  We propose a self-consistent theoretical approach capable to describe the
peculiarities of the anisotropic nanodomain formation induced by a charged AFM
probe on non-polar cuts of ferroelectrics. The proposed semi-phenomenological
approach accounts for the difference of the threshold fields required for the
domain wall motion along non-polar X- and Y - cuts, and polar Z - cut of
LiNbO3. The effect steams from the fact, that the minimal distance between the
equilibrium atomic positions of domain wall and the profile of lattice pinning
barrier appeared different for different directions due to the crystallographic
anisotropy. Using relaxation-type equation with cubic nonlinearity we
calculated the polarization reversal dynamics during the probe-induced
nanodomain formation for different threshold field values. The different
velocity of domain growth and consequently equilibrium domain sizes on X-, Y-
and Z-cuts of LiNbO3 originate from the anisotropy of the threshold field. Note
that the smaller is the threshold field the larger are the domain sizes, and
the fact allows explaining several times difference in nanodomain length
experimentally observed on X- and Y-cuts of LiNbO3. Obtained results can give
insight into the nanoscale anisotropic dynamics of polarization reversal in
strongly inhomogeneous electric field.
