Ground state of Ca-doped strontium titanate: Ferroelectricity versus polar nanoregions

The structural properties of Ca-doped SrTiO₃ (SCT) have been investigated by x-ray and neutron diffractions and first-principles calculations. The results of diffraction experiments on Sr0.96Ca0.04TiO₃ show a nonferroelectric $I4∕mcm$ phase at low temperature. Density-functional calculations on the Sr_1-xCaₓTiO₃ system, which were performed in supercells with $x=0.125$ Ca concentration, show that zone center polar soft modes and antiphase antiferrodistortive modes [which correspond to the acoustic zone-boundary modes of pure strontium titanate (STO)] are strongly coupled and confirm that polar instabilities do exist in SCT in the directions perpendicular to the c tetragonal axis and not along. Moreover, the energetic stabilization induced in the tilted phase by such distortions, as well as the associated polarization, is of the same order of magnitude as that in pure tilted tetragonal STO (if the Eᵤ ferroelectric mode would freeze). These results suggest that polar instabilities originating from the (weak) off-center displacements of Ca²⁺ ions (0.080.3em0ex) are not likely to directly polarize the host matrix by an electrostatic mechanism. Instead, we suggest the possible role of random fields in inducing the presence of disordered polar clusters, which is similar to polar nanoregions in relaxor materials.