Note on Oxygen Isotope Effect and Ferroelectric Transition in Quantum Paraelectrics

By extending the soft-phonon theory, a quantum paraelectric(PE)-ferroelectric(FE) transition in SrTi
¹⁶
O
₃
(ST016) is studied from the viewpoint of the important role of optical phonons in perovskite-oxides. In spite of intrinsic quantum fluctuation of large zero-point vibration induced from light O-atoms, the FE transition due to the O-isotope exchange
¹⁶
O
_1-x

¹⁸
O
_x
is explained in a unified picture by combining with the applied pressure (or uniaxial stress) effect. The calculated T
_c
as the function of x is compared with the experimental data in rather good agreement, and the origin of quantum paraelectricity in STO 16 is discussed in comparison with pressure effect in hydrogen-bonded ferroelectrics KH
₂
PO
₄
(KDP). As the result, it is suggested that quantum PE-FE transition with the critical exponent 1/2 at T
_c
=0 where the FE transition will start, must be analyzed by a microscopic theory exceeding soft phonon theory.