Phase transitions in frustrated slightly nonstoichiometric ErBaCo$_4$O$_{7+x}$ ($x\approx0$, $0.03$) cobaltites

The results of the first experimental studies on the structural (lattice parameters) and elastic characteristics of ErBaCo$_4$O$_{7+x}$ cobaltites in the range of structural and magnetic phase transitions are presented. The samples obtained using different thermal treatments and characterized by a small oxygen excess $x$ are studied. It is found that the parameter $\Delta a/a$ for the stoichiometric ErBaCo$_4$O$_7$ sample annealed in vacuum exhibits no anomalies in the course of a structural transition, whereas the parameters $b$ and $c$ undergo stepwise changes of opposite signs. The different values of these changes $\Delta b/b\approx 4\times10^{-3}$ and $\Delta c/c\approx-5\times10^{-3}$ result in the stepwise volume change $\Delta V/V\approx -10^{-3}$. A slight deviation from the oxygen stoichiometry affects the character of the structural distortion; namely, the magnitude of the anisotropic strain and the sign of the isotropic strain change. The structural distortion in the stoichiometric sample is accompanied by a sharp stepwise change in the Young's modulus $\Delta E(T)/E_0\sim 8\times10^{-2}$, whereas the magnitude of elastic anomalies near $T_{\mathrm{S}}$ in slightly nonstoichiometric samples with $x \sim 0.03$ decreases by an order of magnitude. Comparison of elastic anomalies manifesting themselves near the magnetic phase transition temperature $T_{\mathrm{N}}$ for distorted samples with different deviations from stoichiometry suggests that the arising long-range magnetic order in the cobalt subsystem is apparently affected not only by structural distortions but also by disorder introduced by nonstoichiometric oxygen.