  The interaction of electric field with charged domain walls in ferroelectrics
is theoretically addressed. A general 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, it was found that
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 planar charged 180-degree domain wall normal
to the polarization direction in a periodic domain pattern in a proper
ferroelectric is analytically solved in terms of Landau theory. It is shown
that, in small applied fields (in the linear regime), the forces acting on
walls in such pattern increase with decreasing the wall spacing, the direction
of the forces coinciding with those for the case of the corresponding neutral
walls. At the same time, for large enough wall spacings and large enough
fields, these forces can be of the opposite sign. 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. It is shown that, except for a special situation, the presence of
charge domain walls can make poling more difficult. It is demonstrated that the
results obtained are also applicable to zig-zag walls under the condition that
the zig-zag amplitude is much smaller than the domain wall spacing.
