Critical thickness and the size-dependent Curie temperature of BaTiO ₃ nanofilms

The Curie temperature and critical thickness of BaTiO ₃ nanofilms are investigated using the molecular dynamics method and Ginzburg-Landau theory. It is found that the critical thickness is 2. 8 nm, which agrees with others' experiments and first-principle calculations. Based on the Landau-Ginzburg theory, an analytical relation of the Curie temperature with the film thickness and the external stress is derived, and an explicit solution of the critical thickness is obtained. Comparisons with the MD simulations and experimental results illustrate thoe: accuracy of the analytical results. Furthermore, a simplified linear scaling law of the Curie temperature (or the critical strain) versus the reciprocal of film thickness is proposed based on the MD and theoretical results.