A phase-field study of the scaling law in free-standing ferroelectric thin films

The scaling law for ferroelectric stripe domains is investigated in free-standing BaTiO₃ and PbTiO₃ thin films via phase-field simulations. The results agree with the Kittel law, where the square of the domain width is found to be proportional to the thin film thickness. After being rescaled by the corresponding domain wall thickness, the generalized scaling law is also demonstrated, with the dimensionless scaling constant M estimated to be ∼3.3 in two ferroelectric materials. Moreover, we predict the effect of the exchange constant which is incorporated in Ginzburg–Landau theory on the equilibrium domain width and the critical thickness of the ferroelectric thin films. (paper)