  The interaction of ferroelectric 180 degree domain wall with a strongly
inhomogeneous electric field of biased Scanning Probe Microscope tip is
analyzed within continuous Landau-Ginzburg-Devonshire theory. Equilibrium shape
of the initially flat domain wall boundary bends, attracts or repulses from the
probe apex, depending on the sign and value of the applied bias. For large
tip-wall separations, the probe-induced domain nucleation is possible. The
approximate analytical expressions for the polarization distribution are
derived using direct variational method. The expressions provide insight how
the equilibrium polarization distribution depends on the wall finite-width,
correlation and depolarization effects, electrostatic potential distribution of
the probe and ferroelectric material parameters.
