Magnetic, electronic, structural, and thermal properties of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Co</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>BO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> ludwigite in the paramagnetic state

The mixed-valent homometallic ludwigite $({\mathrm{Co}}_{2}^{2+}{\mathrm{Co}}^{3+}){\mathrm{O}}_{2}{\mathrm{BO}}_{3}$ is investigated above the ferrimagnetic ordering temperature ${T}_{C}=43\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ 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 $\ensuremath{\sim}475$ and $\ensuremath{\sim}495\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. 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.