Thermopower in the quadruple perovskite ruthenates

The electrical resistivity and thermoelectric power of the paramagnetic $A\mathrm{C}{\mathrm{u}}_{3}\mathrm{R}{\mathrm{u}}_{4}{\mathrm{O}}_{12}$ quadruple perovskite ruthenates with $A=\mathrm{Na},\mathrm{Ca},\mathrm{C}{\mathrm{a}}_{0.5}\mathrm{L}{\mathrm{a}}_{0.5}$, and $\mathrm{La}$ have been measured from $T=5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ up to 900 K, with the formal Ru oxidation state changing from $3.75\phantom{\rule{0.16em}{0ex}}(A=\mathrm{L}{\mathrm{a}}^{3+})$ to $4.25\phantom{\rule{0.16em}{0ex}}(A=\mathrm{N}{\mathrm{a}}^{+})$. In this series of distorted metallic perovskites, resistivity curves present a metallic behavior, with no sign of saturation up to 900 K, typical of a bad metal. Two regimes are evidenced for the Seebeck coefficient $S$: at high $T$, a quasilinear increase of $S$ is observed up to 900 K, to a common value of $\ensuremath{\sim}29\text{--}32\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at 900 K, while for $Tl200\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, strong differences of $S$ are observed which can be directly correlated with the evolution of the paramagnetic Pauli susceptibility \ensuremath{\chi}. The comparison of these quadruple perovskites with $\mathrm{SrRu}{\mathrm{O}}_{3}$ and $\mathrm{CaRu}{\mathrm{O}}_{3}$ perovskites show that at high $T$, similar $S$ values are obtained, but the $S(T)$ dependences are completely different in the whole $T$ range. In perovskites, the constant $S$ of $\ensuremath{\sim}25\text{--}35\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{V}/\mathrm{K}$ was explained by the spin degeneracy term calculated from the generalized Heikes formula, while in the quadruple perovskites the high $T$ linear $S(T)$ is typical of Mott's formula, used for metals. The origin of the similar $S$ values measured at 900 K could thus be coincidental but remains to be understood. From the comparison of $S(T)$ at low $T$ among all these ruthenates, a clear connection between the low $T$ slope of $S$ and the magnetic behavior is evidenced, with a large slope in the case of ferromagnetic $\mathrm{SrRu}{\mathrm{O}}_{3}$, in contrast to a very small $dS/dT$ in the case of the Pauli paramagnetic $\mathrm{NaC}{\mathrm{u}}_{3}\mathrm{R}{\mathrm{u}}_{4}{\mathrm{O}}_{12}$, which possesses the smallest susceptibility.