Session J32: Focus Session: Dielectric, Ferroelectric, and Piezoelectric Oxides - Domain Structures and Switching

Superdomains and Flux Closure Patterns in Ferroelectrics

Microstructural complexity has been a recognized feature of ferroelectric materials since the earliest optical microscopy studies on BaTiO$_{3}$ over 60 years ago,\footnote{P. W. Forsbergh, Phys. Rev. 76, 1187 (1949).}$^,$\footnote{W. Merz, Phys. Rev. 95, 690 (1954).} in which rich patterns of domain states were observed. Arlt and Sasko\footnote{G. Arlt and P. Sasko, J. Appl. Phys. 51, 4956 (1980).} famously highlighted the existence of bands of domain structures forming herringbone patterns and, in so doing, helped to establish the notion that domain architectures exist over a number of different length scales: hierarchies naturally develop in which coarse-scale ``superdomains'' are themselves composed of sets of finer-scale ``subdomains.'' What was not widely recognised, was that these ``superdomains'' could act as functional entities in their own right, with net polarisation and spontaneous strain being the vector sum of these quantities from constituent ``subdomains''. In this talk, we will explore the dominant role that superdomain functionality can have on the behaviour of ferroelectrics, at least at the meso and nanoscales. Observations made on single crystal thin film sheets and nanodots of BaTiO$_{3}$ (machined using a Focused Ion Beam Microscope) will be presented and several key points will be made: (i) that boundaries between superdomains generally adhere to the same constraints as those seen in subdomains (for example, that the divergence in the net superdomain polarisation across boundaries is zero); (ii) that superdomains demonstrate the same scaling laws (Landau-Kittel scaling) as were originally developed for simple subdomains; (iii) that ferroelectric switching can be entirely mediated by superdomains rather than subdomains; (iv) that flux closure objects, which extend beyond the nanoscale, require the existence of superdomains. The dynamics of flux closure formation, due to depolarising fields, has also been mapped and will be presented.   

Superdomain dynamics in single-crystal BaTiO$_{3}$ lamellae

In the1950's early studies pioneered by Merz established that 180\r{ } domain reversal in bulk BaTiO$_{3}$ could be described by a 3-stage switching process [see H. L. Stadler, Ferroelectrics 137, 1992]. This involved formation of a reversed domain nucleus, forward growth of a needle shaped domain towards the opposite electrode followed finally by sideways expansion. In a recent study [R. G. P. McQuaid, Nat. Comms. 2, 2011] we used Piezoresponse Force Microscopy (PFM) to monitor the switched domain states that developed in single-crystal BaTiO$_{3}$ slices machined (by Focused Ion Beam) to thin film thicknesses and incorporated into a coplanar geometry. We found that switched states are constrained to exist within a rigid framework of ordered ferroelastic stripe domains. Surprisingly, we see that switching occurs solely by the movement of a complex 180\r{ }-type boundary which separates `bundles' of these domain stripes. We see that it is at the collective `superdomain' level, rather than for individual domains, where the classic Merz nucleation and growth modes are observed. We use PFM imaging to track the realtime boundary position during switching and attempt model fits to understand its field driven dynamics.   

Theoretical study of ferroelectric switching of Pt/BaTiO$_{3}$ Slabs

BaTiO$_{3 }$(BTO) is a well known ferroelectric perovskite, which is tetragonal at room temperature. The energy barrier for polarization switching is small at 9.7 meV; however, its energy barrier clamped between two metal electrodes is an open question. It has been shown (Junquera {\&} Ghosez, Nature \textbf{422}, 506 (2003)) that the ferroelectric behavior is highly thickness dependent. We examine thin slabs of BTO sandwiched between electrodes of Pt and calculate the polarization barriers using density functional theory to see whether the barrier should be surmountable. We have found that the energy barrier/unit cell reaches the bulk value at only 10 unit cells of BTO. We also examine the polarization of the relaxed slabs and compare them to bulk BTO, and find that the center of the slab exhibits bulk rumpling at 20 unit cells of BTO.   

Probing Nanoscale Ferroelectric Domain Switching Mechanisms with Scanning Probe Microscopy

Ferroelectric domains and domain walls have been a focus topic for research, owing to their applications in memory devices, ultrasonic imaging devices, etc. Recently, ferroelectric domain walls have been demonstrated to exhibit a rich panoply of nanoscale switching behaviors (V. R. Aravind \textit{et al,} Physical Review B \textbf{82}, 024111 (2010)). In this presentation, we report our study of domain reversal and polarization relaxation behavior of ferroelectric domain walls under localized electric field provided by a scanning probe microscope tip. Our studies show the relaxation behaviors differs at different distances from a 180 degree domain wall, throwing light on the microscopic mechanisms of polarization reversal.   

