Critical exponents of ferroelectric transitions in modulated SrTiO3：Consequences of quantum fluctuations and quenched disorder

The ferroelectric transitions of several SrTiO3-based ferroelectrics are investigated experimentally and theoretically, with special attention to the critical scaling exponents associated with the phase transitions, in order to understand the competition among quantum fluctuations (QFs), quenched disorder, and ferroelectric ordering. Two representative systems with sufficiently strong QFs and quenched disorders in competition with the ferroelectric ordering are investigated. We start from non-stoichiometric SrTiO3(STO) with the Sr/Ti ratio deviating slightly from one, which is believed to maintain strong QFs. Then, we address Ba/Ca co-doped Sr1-x(Ca0.6389Ba0.3611)xTiO3(SCBT) with the averaged Sr-site ionic radius identical to the Sr2+ ionic radius, which is believed to offer remarkable quenched disorder associated with the Sr-site ionic mismatch. The critical exponents associated with polarization P and dielectric susceptibility ε, respectively, as functions of temperature T close to the critical point Tc, are evaluated. It is revealed that both non-stoichiometric SrTiO3 and SCBT exhibit much bigger critical exponents than the Landau mean-field theory predictions. These critical exponents then decrease gradually with increasing doping level or deviation of Sr/Ti ratio from one. A transverse Ising model applicable to the Sr-site doped STO (e.g., Sr1-xCaxTiO3) at low level is used to explain the observed experimental data. It is suggested that the serious deviation of these critical exponents from the Landau theory predictions in these STO-based systems is ascribed to the significant QFs and quenched disorder by partially suppressing the long-range spatial correlation of electric dipoles around the transitions. The present work thus sheds light on our understanding of the critical behaviors of ferroelectric transitions in STO in the presence of quantum fluctuations and quenched disorder, whose effects have been demonstrated to be remarkable.