Magnetic Susceptibilities of Transition Elements in Host Crystals. I.V3+in Corundum

The magnetic susceptibilities of ${\mathrm{V}}^{3+}$-doped corundum crystals have been measured along and perpendicular to the trigonal crystalline axis over the temperature range of 4-500°K. A Faraday balance and a torsional balance were used to measure the absolute and anisotropy susceptibilities, respectively. Theoretical expressions for the magnetic susceptibilities as functions of temperature are obtained by employing the crystal-field approximation in the usual manner. The data of the optical spectrum fix the cubic-field parameter and the mixing ratio of the ${}_{}{}^3{}_{}{}^{}F$ and ${}_{}{}^3{}_{}{}^{}P$ states. The observed values of the magnetic susceptibilities follow a Curie-Weiss law over the temperature range of 77-500°K. Using 1.915 for $g_{\mathrm{II}}$ from the ESR (electron spin resonance) experiment, we obtain $g_{\perp }=1.720\mathrm{}\pm 0.005$ from the ratio of the slopes of the graphs of ${\chi }_i$ versus ${(T+{\theta }_i)}^{-1\mathrm{}}$. The difference in the Van Vleck temperature-independent terms for ${\chi }_{\perp }$ and ${\chi }_{\mathrm{II}}$ which was evaluated by extrapolating the data to $T=\infty$, gives the trigonal splitting of the ground state as 1100±100 ${\mathrm{cm}}^{-1\mathrm{}}$. At temperatures below 30°K the magnetic anisotropy becomes considerably larger and deviations from the Curie-Weiss law are found for both ${\chi }_{\mathrm{II}}$ and ${\chi }_{\perp }$. The zero-field splitting of the ground ${}_{}{}^3{}_{}{}^{}A_2^{}{}_{}{}^{}$ state is determined from the temperature dependence of the magnetic anisotropy as 8.4 ${\mathrm{cm}}^{-1\mathrm{}}$. The $g$ values and the zero-field splitting provide an estimate of 95 ${\mathrm{cm}}^{-1\mathrm{}}$ for the spin-orbit coupling constant. Finally by combining the trigonal splitting of the ground state determined from this work with that of the ${}_{}{}^3{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(P\right)\mathrm{}$ state observed in the optical spectrum, an estimate of the two trigonal field parameters is obtained. Discussions of the crystal-field parameters in terms of the ligand bonding and the point-change model of the crystal are given.