Tuning charge-transport properties and magnetic order in metallic EuTiO$_{3-\delta}$
The stoichiometric antiferromagnetic insulator EuTiO$_3$ is proximate to a ferroelectric phase. Whereas cation substitution has been used as a tuning parameter to introduce charge carriers and manipulate the magnetism, the effects of oxygen-vacancy doping have been less explored. Here we report a detailed study of the charge transport and magnetic properties of metallic, oxygen-vacancy-doped EuTiO$_{3-\delta}$. Using CaH$_2$ as an oxygen getter to achieve a higher carrier concentration than previously reported, we find that the phase diagram of the oxygen-vacancy-doped system is distinct from that obtained via cation doping. In particular, we uncover a change from antiferromagnetic to ferromagnetic order in the metallic state, with a maximum Curie temperature of TC $\approx$ 11 K at the highest carrier concentration of n $\approx$ 10$^{21}$ cm$^{-3}$. These findings are supported by density functional theory calculations, which indicate a significant change in the nearest-neighbor magnetic exchange constant with increasing electron doping. We also present x-ray diffuse scattering and complementary first-principles results that reveal that, similar to the prominent incipient ferroelectric perovskite SrTiO$_3$, the data for EuTiO$_3$ are consistent with thermal diffuse scattering and with the absence of quasi-elastic contributions. Finally, we report specific heat measurements that confirm the magnetic transition temperatures deduced from magnetization measurements and corroborate the lattice dynamics picture inferred from the diffuse scattering data.