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

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