In situ TEM studies of interaction between ferroelastic and ferroelastic domains during ferroelectric switching

Dynamic interaction between ferroelastic (90 degree) and ferroelectric (180 degree) domains in lead zirconate titanate during ferroelectric switching was investigated by in situ TEM. It was found that 90 degree domain walls were immobile under applied bias and act as obstacles to 180 degree domain wall motion. Pinning of the incident 180 degree domain wall occurs directly at the leading 90 degree domain wall and results in a charged head-to-head polarization vector configuration and thereby a large surface energy. This causes the roughening of the domain wall which was atomically sharp before switching. Subsequent switching occurs through the nucleation of a new domain on the opposite 90 degree domain wall and ultimately results in 180 degree switching across the film with the 90 degree domain wall still present. Although they were immobile, the 90 degree domains could sometimes be erased by an external electrical field parallel to the normal axis polarization and would return when the field was removed. This suggests that a pre-pulse opposite to the desired writing direction which momentarily erases these domains may improve switching efficiency.   

Vortex polarization, strain induced phase transitions and dielectric response in ultra-thin PbTiO$_3$ nanowires from first principles

Nature of ferroelectricity in nanostructures and the resulting dielectric response are of both fundamental and applied interest. Here, using density functional theory (DFT) based computations, we investigate polarization configurations as a function of axial strain in ultra-thin PbTiO$_3$ [001] nanowires. Our computations involved relaxed and axially strained free-standing nanowires with varying sidewall terminations and diameters. While stress-free nanowires with their sidewalls terminated by PbO surfaces displayed purely rectilinear axial polarization at all sizes, the TiO$_2$-terminated nanowires, at a critical diameter of 16 {\AA}, display a non-rectilinear vortex polarization transverse to the nanowire axis. We discuss the origins of such behavior. We also predict the existence of novel stress-induced phase transitions between the mutually exclusive vortex and the axial polarization states in both the PbO- and TiO$_2$-terminated nanowires. Normal mode vibrational frequency analysis of these nanowires further confirms these results. Furthermore, by employing density functional perturbation theory in combination with effective medium dielectric theory we calculate dielectric permittivity of the ferroelectric nanowires and compare it with the corresponding bulk results.   

Domain Wall Nucleation and Propagation within Ferroelectic Nanowires in High Strength Electric Fields

Ferroelectric nanowires have attracted a lot of attention recently, thanks to their ability to develop electric polarization at the nanoscale [1]. Such a unique feature could potentially lead to the use of such nanowires in nanoscale, ultra fast, high-density memory elements. Here we take advantage of accurate first-principles-based simulations to study ultra fast polarization reversal in ultra thin ferroelectric nanowires made of PbTi$_{0.6}$Zr$_{0.4}$O$_{3}$ alloy. Our computational experiments reveal that polarization reversal in such nanowires is both qualitatively and quantitatively different from their bulk counterparts and exhibits unique features that could find potential use in nanoscale ferroelectric memory elements. \\[4pt] [1] P.M. R{\o}rvik, T. Grande, and M.-A. Einarsrud (2011), One-Dimensional Nanostructures of Ferroelectric Perovskites. Advanced Materials, 23: 4007-4034   

Terahertz Frequency Dynamics of Ferroelectric Nanowires

A thorough understanding of ferroelectric nanostructures is imperative considering their utility in creating nanoscale devices for the technology of the future. One such ferroelectric nanostructure which may prove useful in the design of nanosensors is the nanowire. We report our study on ferroelectric nanowires of Pb(Zr$_{0.4}$Ti$_{0.6}$)O$_3$ alloy done using classic molecular dynamics with first-principle-based effective Hamiltonian[1] and Evans-Hoover thermostat. We found that 1) the polarization of such nanowires can be reversed and 2) that the nanowires temperature can be controlled by the application of a terahertz electric field pulse. The dependence of these properties on the frequency, width, and amplitude of the pulse is explored and discussed in addition to a possible energy dissipation mechanism. \newline \newline [1] L. Bellaiche {\it et al}, Phys. Rev. Lett. {\bf 8}, 5427 (2000).   

Origin of 90$^{\circ}$ Domain Wall Pinning in Pb(Zr$_{0.2}$Ti$_{0.8})$O$_{3}$ Heteroepitaxial Thin Films

Researchers have studied the effect of ferroelectric fields in controlling the spin state via electric fields in multiferroic composite structures. For instance, in a bilayer system composed of a ferroelectric perovskite (PbZr$_{0.2}$Ti$_{0.8}$O$_{3})$ and a colossal magnetoresistive (CMR) manganite (La$_{0.8}$Sr$_{0.2}$MnO$_{3}$, LSMO), the spin state in the CMR film can be controlled by switching the ferroelectric polarization state, thereby generating a large magnetoelectric coupling. For this system, the domain's structure and switchability is critically important to the device's performance. We describe transmission-electron-microscopy study of the ferroelectric domains in a epitaxial Pb(Zr$_{0.2}$Ti$_{0.8})$O$_{3}$(PZT) film grown on La$_{0.8}$Sr$_{0.2}$MnO$_{3}$/SrTiO$_{3}$(001). We directly observe the pinning of 90$^{\circ}$ domain walls by pairs of misfit dislocations with Burgers vectors \textbf{\textit{a}}[100] and \textbf{\textit{a}}[001]. Model calculations based on the elastic theory confirm our finding that, in addition to the depolarization field surrounding the dislocation, the strain field of misfit dislocation-pairs plays the primary role in the formation and pinning of \textbf{\textit{a}} domains.   

