Magnetic, electronic, structural, and thermal properties of the ${\mathrm{Co}}_3{\mathrm{O}}_2{\mathrm{BO}}_3$ ludwigite in the paramagnetic state

The mixed-valent homometallic ludwigite $\left({\mathrm{Co}}_2^{2+}{\mathrm{Co}}^{3+}\right){\mathrm{O}}_2{\mathrm{BO}}_3$ is investigated above the ferrimagnetic ordering temperature $T_C=43\mathrm{K}$ through structural, thermal, magnetic, electric, and spectroscopic probes. X-ray absorption at the Co $L_{2,3}$ edges is consistent with the coexistence of ${\mathrm{Co}}^{2+}$ and ${\mathrm{Co}}^{3+}$ ions, as expected by the sample stoichiometry. Magnetic susceptibility shows a relatively large net paramagnetic moment per Co ion above room temperature, $p=4.87$, indicating that the ${\mathrm{Co}}^{3+}$ ions are not in a pure low-spin configuration at high temperatures, also showing a non-Curie-Weiss behavior below 300 K. Electrical conductivity and differential scanning calorimetry measurements on single crystals indicate two phase transitions at $\sim 475$ and $\sim 495\mathrm{K}$. X-ray powder diffraction shows substantial lattice parameter anomalies below 500 K. These results indicate phase transitions associated with changes in the Co oxidation state in each of its four crystallographic sites. Such transitions are possibly dictated by a competition between (i) an ordered ground state with all ${\mathrm{Co}}^{3+}$ ions occupying the same crystallographic site and (ii) either partially or totally charge-disordered states that are favored at high temperatures due to their higher entropy.

Figure 1

Polyhedral representation of the ludwigite structure (space group $Pbam$) projected in the $ab$ plane. The Co sites numbered from 1 to 4 are in the center of the corresponding oxygen octahedra, and the dots represent boron atoms. The unit cell is indicated by the rectangular thin black line. This structure is normally rationalized in terms of specific subunits such as the three-octahedra-wide ladders that extend along the c axis, one formed by edge-sharing octahedra 4-2-4 and the other formed by corner-sharing octahedra 3-1-3 (see Refs. [3, 6, 12, 13, 14]).

Figure 2

Inverse of the magnetic susceptibility $\chi {\left(T\right)}^{-1}$, where the blue and black curves were taken using different instruments. The red solid line is the fit to the Curie-Weiss law for data above room temperature.

Figure 3

Electrical conductivity $\sigma \left(T\right)$ of ${\mathrm{Co}}_3{\mathrm{O}}_2{\mathrm{BO}}_3$, measured along the c direction on heating and cooling. The vertical dashed lines mark the identified phase transitions.

Figure 4

(a) Heat flow as a function of temperature for a single crystal, taken on heating and cooling with a rate of 10 K/min. (b) Background-subtracted heat flow, highlighting the anomalies between 470 and 500 K, for a single crystal [using the raw data displayed in (a)] and the powder sample also employed in the x-ray diffraction experiment.

Figure 5

Raw x-ray powder diffraction profiles taken at (a) $T=300\mathrm{K}$, (b) 450 K, and (c) 600 K with $\lambda =1.7712\AA$. The vertical bars correspond to the Bragg positions of the main phase (space group $Pbam$, red) and of an impurity phase of ${\mathrm{Co}}_3{\mathrm{O}}_4$ (blue).

Figure 6

(a)–(c) $a$, $b$, and $c$ lattice parameters and (d) unit cell volume $V$ as a function of temperature. Four runs of measurements were performed, two of them on warming (first and third runs) and two on cooling (second and fourth runs). In (d), the thermal expansion coefficient ${\alpha }_V$ is indicated for temperatures below 400 and above 500 K. Dashed lines in (a) and (c) correspond to the high-temperature linear behavior extrapolated down to 300 K.

Figure 7

Expanded view of the $c$ lattice parameter in a selected temperature interval [see also Fig. 6]. Dotted lines highlight the change in behavior in the interval between $\sim 470$ and $\sim 500\mathrm{K}$.

Figure 8

(a) Co $L_{2,3}$ XAS spectra of ${\mathrm{Sr}}_2{\mathrm{CoO}}_3\mathrm{Cl}$ [21], ${\mathrm{EuCoO}}_3$ [21], ${\mathrm{Co}}_3{\mathrm{O}}_2{\mathrm{BO}}_3$, ${\mathrm{Co}}_5\mathrm{Sn}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$, and CoO [22] at room temperature. (b) Co $L_{2,3}$ XAS spectra of ${\mathrm{Co}}_3{\mathrm{O}}_2{\mathrm{BO}}_3$ (upper solid line) scaled to the ${\mathrm{Co}}^{2+}$ reference compound ${\mathrm{Co}}_5\mathrm{Sn}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$ (red dashed curve). The corresponding difference spectrum (multiplied by 1.5 for better visualization) is given in blue solid symbols and compared to the ${\mathrm{Co}}^{3+}$ LS reference spectrum of ${\mathrm{EuCoO}}_3$ (middle solid line) and the ${\mathrm{Co}}^{3+}$ HS reference spectrum ${\mathrm{Sr}}_2{\mathrm{CoO}}_3\mathrm{Cl}$ (lower solid line).