Ferroelectrics: Domain Walls
Mixed Bloch-Néel-Ising Character of 180° Ferroelectric Domain Walls
D. Lee, R. Berhera, P. Wu, H. Xu, Y. Li, S. Phillpot, S. Sinnott, L. Chen and V. Gopalan, Phys. Rev. B.-rapid communications, 80, 060102(R) (2009). PDF
Ferroelectric 180° domain walls are well-known to be predominantly Ising-like. Using density functional theory, and molecular dynamics simulations, the 180° domain walls in prototypical ferroelectrics lead titanate (PbTiO3) and lithium niobate (LiNbO3) are shown to have mixed character; while predominantly Ising-like, they also manifest some Bloch- and Néel-like character. Phase-field calculations show that such mixed wall character can be dramatically enhanced in nanoscale thin film heterostructures such as BaTiO3 /SrTiO3, where the internal wall structure can form polarization vortices. Such mixed character walls can be expected to exhibit dynamical wall properties distinct from pure Ising walls.
FIG. 3. (Color online) (a) Structural arrangement of LiNbO3 near the lowest energy y-wall position projected in the (0001) plane; (b) the three polarization components, Pn, Pt, and Pz as a function of the normal coordinate xn across a single y-wall. The solid lines are fits to simulation results. (c) z-direction displacement of Li (uz,LiI =0.001 Å and uz,LiII =0.023 Å) and Nb (uz,NbI =0.019 Å and uz,NbII =0.016 Å) atoms in the near the y-wall; and (d) Wall normal (un) and parallel (ut) displacements of Li (un,LiI =0.026 Å, un,LiII =0.012 Å, ut,LiI =0.029 Å, and ut,LiII =0.088 Å), and Nb atoms (un,NbII =0.001 Å, un,NbI =0.014 Å, ut,NbI =0.012 Å, and ut,NbII =0.026 Å) near a y-wall.
FIG. 4. (Color online) (a) Phase-field modeling of ferroelectric polarization vector distribution in a commensurate periodic (001) (SrTiO3)4 / (001) (BaTiO3)8 superlattice with four 180° domain walls indicated by vertical dashed lines, described in the text. The 24 rows are spaced every half a unit cell, and the 32 columns are spaced every 0.5 nm. (b) The polarization vector variation in the z direction for columns A-H across a single domain wall. The polarization components, Px (or Pxn), Py (or Pxt), and Pz, the total polarization, Ptotal, and the Bragg (θB) and Néel (θN) are shown as a function of coordinate xn for the center of a SrTiO3 layer (panels e, h) center of a BaTiO3 layer (panels c, f), and the interface layer (panels d, g).
Nanoscale Polarization Profile Across a 180° Ferroelectric Domain Wall Extracted by Quantitative Piezoelectric Force Microscopy
L. Tian, A. Vasudevarao, A. N. Morozovska, E. A. Eliseev, S. Kalinin and V. Gopalan, J. Appl. Phys., 104, 074110 (2008). PDF
The structure of a single antiparallel ferroelectric domain wall in LiNbO3 is quantitatively mapped by piezoelectric force microscopy (PFM) with calibrated probe geometry. The PFM measurements are performed for 49 probes with the radius varying from 10 to 300 nm. The magnitude and variation of the experimental piezoelectric coefficient across a domain wall match the profiles calculated from a comprehensive analytical theory, as well as three-dimensional finite element method simulations. Quantitative agreement between experimental and theoretical profile widths is obtained only when a finite disk-type tip radius that is in true contact with the sample surface is considered, which is in agreement with scanning electron microscopy images of the actual tips after imaging. The magnitude of the piezoelectric coefficient is shown to be independent of the tip radius, and the PFM profile width is linearly proportional to the tip radius. Finally we demonstrate a method to extract any intrinsic material broadening of the ferroelectric wall width. Surprisingly wide wall widths of up to 100 nm are observed in the limit of zero tip radius.
FIG. 2. An example of complex PFM displacement, Ũ=UR+iUI=Uoeiθ as a function of wall normal coordinate, x across a 180° domain wall in lithium niobate. (a)UR=Uocos~Uz, (b)UI=Uosinθ, (c)Uo, and (d)θ. Measurements were made with a Ti/Pt coated Si tip with a tip disk radius of ~50–60 nm. An oscillating voltage of 5 Vrms, at 42.35 kHz was applied to the tip.