Dynamics of Nanowalls In Ferroelectric Ultrathin Films

Nanoscale ferroelectric films can exhibit nanostripes that are nanoscopic regions of ``up'' and ``down'' polarizations, hence forming domain walls which separate nanodomains with different polarization directions. The dynamical properties of domain walls are of technological importance since they are at the heart of ultradense ferroelectric memory technology and may play an important role in nanoscale ferroelectric sensors, actuators, and others. Here [1] we take advantage of accurate first-principle-based simulations to reveal the intrinsic dynamics of nanodomains in ultra-thin PbTi$_{0.6}$Zr$_{0.4}$O$_3$ films with thickness ranging from 2 to 20 nm. We first demonstrate that the nanodomain walls oscillate under driving AC-field of sub-switching amplitude. Secondly, we reveal that nanowalls can exhibit two types of intrinsic dynamics (resonance and relaxation) at the same frequencies. Thirdly, we prove that at nanoscale the dynamics is determined by the domain size which manifests itself via a unique size-driven transition from relaxational to resonance dynamics.\\[4pt] [1] Q. Zhang et al, Phys. Rev. Lett. 107, 177601 (2011).   

Nanoscale Ferroelectric Switching in Thin Films by in-situ TEM for Magnetoelectric Applications

The ferroelectric switching along the low-dimensional axis of nanoscale multiferroic BiFeO$_{3}$ thin films is studied in this work using in-situ transmission electron microscopy. With this technique, the atomic scale polarization distribution and the controlling influence of defects on growth kinetics are observed. Despite the inhomogeneous external field applied by a surface probe, nucleation sites are determined by the built-in fields formed within carrier depletion regions at the electrode interfaces. Homogenous full-film switching is often impeded by the pinning of domain growth by such features as point defect assemblies and from independent switching in the near-interface region. This inhomegeneity along the normal film axis has significant implications for the interpretation of surface probe ferroelectric switching measurements and for magnetoelectric applications which require ferroelastic switching at the interface.   

Domain dynamics during ferroelectric switching

Ferroelectric materials are characterized by a spontaneous polarization that can be reoriented by an applied electric field. The ability to form and manipulate domains at the nanometer scale is key to device applications such as nonvolatile memories. The ferroelectric switching is mediated by defects and interfaces. Thus, it is critical to understand how the domain forms, grows, and interacts with defects. Here we show the nanoscale switching of a tetragonal PbZr$_{0.2}$Ti$_{0.8}$O$_{3}$ thin film under an applied electric field using \textit{in situ} transmission electron microscopy. We found that the intrinsic electric fields formed at ferroelectric/electrode interfaces determine the nucleation sites and growth rates of domains and the orientation and mobility of domain walls, while dislocations exert a weak pinning force on domain wall motion. We also show that localized 180\r{ } polarization switching initially form domain walls along unstable planes. After removal of the external field, they tend to relax to low energy orientations. In sufficiently small domains this process results in complete backswitching. Our results suggest that even thermodynamically favored domains are still subject to retention loss, which must be mitigated by overcoming a critical domain size.   

Modeling Micron Size Multi-domain Ferroelectric Switching using a Massively Parallel Time Domain Phase-Field Model

For the study of devices incorporating multi-domain ferroelectric materials, it is necessary to extend the current capabilities of the phase field model up to the micron scale where experiments are typically performed. Also arbitrary electrical and mechanical boundary conditions need to be incorporated relatively easily. In this work, we report a time domain implementation of the 3D phase field model that can simulate multi-domain ferroelectric switching. This massively parallel implementation enables us to study the switching properties of micron size devices with $\sim $10$^{9}$ degrees of freedom. We used a mixed finite difference and finite element grid, for calculating the nonlocal electrostatic and elastic interactions respectively. All the local and non-local interactions are shown to scale linearly up to thousands of processors. The model can take into account arbitrary electrical and mechanical boundary conditions suitable for the study of devices with arbitrary structures. Using this model, we report the simulation results of ferroelectric switching in devices incorporating the multi-ferroic material BiFeO$_{3}$. We explain the domain growth mechanism observed in multiple experiments reported recently on various surfaces of BiFeO$_{3}$.