Local structural origins of the distinct electronic properties of Nb-substituted SrTiO$_3$ and BaTi$O_3$

Near or less than 10% Nb substitution on the Ti site in perovskite SrTiO$_3$ results in metallic behavior, in contrast to what is seen in BaTiO$_3$. Given the nearly identical structure and electron counts of the two materials, the distinct ground states for low substitution have been a long-standing puzzle. Here we find from neutron studies of average and local structure, the subtle yet critical difference that we believe underpins the distinct electronic properties in these fascinating materials. While SrTi$_{0.875}$Nb_${0.125}$O$_3$ possesses a distorted non-cubic structure at 15 K, the BO$_6$ octahedra in the structure are regular. BaTi$_{0.875}$Nb$_{0.125}$O$_3$ on the other hand shows evidence for local cation off-centering whilst retaining a cubic structure.