The Influence of 180° Ferroelectric Domain Wall Width on the Threshold Field for Wall Motion
S. Choudhury, Y. Li, N. Odagawa, A. Vasudevarao, L. Tian, P. Capek, V. Dierolf, A. Morozovska, E. Eliseev, S. Kalinin, L. Chen and V. Gopalan, J. Appl. Phys., 104, 084107 (2008). PDF
Unlike ideal 180° ferroelectric walls that are a unit cell wide (~0.5 nm), real walls in ferroelectrics have been reported to be many nanometers wide (1–10 nm). Using scanning nonlinear dielectric microscopy of lithium niobate (LiNbO3) and lithium tantalate (LiTaO3) ferroelectrics, we show that the wall width at surfaces can vary considerably and even reach ~100 nm in places where polar defects adjoin a wall. The consequence of such variable wall widths is investigated on the specific property of threshold field required for wall motion. Using microscopic phase-field modeling, we show that the threshold field for moving an antiparallel ferroelectric domain wall dramatically drops by two to three orders of magnitude if the wall was diffuse by only ~1–2 nm, which agrees with experimental wall widths and threshold fields for these materials. Modeling also shows that wall broadening due to its intersection with a surface will influence the threshold field for wall motion only for very thin films (1–10 nm) where the surface broadening influences the bulk wall width. Such pre-existing and slightly diffuse domain walls with low threshold fields for wall motion may offer a general mechanism to explain significantly lower experimental coercive fields for domain reversal in ferroelectrics as compared to the thermodynamic predictions.
FIG. 1. (Color online) SNDM images of a circular domain in a 40 nm thick z-cut single crystal lithium niobate [(a) and (b)] and a 31 nm thick z-cut single crystal lithium tantalate [(c) and (d)] at first harmonic, ωp=6 kHz [(a) and (c)] and second harmonic, 2ωp=12 kHz [(b) and (d)] modulation frequencies. Figures 1(d) and 1(e) show typical line profiles from these images as labeled, and pairs of arrows indicate the wall region. Images (a)–(d) are plotted in three-dimensional orthographic view with an ~21° rotation about the horizontal axes of the images. The length scales directly correspond to the horizontal axes of the images. The same domain region is imaged in (a) and (b), and similarly in (c) and (d).
Defect - DomainWall Interactions in Trigonal Ferroelectrics
In The Annual Review of Materials Research, Venkatraman Gopalan, Volkmar Dielorf and David A. Scrymgeour, Annu. Rev. Mater. Res. 2007. 37:449-89 PDF
Domains and domain walls are a fundamental property of interest in ferroelectrics, magnetism, ferroelastics, superconductors, and multiferroic materials. Unlike magnetic Bloch walls, ideal ferroelectric domain walls are well accepted to be only one to two lattice units wide, over which polarization and strain change across the wall. However, walls in real ferroelectrics appear to show unexpected property variations in the vicinity of domain walls that can extend over micrometer length scales. This chapter specifically reviews the local electrical, elastic, optical, and structural properties of antiparallel domain walls in the trigonal ferroelectrics lithium niobate and lithium tantalate. It is shown that extrinsic point defects and their clustering play a key role in the observed local wall structure and influence macroscale properties by orders of magnitude. The review also raises broader and yet unexplored fundamental questions regarding intrinsic widths, defect–domain wall interactions, and static versus dynamic wall structure.
Domain wall pinning and bowing under an external field of +2 kVmm−1 in congruent LiNbO3. (a) Near-field scanning optical microscopy (NSOM) image of the +z surface of LiNbO3. Pinning sites are indicated by circles. The red arrow indicates the center of the wall. Reprinted with permission from Reference 83. Copyright 1999 by the American Physical Society. (b) Atomic force microscopy images on the +z surface after polishing away 7 μm and chemical etching (125). Reprinted with permission from Reference 84. Copyright 2006, American Institute of Physics.
Nanoscale Piezoelectric response at a single ferroelectric Domain wall
D. Scrymgeour and V. Gopalan, Phys. Rev. B 72, 024103 (2005). PDF
Experiments and three-dimensional numerical modeling of nanoscale piezoelectric response across a single domain wall in ferroelectric lithium niobate are presented. Surprising asymmetry in the local electromechanical response across a single antiparallel ferroelectric domain wall is reported. Piezoelectric force microscopy is used to investigate both the in-plane and out-of- plane electromechanical signals around domain walls in congruent and near-stoichiometric lithium niobate. The observed asymmetry is shown to have a strong correlation to crystal stoichiometry, suggesting defect–domain-wall interactions. A defect-dipole model is proposed. The finite-element method is used to simulate the electromechanical processes at the wall and reconstruct the images. For the near-stoichiometric composition, good agreement is found in both form and magnitude. Some discrepancy remains between the experimental and modeling widths of the imaged effects across a wall. This is analyzed from the perspective of possible electrostatic contributions to the imaging process, as well as local changes in the material properties in the vicinity of the wall.
