Thermopower in the Ba1−δM2+xRu4−xO11 (M=Co, Mn, Fe) magnetic hexagonal ruthenates

Abstract

The magnetism, magnetotransport, and Seebeck coefficients $(S)$ for three ruthenates ${\mathrm{Ba}}_{1\ensuremath{-}\ensuremath{\delta}}{M}_{2+x}{\mathrm{Ru}}_{4\ensuremath{-}x}{\mathrm{O}}_{11}$ $(\ensuremath{\delta}=0.06;$ $M=\mathrm{Mn}, \mathrm{Co}; x=0.4)$ and ${\mathrm{Sr}}_{1\ensuremath{-}\ensuremath{\delta}}{M}_{2+x}{\mathrm{Ru}}_{4\ensuremath{-}x}{\mathrm{O}}_{11}$ $(\ensuremath{\delta}=0.02; M=\mathrm{Fe}; x=0.7)$ compositions have been studied. Their crystallographic structures contain three metal sites, edge-sharing octahedra forming kagome lattices, face-shared octahedra with the shortest $\mathrm{Ru}(M)\text{\ensuremath{-}}\mathrm{Ru}(M)$ distance, and ${M\mathrm{O}}_{5}$ trigonal bipyramids. These three compositions have been selected for their transport behavior exhibiting small resistivity values (\ensuremath{\sim}m\ensuremath{\Omega} cm) together with a complex ferrimagnetic behavior, with localization increasing from $M=\mathrm{Co}$ to $M=\mathrm{Fe}$. This enabled the thermopower to be measured in hexagonal ruthenates in which the conducting kagome layers are more or less diluted by three different magnetic cations substituted for Ru. The positive Seebeck coefficient of the three compounds is found to increase up to 750 K to values in the range of 22 to $35\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{4pt}{0ex}}{\mathrm{K}}^{\text{--}1}$. Such values, similar to those of perovskite ruthenates, reveal a Seebeck coefficient dominated by the Ru network at high temperature whatever the foreign magnetic cation is. In addition, below about 50 K, the values of $S$ are very small for $M=\mathrm{Mn}$ and Co, and the $S(T)$ curves of the ${\mathrm{Ba}}_{1\ensuremath{-}\ensuremath{\delta}}{M}_{2.4}{\mathrm{Ru}}_{3.6}{\mathrm{O}}_{11}$ compounds exhibit similarities with that of ruthenium metal. This is interpreted by shorter Ru-Ru distances as compared with perovskite ruthenates allowing a metallic direct exchange. The ferrimagnetism associated with the $M$ cation does not seem to play a major role in transport, as there is almost no impact of the magnetic ordering on thermopower and electrical resistivity and the values of magnetoresistance remain very small, reaching at most \ensuremath{-}1% in 9 T at 5 K for $M=\mathrm{Mn}$, and \ensuremath{-}0.4% at ${T}_{\mathrm{C}}$ for $M=\mathrm{Co}$. The present results obtained in these phases containing hexagonal Ru networks show that Hund's metal model developed to describe the thermopower of perovskite ruthenates with a Ru square lattice can have a broader range of validity.