Generation of ferroelectric domains in atomic force microscope

A theory of an equilibrium shape of domains formed in an electric field of atomic force microscope (AFM) is proposed. The domain shape depends on parameters of the ferroelectric and on the applied voltage. Under low voltages the length and the diameter of the domain are of the same order of magnitude. With voltage increase the ratio between the length and the diameter increases. A correlation between the lateral sizes and the spontaneous polarization value is considered. It is shown that under the same voltage the thinnest domains are formed in ferroelectrics with high spontaneous polarization. The concept of the domain shape invariant as a combination of the domain length and lateral size, which is constant when changing the AFM parameters, is introduced. Results of the calculation of the invariant value in barium titanate as well as of the domain dimensions and the shape in GASH are in good agreement with the experiment.