Crystal-field interaction in the ${\mathrm{Gd}}_x{\mathrm{Eu}}_{1-x}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ superconductors

We report here experimental data on the crystal-field interaction of gadolinium ions with their environment in ${\mathrm{Gd}}_x{\mathrm{Eu}}_{1-x}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$. The ESR spectrum and a Schottky anomaly in the specific heat of dilute samples ($x\ll 1$) indicate the existence of a crystal-field splitting of the ${}_{}{}^8{}_{}{}^{}S_{\frac{7}{2}}^{}{}_{}{}^{}$ ground state of ${\mathrm{Gd}}^{3+}$ ions of about 1.5 K. We discuss the parametrization of the measured splitting in terms of an effective Hamiltonian, and the microscopic origin of the interaction within the framework of a superposition model. Since the single-ion energies involved are of the same order of magnitude as the energies associated with the magnetic ordering of the ${\mathrm{Gd}}^{3+}$ moments in $\mathrm{Gd}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ ($T_N\cong 2.24$ K), we analyze the effects of the crystal-field interaction on the magnetic transition.