Isotope Effect on the Ferroelectric Phase Transitions in BaTiO 3, SrTiO 3 and PbTiO 3

We discuss theoretically the intriguing isotope effect (opposite trends for oxygen and for cations such as Ti or Ba) on the ferroelectric phase-transition temperatures in BaTiO 3, SrTiO 3 and PbTiO 3 . The transition temperature is defined as the balancing temperature of the two forces; the force reinforcing the ferroelectric (low-temperature) structure (the long-range electron-phonon interaction force), and the thermal fluctuations which will stabilize the paraelectric (higher temperature) structure. Oxygen (anion) isotope exchange induces mainly change in the thermal fluctuation; resulting in that with light isotope introduction the phase transition temperature lowers. The cation isotope exchange induces change in the long-range force; resulting in that with light isotope introduction the phase transition temperature rises.