Local polarization dynamics in ferroelectric materials

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Rep. Prog. Phys. 73 (2010) 056502 S V Kalinin et al Figure 24. Piezoresponse images of (a), (d) written domains in stoichiometric lithium tantalate crystals. Domains after being heated to 100 ◦ C and then cooled (b), (e) once and (c), (f ) twice. (g), (h) Illustrations of domain shrinkage due to heat treatment where dotted circles mark domain corners and arrows show the domain shrinkage direction. Reprinted from [228], copyright 2006, American Institute of Physics. in single crystals and even capacitors switched by external strain [241] have been studied in detail by PFM. Extensive studies of the written domain stability in LNO and LTO single crystals have been performed by the Kitamura group. For large domain sizes, the relaxation driven by surface tension was observed at relatively low temperatures of ∼100 ◦ C, indicative of the high mobility of domain walls in these materials [228] (figure 24). The role of surface adsorbates and ion implantation, i.e. the creation of new pinning centers, on domain stability has been investigated [242, 243]. The effect of intrinsic defects in congruent LNO and associated disorder on the domain relaxation was studied and shown to lead to highly serrated domain walls [244]. A very elegant and detailed study of domain relaxation in thinned lithium niobate (LNO) crystals as a function of domain size and crystal thickness has been reported by Kan et al [231] (figure 25). A two-step mechanism in which a slow relaxation stage involving lateral shrinking of cylindrical domains is followed by fast relaxation after the domain is pinched-off from the bottom surface has been reported. This study was later extended to abnormally switched ‘bubble’ domains, as discussed in section 3.2.5 [245]. Note that while domain growth in the field of an SPM probe is determined by the interplay of the probe-induced field distribution, the field-dependent wall velocity, and the surface charge diffusion and charge injection kinetics, the domain relaxation in the absence of external fields is driven only by wall tension and depolarization fields. Correspondingly it is easier to interpret and quantify, and allows one to study wall dynamics quantitatively. This behavior is reminiscent of, e.g., nanoindentation experiments based on the Oliver– Pharr method [246], where the formation of the contact during loading is not amenable for direct interpretation, whereas the unload curve with constant tip–surface contact offers quantitative information on mechanical properties. That said, while domain formation and growth can always be induced by applying a high enough field, relaxation is controlled by the wall pinning mechanism and driving force, and hence can be much slower (or faster) than the experimentally accessible time scales. Polarization relaxation in ferroelectric polymers [247] and ferroelectric relaxors [248, 249] merits separate mention. While in classical ferroelectrics, relaxation occurs through the motion of domain walls, relaxors demonstrate a gradual fade out of contrast, consistent with slow relaxation of the effective order parameter [250]. In ferroelectric polymers, the dominant factor controlling slow dynamic response is chain rotation [251]. The time-resolved relaxation measurements in relaxors are discussed in detail in section 4.5. 3.2.3. Domain–defect interactions. The characteristic aspect of all realistic materials is the presence of defects that serve as nucleation sites and pinning centers for moving domain walls. In PFM-based point switching experiments, the concentration of the electric field in the vicinity of the probe apex typically results in nucleation at the probe apex and the as-formed domain grows rapidly. Hence, the observation of a defect effect on nucleation is possible only in the spectroscopic mapping PFM as discussed in section 4.4. At the same time, the domain wall pinning at the defects can be observed directly from the domain wall geometry and domain shape. The first analysis of domain wall geometry in terms of the pinning mechanism was performed by Paruch et al [234] and extensively summarized in a recent review [222]. These studies were later extended to model domain energetics in ultrathin films [235]. The domain wall velocity in the presence of surface defects was also investigated [252]. A similar approach was adopted by Pertsev et al to address domain wall dynamics [233]. The extensive effort by the group of Kitamura [228, 242–244] has demonstrated control of pinning by artificial defects. The domain wall geometry represents the result of multiple defect interactions in which the effect of individual defects cannot generally be resolved. The study by Agronin et al [253] has addressed the pinning on macroscopic morphological defects. 25
Rep. Prog. Phys. 73 (2010) 056502 S V Kalinin et al Figure 25. (a) Domain decay dynamics. (b) Domain lifetime dependence on the initial domain radius. (c) Decay process for different initial radii. (d) Critical initial domain radius for samples of different thicknesses. Reprinted from [231], copyright 2007, American Institute of Physics. Fundamental studies of pinning mechanisms require the structure of defects to be known. Given that the width of a typical ferroelectric domain wall is on the order of 1–3 unit cells, the defect has to be defined on the atomic level, significantly narrowing the range of systems with known localized defects. Ferroelastic domain walls offer an advantage of known structure and geometry. The effect of ferroelastic domain walls and in-plane domain twins on ferroelectric switching and domain wall dynamics in (1 0 0) tetragonal ferroelectric films has been studied in detail by Ganpule et al [254, 255]. The switching in the vicinity of a 90 ◦ domain twin is shown to proceed through the correlated domain motion as illustrated in figure 26. This mechanism was recently confirmed by in-plane observations by Aravind et al [256]. The effect of ferroelastic domain walls on relaxation was studied on mesoscopic and single wall levels in [255], and the walls were found to serve as effective pinning centers. At the same time, within the cells formed by 90 ◦ twins, the formation of faceted domains was observed. These studies allowed the relaxation rate to be related to wall curvature (figure 27). Finally, the effect of grain boundaries, the dominant defect type in polycrystalline films, was studied by Gruverman [128]. In many materials, the grain boundaries serve as natural barriers for wall motion, resulting in a single-grain switching. The analysis of the grain boundary–domain interaction is limited by the fact that the GB structure, including both the grain misorientation and the presence of secondary phases, charge, etc, is generally unknown. At the same time, EM methods such as aberration corrected EM and energy loss spectroscopy [257–259] that have been shown to be extremely powerful methods to analyze GB structure and charge are not yet compatible with PFM measurements [260]. Artificially engineered bicrystal defects offer an alternative, and the direct observation of domain wall pinning on a well-defined GB has recently been reported [261]. The use of well-defined defects allows the deterministic polarization switching mechanisms to be deciphered, as discussed in section 5. 3.2.4. Non-180 ◦ switching. In ferroelectric materials, the application of electric field in most cases induces only 180 ◦ polarization switching, since non-uniform ferroelastic (i.e. non-180 ◦ ) switching increases the strain state of the system and is generally believed to be less likely. However, in multiaxial ferroelectrics and in disordered systems, non-180 ◦ switching was observed, and in some cases controlled, by PFM. In a polycrystalline film, elastic clamping between the domains can result in the mechanism when ferroelectric switching of one grain triggers in-plane switching of the neighboring grains. Similar effects were found in ferroelectric capacitors 26
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