“…So, we suggest that the Ti 3+ off-center displacement from Sr 2+ site is not along one of C 2 axes, but along one of C 4 axes, thus, the symmetry and symmetry axes for the low-symmetry Ti 3+ centers in both phases of SrTiO 3 are consistent with those in the experiments. This displacement direction is the same as that of Mn 2+ ion in similar perovskite crystal KTaO 3 (where because of its smaller radius, Mn 2+ ion does not occupy the ideal K + site, but is shifted by about 0.9 Å along one of six [ first-principles study [3], the density functional theory in generalized gradient approximation (GGA) [4] and the dipole moment study [5]) and can be regarded as possible. In order to confirm this suggestion and to explain reasonably the anisotropic g factors and hyperfine structure constants A for the two Ti 3+ centers in both phases of SrTiO 3 crystals (note: these EPR parameters have not been explained reasonably until now), in this paper, we calculate these EPR parameters form the high-order perturbation formulas of EPR parameters for 3d 1 ions in tetragonal and rhombic symmetries.…”