FIG. 11. Finite-element method (FEM) calculations of surface displacements for +5 V applied to the +Ps surface for: a uniform domain with source at S=0 in (a), (b), (c), domain wall at x=0 and source at S=0 in (d), (e), (f), and domain wall at x=0 with source at S =100 nm in (g), (h), (i). Distortion Ux is shown in column 1 (a), (d), (g), Uy in column 2 (b), (e), (h), and Uz, in column 3 (c), (f), (i) with all distortions in picometers shown in common color bar on the right. Crosshairs indicate the position of tip, and the dotted vertical line indicates the domain wall. Each figure is 2000x2000 nm.
Phenomenological Theory of a Single Domain Wall in Uniaxial Trigonal Ferroelectrics: Lithium Niobate and Lithium Tantalate
D. Scrymgeour, V. Gopalan, A. Itagi, A. Saxena and P. Swart, Phys. Rev. B, 71, 184110-1/13 (2005). PDF
A phenomenological treatment of domain walls based on the Ginzburg-Landau-Devonshire theory is developed for uniaxial trigonal ferroelectrics, lithium niobate and lithium tantalate. The contributions to the domainwall energy from polarization and strain as a function of orientation are considered. Analytical expressions are developed that are analyzed numerically to determine the minimum polarization, strain, and energy configurations of domain walls. It is found that hexagonal y walls are preferred over x walls in both materials. This agrees well with experimental observation of domain geometries in stoichiometric composition crystals.
FIG. 14. Strain ε~(needs character)5 for a theoretical x wall shown as dotted lines in LiTaO3. The horizontal dashed line is a cut through hexagon along the x direction. At the corners of the domain walls are high energy points as the sign of the strain switches.
Enhancement of ferroelectricity in strained BaTiO3 thin films
K. Choi, M. Biegalski, Y. Li, A. Sharan, J. Schubert, R. Uecker, P. Reiche, Y. Chen, X. Pan, V. Gopalan, L. Chen, D. Schlom and C. Eom, Science, 306, 1005 (2004). PDF
Biaxial compressive strain has been used to markedly enhance the ferroelectric properties of BaTiO3 thin films. This strain, imposed by coherent epitaxy, can result in a ferroelectric transition temperature nearly 500°C higher and a remanent polarization at least 250% higher than bulk BaTiO3 single crystals. This work demonstrates a route to a lead-free ferroelectric for nonvolatile memories and electro-optic devices.
Long range strains and the effects of applied fields at 180° ferroelectric domain walls in lithium niobate
T. Jach, S. Kim, V. Gopalan, S. Durbin and D. Bright, Physical Review B, 69,064113-1/9 (2004). PDF
Ferroelectric domains with antiparallel polarization are readily induced in congruent LiNbO3 with electric fields above 240 kV/cm at room temperature. Even in the absence of external fields, these 180° walls exhibit wide regions of shear strain, on the order of 10-5, within a 10μm range of the domain walls. Using x-ray topography on samples while applying electric fields of 0–90 kV/cm, we have observed large-scale reversible domain changes. A detailed strain analysis of the piezoelectric behavior at the domain walls, as well as within
the domains, indicates that substantial surface displacement is associated with the high contrast of ferroelectric domains in x-ray topographs. These observations show that long-range strain interactions due to applied fields are present around domain walls long before permanent changes are induced.
FIG. 2. (00.12) Bragg topograph of LiNbO3 crystal (a) at applied voltage V=0, (b) at applied voltage V=+4500 V (forward
bias: electric field parallel to polarization inside the hexagonal domains), and (c) at applied voltage V=-4400 V (reverse bias: electric field antiparallel to polarization inside the hexagonal domains). The domain outlines as seen for V=0 are shown in (b) and (c). The small arrows show the apparent motion of defect features from the position at V=0.
Domain reversal and non-stoichiometry in LiTaO3
S. Kim, V. Gopalan, K. Kitamura and Y. Furukawa, J. Appl. Phys., 90, 2949 (2001). PDF
Recent studies have shown that lithium nonstoichiometry has a tremendous influence on domain reversal characteristics in ferroelectric lithium tantalate. This work presents a systematic study of the domain reversal characteristics such as threshold coercive fields for domain reversal, domain stabilization times, ‘‘backswitching’’ phenomena, domain switching and wall pinning times, and sideways wall mobility in near-stoichiometric LiTaO3 with Li/(Li+Ta)~0.498. These properties are contrasted with those of congruent LiTaO3 [Li/(Li+Ta)~0.485]. A qualitative model is proposed based on nonstoichiometric dipolar defects to explain the dependence of threshold coercive field on defect density, and on repeated field cycling, the origin of domain backswitching, and domain stabilization times.
