Landau expansion parameters for BaTiO₃

The 6th order Taylor expansion of the free energy in terms of the order parameter has been generally accepted to describe first order structural phase transitions. In recently years, some researchers added the 8th order terms in order to explain the two branches in dielectric loops observed in the BaTiO ₃ single crystal. We show that the Landau free energy terminated at the 6th orders is sufficient to fit the experimental observations if the rich information in the field-induced phase transitions is explored. By using the typical characteristics of ferroelectric and dielectric double loops above the Curie temperature T_c, the temperature-dependent expansion coefficients can be determined with high accuracy.