Electrical Transport in the Ferromagnetic State of Manganites: Small-Polaron Metallic Conduction at Low Temperatures

We report measurements of the resistivity in the ferromagnetic state of epitaxial thin films of ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ and the low-temperature specific heat of a polycrystalline ${\mathrm{La}}_{0.8}{\mathrm{Ca}}_{0.2}{\mathrm{MnO}}_3$. The resistivity below 100 K can be well fitted by $\rho -{\rho }_0=E{\omega }_s/{sinh}^2\left(ħ{\omega }_s/{2k}_{B}T\right)$ with $ħ{\omega }_s/k_B\simeq 80\mathrm{K}$ and $E$ being a constant. Such behavior is consistent with small-polaron coherent motion which involves a relaxation due to a soft optical phonon mode that is strongly coupled to the carriers. The specific-heat data also suggest the existence of such a phonon mode. The present results thus provide evidence for small-polaron metallic conduction in the ferromagnetic state of manganites.