Lattice-Dynamical Theory of Switching in Barium Titanate Single Crystals

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Abstract
A lattice‐dynamical approach to calculation of the switching probability is developed for use in connection with the Miller‐Weinreich model of 180° domain‐wall motion in barium titanate single crystals. According to the new approach, the nuclei of permanently reversed polarization, which appear on the domain‐wall surface in the presence of a field, are produced by a superposition of optic modes. The probability that this superposition will attain the amplitude required to switch a nucleus can be calculated as the probability for the outcome of a random walk. This probability is a function of the optical frequency and of the number of modes which contribute to switching. From a previous renormalization of the Hamiltonian which describes the lowest transverse optic mode, the field and thickness dependence of the parameters which govern switching can be determined. In this way it is predicted that (1) the product of field and activation energy will increase with the field; and (2) the thickness dependence of the switching activation energy, which is primarily of lattice‐dynamical origin, should exceed the corresponding thickness dependence of the electric susceptibility measured on the same crystal. The role of the surface layer is assumed, following Janovec, to lie in the production of backswitched microdomains behind the advancing domain wall. This backswitching can produce electrostatic fields which retard the wall in the same way as depolarization fields which earlier theories have attributed to charges deposited on the inner surface of an unswitched layer. This picture of retardation permits us to separate the mechanism which slows the wall from that which accounts for the thickness dependence of switching and thus to avoid contradictions which have arisen in attempts to explain the latter effect by depolarization fields.