Incipient ferroelectrics: Anomalous T 1 behaviors and their rotor interpretation

The quantum temperature (denoted byT1) behaviors of three typical incipient ferroelectrics, SrTiO3, KTaO3and CaTiO3, are studied. This quantity is argued to serve fundamentally in identifying the nature of the local mode responsible for the dielectric responses. Our main findings are as follows. For all compounds,T1saturates at low temperatures. For CaTiO3,T1monotonically increases with temperature and no clear saturation is discernible at high temperatures. For KTaO3, similar behaviors are observed but with a little twist: a dip shows up around 35 K, above whichT1increases but below itT1decreases with temperature. Although it is hardly seeable in this compound, this dip might mark a transition, whose nature is unclear for the moment. In parallel with KTiO3, SrTiO3also has a dip, which is much stronger and broader. It happens around 105 K, at which the famous anti-ferrodistortive (AFD) transition occurs. Were it not for this dip,T1would drop to zero in SrTiO3at low temperatures and the ferroelectric (FE) transition would take place. The dip halts the drop and makesT1rise up to a value that is enough to stabilize the FE instability. In this respect, the dip is essential in preventing the FE transition in SrTiO3. Since the dip and the AFD transition occur at roughly the same temperature, we attempt to ascribe the former to the latter. This ascription is compatible with previous work [A. Yamanaka, M. Kataoka, Y. Inaba, K. Inoue, B. Hehlen, E. Courtens, Europhys. Lett., 50:(2000) 688]. To interpret theT1behaviors, we utilize an anisotropic rotor model, according to which the local variable is supposed to move on a non-uniform sphere. By tuning the anisotropy parameter, υ, qualitative agreement can be achieved. Especially, a single υ≈100 can fit theT1of CaTiO3over the entire temperature range under consideration, whereas the fitting for KTaO3requires two different υ, namely, υ≈260 above the dip temperature and υ≈40 below it. Analogously, two υ are also required for SrTiO3. Below the dip temperature, a very good fitting can be obtained with υ≈40. We did not try to fit the high temperature data of SrTiO3, because the data in this range are scarce and inaccurate. Nevertheless, we believe that a different and bigger υ should be at work, considering the case with KTaO3. Assuming the AFD transition as the cause of the dip in SrTiO3, we may claim that, the true role of the AFD transition in stabilizing the FE instability is to reduce the υ and then enhance quantum fluctuations.