Session H39: Focus Session: Phase Transitions and Domains in Ferroelectric Nanostructures II

Unusual phenomena in ferroelectric nanostructures

First-principles based computations are nowadays capable of tackling really complex challenges of fundamental and technological importance. For example, a dipole vortex structure has been discovered, by means of these methods, in isolated nanoparticles of ferroelectrics --which may lead to a new generation of efficient nanoscale memory devices [1]. Here, we use first-principles-based approaches to address the following issues: (i) what are the elastic signatures and field charateristics of dipole vortices in isolated ferroelectric nanodots? (ii) how to control the chirality of such dipole vortices (which is an important challenge to solve for future applications)? and (iii) what are the possible ground states of arrays of ferroelectric dots embedded in a crystal lattice? Regarding item (i), we found that the tetragonal axial ratio in the vortex state is lower than 1 (unlike in ``normal'' ferroelectric or antiferrodistortive phases), and that the electric field produced by the dipole vortex outside the dot oscillates in space when changing the polar angle of the cylindrical coordinate system. Such features can serve as fingerprints of the vortex state to experimentally confirm the existence of such unusual state. Moreover, we demonstrate that, and explain why, using inhomogeneous electric fields is an efficient solution to item (ii) [2]. Finally, it is predicted that array of embedded dots can adopt new phases, depending on the temperature and difference in polarizability between the dots and medium [3]. Atomistic details of such phases, as well as their governing mechanisms, will be provided. \newline \newline Coauthors: I. Ponomareva, I. Kornev, I. Naumov, and L. Bellaiche, University of Arkansas. \newline \newline [1] I. Naumov, L. Bellaiche, \& H. Fu. ``Unusual phase transitions in ferroelectric nanodisks and nanorods, '' Nature 432, 737 (2004). \newline [2] S. Prosandeev, I. Ponomareva, I. Kornev, I. Naumov, \& L. Bellaiche. ``Controlling toroidal moment by means of an inhomogeneous static field: an ab initio study,'' Phys. Rev. Lett. 96, 237601-1-4 (2006). \newline [3] S. Prosandeev \& L. Bellaiche. ``Properties of ferroelectric nanodots embedded in a polarizable medium: atomistic simulations.,'' Phys. Rev. Lett. 97, 167601 (2006).   

Influence of the growth direction on properties of ferroelectric ultrathin films

Ferroelectric thin films have been intensively studied recently because of their potential applications in nonvolatile memories, infrared detectors and microelectromechanical systems. Many interesting features of these systems, such as the strong dependency of their dipole patterns on boundary conditions and size thickness, are now well understood. However, an overwhelming majority of past studies focused on films grown along the [001] direction. As a result, one remaining mystery in thin films is the influence of the {\it growth direction} on their properties. Here we report results of first-principles-based calculations of PZT ferroelectric thin films that are grown along different directions and subject to different boundary conditions [1]. A wide variety of dipole patterns is discovered, including ferroelectric phases absent in the bulk and complex periodic stripe nanodomains. Moreover, a large enhancement of dielectricity is found in ultrathin films exhibiting a growth direction that differs from a possible direction of the polarization in the corresponding bulk. A set of two general and simple rules is provided to analyze and understand all these features. [1] I. Ponomareva and L. Bellaiche, Phys. Rev. B {\bf 74}, 064102 (2006).   

Phase field modeling of domain structures in nano-composite ferroelectric multilayers

The formation of domain structures in differently patterned multilayers with a nano-composite structure containing ferroelectric structure components has been studied by using a phase field method based on the microelasticity theory and the Fourier spectral analysis of electrostatic interactions. The effects of the depolarizing electric field, the thickness of the film, and the misfit between a film and a substrate on the domain pattern and switching properties have been analyzed. The effect of a relative strength of elastic interactions in the multilayer on the dielectric response and effective piezo coefficients has been studied. A correlation between the results of the phase field modeling and the existing results of first principle calculations has been demonstrated, thus allowing us to describe ferroelectric films on different scale levels.   

Depolarizing Field and ``Real'' Hysteresis Loops in Nanometer Scale Ferroelectric Films

We give detailed analysis of the effect of depolarizing field in nanometer-size ferroelectric capacitors studied by Kim \textit{et al.} [Phys. Rev. Lett. \textbf{95}, 237602 (2005)]. We calculate a critical thickness of the homogeneous state and its stability with respect to domain formation for strained thin films of BaTiO$_3$ on SrRuO$_3$/SrTiO$_3$ substrate within the Landau theory. While the former (2.5nm) is the same as given by ab- initio calculations, the actual critical thickness is set by the domains at 1.6nm [1]. There is a large Merz's activation field for polarization relaxation. Remarkably, the results show a \emph {negative} slope of the ``actual'' hysteresis loops, a hallmark of the domain structures in ideal thin films with imperfect screening[2]. \newline [1] A.M. Bratkovsky and A.P. Levanyuk, Appl. Phys. Lett. (in print), cond-mat/0608283. \newline [2] A.M. Bratkovsky and A.P. Levanyuk, Phys. Rev. B {\bf 63}, 132103 (2001).   

