Electronic spin susceptibility in metallic strontium titanate

Metallic strontium titanate (SrTiO$_3$) is known to have both normal-state and superconducting properties that vary strongly over a wide range of charge carrier densities. This indicates the importance of nonlinear dynamics, and has hindered the development of a clear qualitative description of the observed behaviour. A major challenge is to understand how the charge carriers themselves evolve with doping and temperature, with possible polaronic effects and evidence of an effective mass that strongly increases with temperature. Here we use $^{47,49}$Ti nuclear magnetic resonance (NMR) to perform a comprehensive study of the electronic spin susceptibility in the dilute metallic state of strontium titanate across the doping-temperature phase diagram. We find a temperature-dependent Knight shift that can be quantitatively understood within a non-degenerate Fermi gas model that fully takes into account the complex band structure of SrTiO$_3$. Our data are consistent with a temperature-independent effective mass, and we show that the behavior of the spin susceptibility is universal in a wide range of temperatures and carrier concentrations. These results provide a microscopic foundation for the understanding of the properties of the unconventional low-density metallic state in strontium titanate and related materials.