Thermooptical and dielectric studies of a calcium-induced ferroelectric phase in a SrTiO$_{3}$ incipient ferroelectric

We have examined temperature changes of the light refraction, birefringence, dielectric permittivity, and dielectric hysteresis loops in Sr$_{1-x}$Ca$_{x}$TiO$_{3}$ single crystals with $x$ = 0.014 (SCT-1.4). The dielectric properties of Sr$_{1-x}$Ca$_{x}$TiO$_{3}$ with $x$ = 0.007 (SCT-0.7) have been studied. We have performed ab initio calculations of equilibrium structures and total energies for three low-temperature phases of SrTiO$_3$ and CaTiO$_3$, based on which we have determined an expected symmetry of the ground state of their solid solution and spontaneous polarization directions in a calcium-induced ferroelectric phase in Sr$_{1-x}$Ca$_{x}$TiO$_{3}$. In SCT-1.4, we have separated a spontaneous contribution to the light refraction, which arises due to the spontaneous electrooptical effect caused by the spontaneous polarization and its fluctuations. From the spontaneous contribution to the light refraction, based on a previously developed our phenological approach, we have quantitatively determined for the first time the values and temperature dependences of root-mean-square fluctuations of the order parameter—the polarization $P_{sh}=\langle P^{2}_{fl}\rangle^{1/2}$ (short-range, local polar order) in the ferroelectric phase. From optical and dielectric measurements in SCT-1.4, the average value of spontaneous polarization $P_s$ (the contribution from the long-range order) has been determined. We have estimated the values of $P_{sh}$ and $P_s$ , which characterize the short- and long-range orders in the ferroelectric phase of SCT-0.7. Separate determination of the values and temperature dependences of $P_s$ and $P_{sh}$ (which considerably exceeds the value of $P_s$ in the ordered phase) has allowed us to reveal on a quantitative level new particular features of the formation of the induced polar phase in Sr$_{1-x}$Ca$_{x}$TiO$_{3}$.