Relaxation of 90° Domain Walls of BaTiO₃ and Their Equation of Motion

Abstract

The motion of 90° walls and wedge domains in BaTiO₃ single crystals under ac-fields ranged from 50 c/s to 200 Kc/s has been observed by the use of the stroboscopic illumination with short flash, which enables the measurement of the displacement of the walls in a desired phase of the field. The relaxation has been found to occur in the present range of the frequency. The position of the wall (wedge) plotted against voltage shows hystesis loop, which deforms as the frequency increases.
Several other aspects of domain motion have been studies as a function of frequency. An equation of motion is proposed:
M\ddotx+β\dotx+c(x−p)+A\fracπusin\fracπ(x−p)u=BV₀sinωt.
The third term is due to the bound charge on the surface of the crystal or the charge compensating it. The fourth term reflects periodic potential for the wall due to lattice defects. Most aspects of the wall motion in the given frequency range have been shown to be described by the equation of the relaxation type (M→0).