Size Effects in Ferroelectric Thin Films: The Role of 180 degree domains

The depolarization fields set up to due to uncompensated surface charges in a ferroelectric thin film can suppress the ferroelectric phase below a critical size. However, recent experiments show that 180 degree domain structures can help to stabilize ferroelectricity in films which are as small as about 3 unit cells thick. We study the influence of these domain structures on the size dependent properties of ferroelectric thin films using a Ginzburg-Landau theory. The model incorporates the effect of depolarization field by considering non-ferroelectric passive layers at the top and bottom surfaces. It is shown that the wavelength of the 180 degree domains decreases as the film thickness is reduced and eventually the film abruptly becomes paraelectric below a critical size. It is also shown that 180 degree domains appear during the process of polarization switching causing a time dependent relaxation of the remnant polarization , consistent with recent experiments. Further, it is observed that the depolarization induced domain wall motion significantly alters the shape of the polarization vs electric field (P-E) loops at small thicknesses.   

Domain structure and polarization of ferroelectric graded multilayers and nanograded films.

The equilibrium domain structure and its evolution under an electric field in ferroelectric graded films and multilayers are considered. The equilibrium graded film is self-poled and contains a single-domain and a polydomain (with 180\r{ } domains) layers. The polarization of a graded multilayer and films proceeds by movement of wedge-like domains as a result of progressive transformation of polydomain layers to a single-domain state. The change of the energy of domain walls accompanying growth and shrinkage of wedge domains can be taken into account by introducing a local effective field on the boundary between polydomain and single-domain parts of a film. It makes the movements of this boundary irreversible and contributes to the hysteresis of polarization. The theory provides the principal explanation of dielectric and pyroelectric behavior of graded ferroelectric films including enhanced dielectric constant and giant pyroeffect. The theory will be applied to the discussion of several related problems: (1) elastic domains as a result of structural transformations in graded materials; (2) domains in graded ferromagnetic films; (3) domain structures under non-uniform fields, particularly, the formation of zigzag interdomain and interfacial walls under a local field.   

Dielectric Permittivity and Tunability of Ferroelectric Bilayers and Multilayer Heterostructures

Ferroelectric multilayers and superlattices have gained interest for many applications in the telecommunications industry. A thermodynamic analysis is presented to demonstrate that ferroelectric multilayers interact through internal elastic, electrical, and electromechanical fields and the ``strength'' of the coupling can be quantitatively described using Landau theory, theory of elasticity, and principles of electrostatics. The modeling indicates that the electrostatic coupling between the layers leads to the suppression of ferroelectricity at a critical paraelectric layer thickness for ferroelectric-paraelectric bilayers. This bilayer is expected to have a huge dielectric response and tunability at this critical thickness. We carry out a numerical analysis for prototypical BaTiO$_{3}$-SrTiO$_{3}$ bilayers (40 to 800 nm total thickness) as a function of SrTiO$_{3}$ fraction. There exists a critical fraction of SrTiO$_{3}$ at which the polarization is suppressed due to the depolarization field and a large dielectric response is predicted. It is shown that this critical fraction decreases with decreasing total bilayer thickness indicating that the interfacial effects are more pronounced in thinner bilayers.   

Phase diagrams of epitaxial BaTiO$_3$/SrTiO$_3$ superlattices from first principles

The fabrication of artificial superlattices (SL) consisting of alternating layers of two or more ferroelectric oxides is nowadays possible. Such heterostructures may possess properties that dramatically differ from those of bulk ferroelectrics, since, e.g., physical properties of ferroelectric SL should be very sensitive to the epitaxial strain arising from the substrate on which the SL is grown. Determining the temperature-misfit strain diagram of SL is thus of considerable importance. Here, a first-principles-based effective Hamiltonian approach (that has been recently developed and successfully tested for disordered or ordered Ba$_x$Sr$_{1-x}$TiO$_3$ systems [1]) is used within Monte-Carlo simulations to determine such phase diagram in epitaxially grown (001) BaTiO$_3$/SrTiO$_3$ SL of different period. We found that, unlike in the short SL, that exhibit a phase diagram that resemble that of (001) BaTiO$_3$ thin films under short-circuit-like conditions, original domain patterns with unusual inhomogeneous atomistic features occur in the longer SL. The reason behind such dramatic difference is revealed. [1] L. Walizer {\em et al,}, {\em Phys. Rev. B}, {\bf 73}, 144105, (2006).   

Super-pyroelectric effect in nanocrystalline films of BaTiO3 with macro-domain organization

Self-supported films of nanocrystalline BaTiO3 exhibit an earlier unreported phenomenon: orders of magnitude increase of pyroelectric effect (``super-pyroelectricity''). The measured value ($\sim $ 1$\mu $C/(cm2$\cdot $K)) is one the highest ever reported for ferroelectric materials. The super-pyroelectricity arises due to self-organization of hundreds of millions nanocrystalline ferroelectric grains in macro-domains: the regions where directions of the crystallographic axes are strongly correlated. Small temperature variations cause reversible changes in the direction of spontaneous polarization of ferroelectric grains in macro-domains producing gigantic pyroelectric current. In contrast to regular pyroelectricity observed in ferroelectrics, super-pyroelectric effect reaches maximum at 80-100 K below the temperature of the para-to-ferroelectric phase transition. This work demonstrates that polycrystalline macro-domains are capable of fast ($<$10 $\mu $sec!) and reversible adaptation to minute changes of external conditions, which promises creation of pyroelectric and piezoelectric devices with previously unattainable performance.