Magnetic properties of ${\mathrm{EuTiO}}_3$, ${\mathrm{Eu}}_2$${\mathrm{TiO}}_4$, and ${\mathrm{Eu}}_3$${\mathrm{Ti}}_2$${\mathrm{O}}_7$

We have investigated the magnetic properties of ${\mathrm{EuTiO}}_3$ ($T_N=5.3\mathrm{}\pm 0.2$ K), ${\mathrm{Eu}}_2$${\mathrm{TiO}}_4$ ($T_C=7.8\mathrm{}\pm 0.2$ K), and ${\mathrm{Eu}}_3$${\mathrm{Ti}}_2$${\mathrm{O}}_7$ ($T_C=8\mathrm{}\pm 0.3$ K) with the technique of ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$ Mössbauer spectroscopy. The magnetic exchange constants of these substances were obtained from the spectra using molecular-field theory and were interpreted in terms of $5d$ admixtures to the $4f$ wave functions of the ${\mathrm{Eu}}^{2+}$ ion. In ${\mathrm{Eu}}_3$${\mathrm{Ti}}_2$${\mathrm{O}}_7$ we have found two magnetic inequivalent sites, with different temperature dependence of the sublattice magnetization. The quadrupole moment ratio of the 21.6-keV state to the ground state of ${}_{}{}^{151}{}_{}{}^{}\mathrm{Eu}$ was measured to be 1.34 ± 0.03 using ${\mathrm{Eu}}_2$${\mathrm{TiO}}_4$, which has an axially symmetric electric field gradient ($\eta =0\mathrm{}$) at the Eu sites. A calculation of the splitting of the admixed $5d$ electronic levels and of the electric field gradient at the nucleus was performed by summing the lattice contributions with the method of chargeless cluster. The results provided an interpretation of the magnetic properties and of the nuclear quadrupole interaction in the substances studied.