The Interaction of an 180 degree Ferroelectric Domain Wall with a Biased   Scanning Probe Microscopy Tip: Effective Wall Geometry and Thermodynamics in   Ginzburg-Landau-Devonshire Theory
  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. 
Anna N. Morozovska, Sergei V. Kalinin, Eugene A. Eliseev, V. Gopalan,   and Sergei V. Svechnikov