Ferroelectric charged domain walls in an applied electric field

The interaction of electric field with charged domain walls in ferroelectrics is theoretically addressed. Ageneral expression for the force acting per unit area of a charged domain wall carrying free charge is derived. It is shown that, in proper ferroelectrics, the free charge carried by the wall is dependent on the size of the adjacent domains. As a result, the mobility of such domain wall (with respect to the applied field) is sensitive to the parameters of the domain pattern containing this wall. The problem of the force acting on a charged planar 180 degrees domain wall normal to the polarization direction in a periodic domain pattern in a proper ferroelectric is analytically solved in terms of Landau theory. In small applied fields (in the linear regime), the force acting on the wall in such pattern increases with decreasing the wall spacing. It is shown that the domain pattern considered is unstable in a defect-free ferroelectric. The poling of a crystal containing such pattern, stabilized by the pinning pressure, is also considered. Except for a special situation, the presence of charge domain walls makes poling more difficult. The results obtained are also applicable to zigzag walls under the condition that the zigzag amplitude is much smaller than the sizes of the neighboring domains.