Isotope-Induced Ferroelectric Phase Transition in Strontium Titanate Only by a Decrease in Zero-Point Vibration Frequency

The possibility of the ferroelectric phase transition in SrTi 18 O 3 only by decreasing the frequency of zero-point vibration due to the substitution of 18 O for 16 O is investigated by the self-consistent phonon approximation (SCPA) of an anharmonic lattice vibration system. The SC equation for the soft-mode frequency is shown to be described by only two parameters; the paraelectric Curie–Weiss temperature T 0 in SrTi 16 O 3 and the quantum factor T 1 inversely proportional to the square root of the effective mass M . The experimental finding that T c =0 in the mixed crystal SrTi( 18 O x 16 O 1- x ) 3 at x =0.33 is used to determine T 1 at this concentration and that at another x using only the ratio of M . The transition temperature T c in SrTi 18 O 3 is numerically calculated for comparison with the experimental value. Several factors determining T c are discussed on the basis of numerical results.