Spin, charge, and lattice coupling in triangular and Kagomé sublattices of $\mathrm{Co}{\mathrm{O}}_4$ tetrahedra: $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_{7+\delta }$ $(\delta =0,1)$

The structural and physical properties of $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_{7+\delta }$ have been studied. The polycrystalline samples of this “114” phase of composition ${\mathrm{Yb}}_{0.95}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_{7+\delta }$ have been prepared in air. By postannealing, two samples corresponding to $\delta \sim 0$ and $\delta \sim 1$ have been obtained. The physical properties of the compound “${\mathrm{O}}_7$” $(\delta \sim 0)$ exhibit a hysteretic transition at $T_{\mathrm{S}}=160\mathrm{K}–180\mathrm{K}$ as a function of $T$ as shown by resistivity, magnetization, and thermoelectric power measurements. These measurements indicate a hole-doped electrical conduction compatible with an activated regime for the hopping of high spin ${\mathrm{Co}}^{3+}$ holes in a matrix of high spin ${\mathrm{Co}}^{2+}$. By increasing the oxygen content, i.e., the cobalt oxidation state from 2.25 for “${\mathrm{O}}_7$” to 2.75 for “${\mathrm{O}}_8$,” the signatures of this transition are suppressed. This shows that below the structural transition at $T_{\mathrm{S}}$, the release of the magnetic frustration helps the development of antiferromagnetic order. The latter in turn creates the charge localization at $T_{\mathrm{S}}$.

Figure 1

(a) Perspective view of $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_7$ [left, $\left(ab\right)$ plane] and projection along $c$ showing the top two layers of $\mathrm{Co}{\mathrm{O}}_4$ tetrahedra (right). ${\mathrm{Ba}}^{2+}$ and ${\mathrm{Yb}}^{3+}$ are represented by large and small spheres, respectively. (b) Rietveld pattern of $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_7$. The difference between experimental and calculated diffraction pattern is shown at the bottom as a solid line. The row of markers shows the position of allowed reflections for space group $P{6}_{3}mc$. (c) Cell parameters evolution vs temperature.

Figure 2

(a) $T$-dependence resistivity $\rho$ for $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_7$ $\left({\mathrm{O}}_7\right)$ and $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_8$ $\left({\mathrm{O}}_8\right)$. The arrows indicate the warming or cooling processes. Inset: enlargement of the transition observed for $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_7$. (b) $\rho \left(T^{-1}\right)$ and $\rho \left(T^{-1∕2}\right)$ for the compounds ${\mathrm{O}}_7$ (lower $x$ axis) and ${\mathrm{O}}_8$ (upper $x$ axis), respectively. Inset: measurements collected up to $800\mathrm{K}$.

Figure 3

$T$-dependent Seebeck coefficient $\left(S\right)$ of $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_7$ $\left({\mathrm{O}}_7\right)$ and $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_8$ $\left({\mathrm{O}}_8\right)$. The arrows indicate data collected on cooling or warming. A clear hysteretic transition is obtained for ${\mathrm{O}}_7$. Inset: data collected for the ${\mathrm{O}}_7$ sample upon warming up to $850\mathrm{K}$.

Figure 4

$T$-dependent magnetization curves of $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_7$ $\left({\mathrm{O}}_7\right)$ and $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_8$ $\left({\mathrm{O}}_8\right)$ registered in field cooling cooling (fcc) and field cooling warming (fcw) processes as indicated by the arrows. Inset: the curves for $\mathrm{Yb}\mathrm{Ba}\mathrm{Co}{\mathrm{O}}_7$ are enlarged for $T$ near the transition.

Figure 5

$T$-dependent reciprocal magnetic susceptibility $(\chi =M∕H)$ for the $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_7$ $\left({\mathrm{O}}_7\right)$ and $\mathrm{Yb}\mathrm{Ba}{\mathrm{Co}}_4{\mathrm{O}}_8$ $\left({\mathrm{O}}_8\right)$.

Figure 6

Drawing of the $t_{2\mathrm{g}}$ and $e_{\mathrm{g}}$ orbitals for ${\mathrm{Co}}^{2+}$ and ${\mathrm{Co}}^{3+}$ in the $\mathrm{Co}{\mathrm{O}}_4$ tetrahedral configuration. (a) Hole hopping in the $e_{\mathrm{g}}$ orbitals between high spin ${\mathrm{Co}}^{3+}$ to ${\mathrm{Co}}^{2+}$ (curved arrow). (b) Hole hopping in the $t_{2\mathrm{g}}$ orbitals between two neighboring cobalt cations, intermediate spin ${\mathrm{Co}}^{3+}$ and high spin ${\mathrm{Co}}^{2+}$. (c) If the $t_{2\mathrm{g}}$ spins of the neighboring cobalt are antiparallel, the hole hopping described in (a) requires a spin flip.