the ratio of the internal decay rate to the detection rate is much smaller than the ratio of the cooling limit predicted by the protocol to the common dispersive-coupling assisted sideband cooling limit. More over, we establish that the condition of applicability of theory of that protocol is the requirement that the latter ratio is much smaller than one. A detailed comparison of the cooling protocol in question with the dispersive-coupling-assisted protocols which use the red sideband excitation or feedback is presented.

Using the dynamical matrix of a crystal obtained from ab initio calculations, we have evaluated for the first time the strength of the dynamic flexoelectric effect and found it comparable to that of the static bulk flexoelectric effect, in agreement with earlier order-of-magnitude estimates. We also proposed a method of evaluation of these effects directly from the simulated phonon spectra. This method can also be applied to the analysis of the experimental phonon spectra, being currently the only one enabling experimental characterization of the static bulk flexoelectric effect.

Using Landau-Ginzburg-Devonshire theory we describe 180-degree domain wall structure, intrinsic energy and carrier accumulation in rhombohedral phase of BaTiO3 as a function of the wall orientation and flexoelectric coupling strength. Two types of domain wall structures (phases of the wall) exist depending on the wall orientation. The low-energy 'achiral' phase occurs in the vicinity of the {110} wall orientation and has odd polarization profile invariant with respect to inversion about the wall center. The second 'chiral' phase occurs around {211} wall orientations and corresponds to mixed parity domain walls that may be of left-handed or right-handed chirality. The transformation between the phases is abrupt, accompanied with 20-30% change of the domain wall thickness and can happen at fixed wall orientation with temperature change. We suggest that the phase transition may be detected through domain wall thickness change or by c-AFM. The structure of the domain wall is correlated to its conductivity through polarization component normal to the domain wall, which causes free carriers accumulation. Depending on the temperature and flexoelectric coupling strength relative conductivity of the wall becomes at least one order of magnitude higher than in the single-domain region, creating c-AFM contrast enhancement pronounced and detectable., Comment: 31 pages, 10 figures, Supplementary materials

It is demonstrated that for classical perovskites such as BaTiO3, SrTiO3 and PbTiO3 electrostrictive strain induced by an electric field may not obey traditionally considered "extension along the field, contraction perpendicular to it" behavior if a sample is cut obliquely to the cubic crystallographic directions.

Currently used methods for the description of thermodynamics of ferroelectric thin films (Landau theory or ab initio based Monte-Carlo simulations) are based on an energy expansion in terms of internal degrees of freedom. It was shown that these methods can suffer from a substantial inaccuracy unless higher-order electromechanical interactions are not taken into account. The high-order electromechanical couplings strongly renormalize the sixth-power polarization terms of the thermodynamic energy expansion. In this paper, apart from the general statement, we illustrate it with an example of a temperature - misfit strain phase diagram of a BaTiO3 thin film derived with high-order electromechanical interactions evaluated using first principles calculations.

The interaction of electric field with charged domain walls in ferroelectrics is theoretically addressed. A general expression for the force acting per unit area of a charged domain wall carrying free charge is derived. It is shown that, in proper ferroelectrics, the free charge carried by the wall is dependent on the size of the adjacent domains. As a result, it was found that the mobility of such domain wall (with respect to the applied field) is sensitive to the parameters of the domain pattern containing this wall. The problem of the force acting on a planar charged 180-degree domain wall normal to the polarization direction in a periodic domain pattern in a proper ferroelectric is analytically solved in terms of Landau theory. It is shown that, in small applied fields (in the linear regime), the forces acting on walls in such pattern increase with decreasing the wall spacing, the direction of the forces coinciding with those for the case of the corresponding neutral walls. At the same time, for large enough wall spacings and large enough fields, these forces can be of the opposite sign. It is shown that the domain pattern considered is unstable in a defect-free ferroelectric. The poling of a crystal containing such pattern, stabilized by the pinning pressure, is also considered. It is shown that, except for a special situation, the presence of charge domain walls can make poling more difficult. It is demonstrated that the results obtained are also applicable to zig-zag walls under the condition that the zig-zag amplitude is much smaller than the domain wall spacing., Comment: 5 figures

