Non-RPA behavior of the valence plasmon in SrTi1−xNbxO3

Doped ${\mathrm{SrTi}}_{1\ensuremath{-}x}{\mathrm{Nb}}_x{\mathrm{O}}₃$ is a dilute polaronic metal that exhibits superconductivity and a mid-infrared optical response suggesting parallels with copper oxides. A peculiar feature of ${\mathrm{SrTi}}_{1\ensuremath{-}x}{\mathrm{Nb}}_x{\mathrm{O}}₃$ is that its plasma frequency, ${\ensuremath{\omega}}_p$, is highly temperature dependent, increasing by more than a factor of 2 when the system is cooled from 300 to 100 K [F. Gervais et al., Phys. Rev. B 47, 8187 (1993); D. M. Eagles et al., Phys. Rev. B 54, 22 (1996); C. Z. Bi et al., J. Phys.: Condens. Matter 18, 2553 (2006)]. There is still no generally accepted explanation for this dramatic shift. Here, we present momentum-resolved electron energy-loss spectroscopy measurements of ${\mathrm{SrTi}}_{1\ensuremath{-}x}{\mathrm{Nb}}_x{\mathrm{O}}₃$ at nonzero momentum, $q$. We also calculate the collective excitations of ${\mathrm{SrTi}}_{1\ensuremath{-}x}{\mathrm{Nb}}_x{\mathrm{O}}₃$ using the random phase approximation (RPA), to assess whether the behavior of the collective modes conforms to established explanations. We find that the plasmon energy and linewidth are momentum independent, in contrast to RPA predictions, and that its shift with temperature takes place everywhere in the Brillouin zone, from $q=0$ to the zone boundary, $q=0.5$ reciprocal lattice units. We also find that the phonon frequencies do not shift with $q$ in the expected way, suggesting the screening properties of the material deviate significantly from RPA predictions. We conclude that a radically different starting point, perhaps based on lattice anharmonicity, may be needed to explain the collective charge excitations of ${\mathrm{SrTi}}_{1\ensuremath{-}x}{\mathrm{Nb}}_x{\mathrm{O}}₃$.