  Thermodynamics of tip-induced nanodomain formation in scanning probe
microscopy of ferroelectric films and crystals is studied using the
Landau-Ginzburg-Devonshire phenomenological approach. The local redistribution
of polarization induced by the biased probe apex is analyzed including the
effects of polarization gradients, field dependence of dielectric properties,
intrinsic domain wall width, and film thickness. The polarization distribution
inside subcritical nucleus of the domain preceding the nucleation event is very
smooth and localized below the probe, and the electrostatic field distribution
is dominated by the tip. In contrast, polarization distribution inside the
stable domain is rectangular-like, and the associated electrostatic fields
clearly illustrate the presence of tip-induced and depolarization field
components. The calculated coercive biases of domain formation are in a good
agreement with available experimental results for typical ferroelectric
materials. The microscopic origin of the observed domain tip elongation in the
region where the probe electric field is much smaller than the intrinsic
coercive field is the positive depolarization field in front of the moving
counter domain wall. For infinitely thin domain walls local domain breakdown
through the sample depth appears. The results obtained here are complementary
to the Landauer-Molotskii energetic approach.
