Interaction of a 180° 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° -domain wall with a strongly inhomogeneous electric field of biased scanning probe microscope tip is analyzed within continuous Ginzburg-Landau-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 into 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.