Thermopower in the ${\mathrm{Ba}}_{1-\delta }{M}_{2+x}{\mathrm{Ru}}_{4-x}{\mathrm{O}}_{11}$ $(M=\mathrm{Co}, \mathrm{Mn}, \mathrm{Fe})$ magnetic hexagonal ruthenates

The magnetism, magnetotransport, and Seebeck coefficients $\left(S\right)$ for three ruthenates ${\mathrm{Ba}}_{1-\delta }{M}_{2+x}{\mathrm{Ru}}_{4-x}{\mathrm{O}}_{11}$ $(\delta =0.06;$ $M=\mathrm{Mn}, \mathrm{Co}; x=0.4)$ and ${\mathrm{Sr}}_{1-\delta }{M}_{2+x}{\mathrm{Ru}}_{4-x}{\mathrm{O}}_{11}$ $(\delta =0.02; M=\mathrm{Fe}; x=0.7)$ compositions have been studied. Their crystallographic structures contain three metal sites, edge-sharing octahedra forming kagome lattices, face-shared octahedra with the shortest $\mathrm{Ru}\left(M\right)\text{−}\mathrm{Ru}\left(M\right)$ distance, and ${M\mathrm{O}}_5$ trigonal bipyramids. These three compositions have been selected for their transport behavior exhibiting small resistivity values (∼mΩ 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 $35\mu \mathrm{V}{\mathrm{K}}^{\text{–}1}$. 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 $S\left(T\right)$ curves of the ${\mathrm{Ba}}_{1-\delta }{M}_{2.4}{\mathrm{Ru}}_{3.6}{\mathrm{O}}_{11}$ 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 −1% in 9 T at 5 K for $M=\mathrm{Mn}$, and −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.

Figure 1

$A{M}_{2\pm x}{\mathrm{Ru}}_{4\mp x}{\mathrm{O}}_{11}$ structure of $P{6}_3/mmc$ space group with $A$ alkaline-earth (yellow) in $2a$ sites, $2d$ trigonal bipyramid sites $M\left(3\right){\mathrm{O}}_5$ (blue), $4e$ face-shared octahedra sites $M{\left(1\right)}_2{\mathrm{O}}_9$ (green), and $6g$ edge-shared octahedra sites $M\left(2\right){\mathrm{O}}_6$ forming a kagome network as illustrated in plan [001] (right).

Figure 2

Rietveld refinement of ${\mathrm{Ba}}_{0.94}{\mathrm{Mn}}_{2.4}{\mathrm{Ru}}_{3.6}{\mathrm{O}}_{11}$ (upper panel), ${\mathrm{Sr}}_{0.98}{\mathrm{Fe}}_{2.7}{\mathrm{Ru}}_{3.3}{\mathrm{O}}_{11}$ (middle panel), and ${\mathrm{Ba}}_{0.94}{\mathrm{Co}}_{2.4}{\mathrm{Ru}}_{3.6}{\mathrm{O}}_{11}$ (bottom panel) with their respective quality factor. Red crosses are experimental data, black lines are calculated fits, and blue lines are the differences between fits and data. Note the presence of ${\mathrm{BaRuO}}_3$ (red triangles) as impurity in ${\mathrm{Ba}}_{0.94}{\mathrm{Mn}}_{2.4}{\mathrm{Ru}}_{3.6}{\mathrm{O}}_{11}$, and Fe (red triangles) in ${\mathrm{Sr}}_{0.98}{\mathrm{Fe}}_{2.7}{\mathrm{Ru}}_{3.3}{\mathrm{O}}_{11}$.

Figure 3

Crystal model and STEM ADF image of ${\mathrm{Ba}}_{0.94}{\mathrm{Mn}}_{2.4}{\mathrm{Ru}}_{3.6}{\mathrm{O}}_{11}$ (left panel) with ED pattern (left panel bottom inset), simulation (left panel upper inset), and superposition of the crystallographic structure extracted from Rietveld refinements with atom in color (gray: Ru/Mn in $4e$ and $6g$ sites, blue: Mn in $2d$ sites, and yellow Ba in $2a$ sites).

Figure 4

Mössbauer spectra of ${\mathrm{Sr}}_{0.98}{\mathrm{Fe}}_{2.7}{\mathrm{Ru}}_{3.3}{\mathrm{O}}_{11}$ at 295 K (a) and 20 K (b). The spectra were decomposed into three subspectra corresponding to the Fe1 (orange), Fe2 (pink), and Fe3 (green) sites where the iron cations are positioned.

Figure 5

Temperature-dependent DC magnetic susceptibilities $\chi \left(T\right)$ in 100 Oe for ${\mathrm{Ba}}_{0.94}{\mathrm{Co}}_{2.4}{\mathrm{Ru}}_{3.6}{\mathrm{O}}_{11}$ and ${\mathrm{Ba}}_{0.94}{\mathrm{Mn}}_{2.4}{\mathrm{Ru}}_{3.6}{\mathrm{O}}_{11}$ (a) and in 25 kOe (b) and 100 Oe for ${\mathrm{Sr}}_{0.98}{\mathrm{Fe}}_{2.7}{\mathrm{Ru}}_{3.3}{\mathrm{O}}_{11}$ (inset of b). Empty symbols correspond to the ZFC curves and the full ones to FC curves.

Figure 6

Temperature-dependent inverse DC magnetic ${\chi }^{-1}\left(T\right)$ in 100 Oe for ${\mathrm{Ba}}_{0.94}{\mathrm{Co}}_{2.4}{\mathrm{Ru}}_{3.6}{\mathrm{O}}_{11}$ and ${\mathrm{Ba}}_{0.94}{\mathrm{Mn}}_{2.4}{\mathrm{Ru}}_{3.6}{\mathrm{O}}_{11}$ (a) and in 25 kOe for ${\mathrm{Sr}}_{0.98}{\mathrm{Fe}}_{2.7}{\mathrm{Ru}}_{3.3}{\mathrm{O}}_{11}$ (b), with the Curie-Weiss fitting (parameters are given in Table 4).

Figure 7

Field-dependent magnetization at 5 K with, for Mn- (blue), Co- (red), and Fe- (green) 124 oxides, low-field magnetization (lower inset) and high-field magnetization up to 14 T (upper inset).

Figure 8

Temperature-dependent resistivity. Arrows denotes the magnetic transitions. Inset: dρ/dT curves.

Figure 9

$T^2$-dependent resistivity of ${\mathrm{Ba}}_{0.94}{\mathrm{Co}}_{2.4}{\mathrm{Ru}}_{3.6}{\mathrm{O}}_{11}$. Also shown is the linear fit (yellow) to the data in the range 50 to 90 K.

Figure 10

(a) (-MR) of Co-, Mn-, and Fe-124 oxides as a function of temperature at 9 T with MR defined as 100 × [(ρ($H$)−ρ(0))/ρ(0)], and MR as a function of magnetic field in (b).

Figure 11

Temperature-dependent Seebeck coefficient. Inset: low-temperature $S$($T$) of Co-, and Mn- 124 oxides and Ru metal, from 8 to 150 K.