Kinetics of Domain Wall Motion in Ferroelectric Switching. I. General Formulation

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Abstract
Detailed theoretical study has been made of the nucleation model for wall motion in ferroelectrics. Kinetics of the wall motion has been worked out both analytically and by simulation. The wall velocity v is expressed in terms of nucleation rate I and sideways growth velocity u s of nuclei on the wall by the formula v = c w 0 I or v =1.4 c ( u s I ) 1/2 according as w 0 2 I / u s ≫1 or w 0 2 I / u s ≪1. ( c : minimum advancement of wall, w 0 : width of critical nucleus.) The nucleation rate I and the sideways growth velocity u s have been calculated on the basis of the theory of absolute reaction rates. It is shown that at very high fields two-dimensional nuclei can not nucleate, instead one-dimensional nuclei are formed, whose nucleation rate depends on field following a power law. From these results, general formulae for absolute wall velocities in various field ranges have been derived.