Spin-state ordering and intermediate states in the mixed-valence cobalt oxyborate ${\mathrm{Co}}_3{O}_2{\mathrm{BO}}_3$ with spin crossover

Spin-state ordering—a periodic pattern of ions with different spin-state configurations along a crystal lattice—is a rare phenomenon, and its possible interrelation with other electronic degrees of freedom remains little explored. Here we perform a structural investigation of the mixed-valence Co homometallic ludwigite ${\mathrm{Co}}_2^{2+}{\mathrm{Co}}^{3+}{O}_2{\mathrm{BO}}_3$. A superstructure consistent with a long-range ${\mathrm{Co}}^{3+}$ spin-state ordering is observed between $T_4=580$ K and $T_3=510$ K. Intermediate states with mesoscopic correlations are detected below $T_3$ down to $T_1=480$ K with a change of dimensionality at $T_2=495$ K. The spin-state correlations are connected to the charge sector as revealed by the abrupt changes in the electrical resistance at $T_1$ and $T_2$. The evolution of the structural parameters below $T_1$ indicate that the spin crossover is ignited by a moderate degree of thermally induced ${\mathrm{Co}}^{2+}$ and ${\mathrm{Co}}^{3+}$ charge disorder. Charge and spin-state degrees of freedom can be interrelated in mixed-valence spin-crossover materials, leading to sharp transitions involving intermediate spin-state and charge-correlated states at the mesoscale.