Double-impurity doping-induced quantum critical behaviors in Sr1−xBaxTi1−yRuyO3

It has been reported both experimentally and theoretically that the Ba2+-doping at the A-site of quantum paraelectric SrTiO3 suppresses the quantum fluctuations by activating the ferroelectric mode, while the Ru4+-doping at the B-site plays the opposite role. For a double-impurity doped SrTiO3, i.e., Sr1−xBaxTi1−yRuyO3, where the two types of opposite effects compete with each other, we propose an improved transverse-field Ising model in order to investigate the effect of the double-impurity doping on the quantum phase transitions and critical behaviors. The calculated quantum behavior is quite well consistent with experimental measurements. A linear relationship between the quantum critical doping concentrations for Ba2+ and Ru4+ is predicted, subsequently validated qualitatively by an anharmonic oscillator model.