Screening and retardation effects on 180°-domain wall motion in ferroelectrics: Wall velocity and nonlinear dynamics due to polarization-screening charge interactions E. A. Eliseev Institute for Problems of Materials Science, National Academy of Sciences of Ukraine, 3 Krjijanovskogo, 03142 Kiev, Ukraine A. N. Morozovska* and G. S. Svechnikov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, 41 pr. Nauki, 03028 Kiev, Ukraine E. L. Rumyantsev, E. I. Shishkin, and V. Y. Shur Institute of Physics and Applied Mathematics, Ural State University, Ekaterinburg 620083, Russia S. V. Kalinin † The Center for Nanophase Materials Sciences and Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA Received 7 September 2008; revised manuscript received 7 November 2008; published 8 December 2008 The effect of the domain wall intrinsic width, relaxation time of the screening charges, and the dead layer thickness on the velocity of the planar 180°-domain wall moving under homogeneous external electric field in ferroelectric capacitor is analyzed. The limiting cases of domain wall motion, including i the motion induced by the external and local internal field originated at the wall-surface junction for nonzero dead layer thickness and ii the motion induced by the effective electric field averaged over the domain wall surface, are consid- ered. We demonstrate the crossover between two screening regimes: the first one corresponds to the low domain wall velocity, when the wall drags the sluggish screening charges, while the second regime appears for high domain wall velocity, when the delay of sluggish screening charges are essential and the wall depolar- ization field is screened by the instant free charges located at the electrode. The integral and approximate analytical expressions for electric field and algebraic equation for the domain wall velocity are derived. It is shown that in the local-field limit the motion can be unstable, since the internal field at the wall-surface junction decreases for larger domain wall velocities, making possible self-acceleration of the wall near the top surface. The instability may lead to the domain wall-surface bending and actual broadening in thick samples, as well as formation of periodic domain structures in the direction of wall motion. The motion in the limit of the averaged effective field is always stable. DOI: 10.1103/PhysRevB.78.245409 PACS numbers: 77.80.Fm, 77.22.Ej I. INTRODUCTION Domain wall DW motion in ferroelectric and ferromag- netic materials is one of the critical factors in determining the functionality of ferroic devices, including the ultimate switching speed, uniformity of switching behavior, and sta- bility of domain patterns in periodic fields. In the ideal bulk materials, the wall motion mechanisms are governed by the wall-lattice interactions as studied in detail by Vanderbilt. 1 The relationship between the lattice pinning and wall veloc- ity has been addressed in great detail starting from the pio- neering work by Muller and Weinreich 2 until recent advances by density-functional theory. 3 The presence of bulk disorder due to the random-bond and random-field defects coupling to order parameter and thermal excitations gives rise to a broad spectrum of remarkable physical phenomena including tran- sitions between pinned, creep, and sliding regimes, dynamic phase transitions, and self-organized criticalities. 4–6 In this case, the domain wall dynamics is assumed to be effectively local and controlled only by the driving force and disorder rather than interface and boundary conditions. However, it is well known that properties of ferroelectric materials are ultimately sensitive to the boundary conditions on surfaces and interfaces that define the depolarization fields inside the materials. Recently Qiu et al. 7 developed methodology that accounts for electrostatic boundary condi- tions, the formation of misfit dislocations, and polydomain structures, which produces the strain-thickness diagram of phase stability in epitaxial PbTiO 3 ultrathin ferroelectric films. These nonlocal effects define stability of ferroelectric phase and were predicted to trigger transitions to spatially modulated and toroidal phases 8,9 in rigid ferroelectric mate- rials. In realistic materials, the depolarization energy affects the stability of materials with respect to charge species adsorption, 10–12 formation of surface charge layers, 13,14 or oxygen vacancy formation 15 that provide efficient screening mechanisms on free surfaces. In capacitor structures, the for- mation of layers with reduced ferroelectric properties 16 and propagation of ferroelectric distortion through the interfaces 17–19 have been reported. However, these theoreti- cal studies address mainly static properties of ferroelectric materials as controlled by nonlocal depolarization field ef- fects. To complement the static studies, many experimental and theoretical studies report the broad spectrum of dynamic nonequilibrium phenomena at high domain wall velocities, including domain nucleation in front of the moving domain wall. 20,21 The effect of domain-domain electrostatic interac- PHYSICAL REVIEW B 78, 245409 2008 1098-0121/2008/7824/24540910 ©2008 The American Physical Society 245409-1