Spin state of Co$^{3+}$ ions in EuBaCo$_{2-x}$O$_{5.5-\delta}$ in the paramagnetic temperature range

The magnetic studies of EuBaCo$_{2}$O$_{5.50}$, EuBaCo$_{1.93}$O$_{5.40}$, and EuBaCo$_{1.9}$O$_{5.36}$ have been performed. Layered cobaltites EuBaCo$_{2-x}$O$_{5.5-\delta}$ demonstrated the ferrimagnetic ordering in the temperature range 200 K $<T<$ 650 K. The ferromagnetic Curie temperature $T_C$ almost did not change as the number of Co$^{3+}$–O–Co$^{3+}$ bonds decreased. The contributions of the ferro- and antiferromagnetic interactions were nearly the same and determine the relationship $T_{C}>T_{N}$ and $T_{C}<T_{N}$. At $T>T_C$, the antiferromagnetic order was retained in the EuBaCo$_{1.90}$O$_{5.36}$. As temperature increased, EuBaCo$_{2-x}$O$_{5.5-\delta}$ conserved the IS state in pyramids, and gradual LS $\to$ IS $\to$ HS transitions occurred in octahedron sites. The increase in the effective magnetic moment $\mu_{\operatorname{eff}}$ in EuBaCo$_{1.90}$O$_{5.36}$ at $T>$ 580 K demonstrated the transition of Co$^{3+}$ ions to the HS state at lower temperatures as compared to the EuBaCo$_{2}$O$_{5.5}$ stoichiometric composition, and the structural distortions and the increase in the unit cell volume favored to this transition.