Non-adiabatic phonon renormalization in metallic versus insulating rutile oxides

We present a comparative Raman scattering study of metallic rutile oxides (RuO${}_2$ and IrO${}_2$) and insulating rutiles (TiO${}_2$ and SnO${}_2$). Temperature-dependent Raman spectra reveal that the metallic compounds exhibit pronounced phonon frequency hardening, $\omega (11\mathrm{K})-\omega (300\mathrm{K})=\mathrm{\Delta }\omega \approx 6$-$10{\mathrm{c}\mathrm{m}}^{-1}$, whereas the insulating rutiles show only modest hardening, $\mathrm{\Delta }\omega \approx 1$-$3{\mathrm{c}\mathrm{m}}^{-1}$. In contrast, the linewidth changes, $\mathrm{\Delta }\mathrm{\Gamma }\approx 1$–$7{\mathrm{c}\mathrm{m}}^{-1}$, do not display a systematic metallic-insulating classification. Fits with the conventional Klemens anharmonic decay model reproduce the overall temperature trends but yield inconsistent anharmonic parameters for the metallic compounds when benchmarked against insulating rutile analogues. A modified Klemens framework, incorporating an additional $T^2$ correction to the phonon frequency arising from the electronic contribution to the phonon self-energy, quantitatively accounts for the enhanced renormalization observed in metallic systems. These results establish finite non-adiabatic electron-phonon coupling in metallic rutiles and demonstrate that phonon renormalization can be identified even in the absence of observable Fano asymmetry in the phonon line shapes.