Spin states of cobalt and the thermodynamics of Sm$_{1-x}$Ca$_x$CoO$_{3-\delta}$ solid solutions

In the rare-earth SmCoO$_3$ perovskite, Co$^{3+}$ ions at low temperatures appear to be in the low-spin state with $S = 0$, $t_{2g}^6e_g^0$. If Ca$^{2+}$ ions partially substitute Sm$^{3+}$ ions, oxygen deficient Sm$_{1-x}$Ca$_x$CoO$_{3-\delta}$ solid solutions with $\delta= x/2$ appear. The oxygen deficiency leads to the formation of pyramidally coordinated cobalt ions Co$^{3+}_{\text{pyr}}$ in addition to the existing cobalt ions Co$^{3+}_{\text{oct}}$ within the oxygen octahedra. Even at low temperatures, these ions have a magnetic state, either $S = 1$, $t_{2g}^5e_g^1$ or $S = 2$, $t_{2g}^4e_g^2$. At low temperatures, the magnetization of Sm$_{1-x}$Ca$_x$CoO$_{3-\delta}$ is mainly determined by the response of Co$^{3+}_{\text{pyr}}$ ions. Owing to the characteristic features of the crystal structure of the oxygen deficient perovskite, these ions form a set of nearly isolated dimers. At high temperatures, the magnetization of Sm$_{1-x}$Ca$_x$CoO$_{3-\delta}$ is mainly determined by the response of Co$^{3+}_{\text{oct}}$ ions, which exhibit a tendency to undergo the transition from the $S = 0$, $t_{2g}^6e_g^0$ state to the $S = 1$, $t_{2g}^5e_g^1$ or $S = 2$, $t_{2g}^4e_g^2$ state. In addition, the magnetization and specific heat of the solid solutions under study include the contribution from the rare-earth subsystem, which undergoes a magnetic ordering at low temperatures.