Static flexoelectric effect in a finite sample of a solid is addressed in terms of phenomenological theory for the case of a thin plate subjected to bending. It has been shown that despite an explicit asymmetry inherent to the bulk constitutive electromechanical equations which take into account the flexoelectric coupling, the electromechanical response for a finite sample is "symmetric". "Symmetric" means that if a sensor and an actuator are made of a flexoelectric element, performance of such devices can be characterized by the same effective piezoelectric coefficient. This behavior is consistent with the thermodynamic arguments offered earlier, being in conflict with the current point of view on the matter in literature. This result was obtained using standard mechanical boundary conditions valid for the case where the polarization vanishes at the surface. It was shown that, for the case where there is the polarization is nonzero at the surface, the aforementioned symmetry of electromechanical response may be violated if standard mechanical boundary conditions are used, leading to a conflict with the thermodynamic arguments. It was argued that this conflict may be resolved when using modified mechanical boundary conditions. It was also shown that the contribution of surface piezoelectricity to the flexoelectric response of a finite sample is expected to be comparable to that of the static bulk contribution (including the material with high values of the dielectric constant) and to scale as the bulk value of the dielectric constant (similar to the bulk contribution). This finding implies that if the experimentally measured flexoelectric coefficient scales as the dielectric constant of the material, this does not imply that the measured flexoelectric response is controlled by the static bulk contribution to the flexoelectric effect.

"Head-to-head" and "tail-to-tail" 180-degree domain-walls in a finite isolated ferroelectric sample are theoretically studied using Landau theory. The full set of equations, suitable for numerical calculations is developed. The explicit expressions for the polarization profile across the walls are derived for several limiting cases and wall-widths are estimated. It is shown analytically that different regimes of screening and different dependences for width of charged domain walls on the temperature and parameters of the system are possible, depending on spontaneous polarization and concentration of carriers in the material. It is shown that the half-width of charged domain walls in typical perovskites is about the nonlinear Thomas-Fermi screening-length and about one order of magnitude larger than the half-width of neutral domain-walls. The formation energies of "head-to-head" walls under different regimes of screening are obtained, neglecting the poling ability of the surface. It is shown that either "head-to-head" or "tail-to-tail" configuration can be energetically favorable in comparison with the monodomain state of the ferroelectric if the poling ability of the surface is large enough. If this is not the case, the existence of charged domain walls in bulk ferroelectrics is merely a result of the domain-growth kinetics. Size-effect corresponding to the competition between state with charged domain wall, single domain state, multidomain state, and the state with the zero polarization is considered. The results obtained for the case of an isolated ferroelectric sample were compared with the results for an electroded sample. It was shown that charged domain wall in electroded sample can be either metastable or stable, depends on the work function difference between electrodes and ferroelectric and the poling ability of the electrode/ferroelectric interface., Comment: 47 pages, 10 figures

Comment on paper "Towards a bulk theory of flexoelectricity" by R.Resta [Phys.Rew. Lett. v. 105, 127601 (2010)]

The size effect in ferroelectrics is treated as a competition between the geometrical symmetry of the ferroelectric sample and its crystalline symmetry. The manifestation of this competition is shown to be polarization rotation, which is driven by temperature and/or size variations, thus providing a qualitative indication of intrinsic finite size effect on ferroelectrics. The concept is demonstrated in a simple case of PbTiO3 nanowires having their axis parallel to [111]C direction, where the size effect is shown to include polarization rotation and an additional phase transition., Comment: 10 pages, 3 figures, journal paper

An evidence that the dielectric ageing in the polydomain Pb(Zr0.45Ti0.55)O3 thin films is controlled by progressive pinning of 180 domain walls is presented. To provide such a conclusion, we use a general method, which is based on the study of the time evolution of the nonlinear, but anhysteretic, dielectric response of the ferroelectric to a weak electric field. A thermodynamic model of the ferroelectric system where the dielectric response is controlled by bending movements of pinned 180 domain walls is developed. Within this model, the nonlinear permittivity of the ferroelectric is expressed as a function of the microstructural parameters of the domain pattern. It is shown that using the analysis of the time evolution of the nonlinear permittivity, it is possible to estimate changes in the concentration of the pinning centers that block the movements of the 180 domain walls during aging in polydomain perovskite ferroelectrics., Comment: This version is modifed and corrected according to recently published Erratum: Phys. Rev. B 79, 219903(E) (2009). 21 pages, 3 figures

The paper comments on a paper by Dawber and Scott published in Appl. Phys. Lett, 76,1060 (2000) and addendum (ibid. p.3655), which addresses an important issue of the physics of ferroelectric thin films - the role of oxygen vacancies in polarization fatigue. It is shown that the content of this paper (starting equations, calculations, parameters used in calculations and the way the obtained results are compared to the experimental data available in the literature) enables questioning the results and conclusions reported in it.