FIG. 2. Tracking domain wall motion under external field in a z-cut near-stoichiometric LiTaO3 crystal. Electrode area was 1.2 mm2. (a) The applied step field of ~20 kV/cm and the corresponding transient current response, and (b) the corresponding optical images of the moving wall recorded with a video camera (33 frames/s). The time instants of the five frames shown in (b) are marked by F1–F5 in (a).
Crystal Growth, Characterization, and Domain Studies in Lithium Niobate and Lithium Tantalate Ferroelectrics
In The Handbook of Advanced Electronic and Photonic Materials and Devices, Venkatraman Gopalan, Norman A. Sanford, J. A. Aust, K. Kitamura and Y. Furukawa, Volume 4, Chapter 2, pp 58-112 (2000) PDF
In-situ video observation of 180° domain kinetics in congruent LiNbO3 crystals
V. Gopalan, Q. X. Jia, T. E. Mitchell, “ Appl. Phys. Lett. 75, 16 (1999). PDF
We report in situ observation of the nucleation and growth of ferroelectric 180° domains in congruent LiNbO3 crystals. The domains nucleate and grow as six-sided polygons. The wall velocity measured at a constant field shows a spike-like behavior with time, suggesting a strong pinning–depinning type of growth mechanism. This behavior is similar to the corresponding transient current measurement which also shows current spikes during domain reversal.
FIG. 2. Selected video frames from in situ video recording of the 180° domain kinetics in congruent Z-cut LiNbO3 under and external field of 21.6 kV/mm (applied at time t=0). The time, t (in seconds) corresponding to each frame is (a) 18.47, (b) 21.44, (c) 24.44, (d) 27.44, (e) 33.874, (f) 33.907, (g) 33.940, (h) 33.974, (i) 35.574, (j) 35.640, (k) 35.674, (l) 35.707, (m) 35.907, (n) 35.904, (o) 35.974, (p) 36.040, (q) 36.074, (r) 37.907. The polarization axes are normal to the image plane, and the crystallographic x and y axes marked in frame (a) point northwest and northeast, respectively. Domain clusters I and II, and merged domain front III are labeled.
Mobility of 180° domain walls in congruent LiTaO3 measured using in-situ electro-optic imaging microscopy
V. Gopalan, S. S. A. Gerstl, A. Itagi, Q. X. Jia, T. E. Mitchell, T. E. Schlesinger, D. D. Stancil, J. Appl. Phys. 86, 1638 (1999). PDF
We report the electric-field dependence of 180° domain-wall mobility in congruent LiTaO3 measured at room temperature using in situ electro-optic imaging microscopy. The measured sideways domain-wall velocity of serrated domain fronts formed upon merger of domains was an order of magnitude larger than that for independently growing domains. The wall velocities also show a strong dependence on the nature of the applied electric field, being an order of magnitude larger for steady-state voltages as compared to pulsed voltage measurements. This is shown to be due to wall stabilization between applied voltage pulses resulting in an inertial delay in moving a domain wall which has been at rest for many seconds.
FIG. 3. Selected video frames from in situ recording of the nucleation and growth of 180° domains in congruent LiTaO3 (sample F208) under an external field of 207.6 kV/cm (applied at time t=0 s) using EOIM. Frame (a) corresponds to t=30 s, and all successive frames [(b)–(o)] are 15 s apart from each other. The polarization axis is normal to the plane of the figure ~the z plane! and the crystallographic x and y axes are marked. For independently growing domains (I, II, III, IV) and three merged domain fronts (V, VI, VII), for which domain mobilities were measured, are labeled. The arrows in frames (e) and (g) indicate the location and direction of the wall velocity measurement for the merged fronts V, VI, and VII.
Direct observation of pinning and bowing of a single ferroelectric domain wall
T. J. Yang, U. Mohideen, V. Gopalan, P. Swart, Phys. Rev. Lett. 82, 4106 (1999). PDF
We have made a direct optical observation of pinning and bowing of a single 180° ferroelectric domain wall under a uniform applied electric field using a collection mode near-field scanning optical microscope. The domain wall is observed to curve between the pinning defects, with a radius of curvature determined by the material parameters and the applied electric field. The change in birefringence with applied field is used to infer the orientation of the internal field at the domain wall.
FIG. 3. Schematic of bowing of a pinned domain wall (defects are dots) under an applied electric field.