Low-Temperature Magnetic Anisotropy in ${\mathrm{Al}}_2$${\mathrm{O}}_3$: ${\mathrm{V}}^{3+}$

Magnetic-anisotropy measurements on ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$: ${\mathrm{V}}^{3+}$ single crystals have been made with a sensitive torsion balance at temperatures between 1.5-5°K. A least-squares method was used to fit the theoretical expression for $\Delta \chi (\equiv {\chi }_{\perp }-{\chi }_{\parallel })$ to the data. $\Delta \chi$ was found to be much more sensitive to $g_{\perp }$ and $\delta$, the zero-field splitting, in this temperature range than at higher temperatures. This sensitivity permitted a new determination of these parameters, with the results $g_{\perp }=1.744\mathrm{}\pm 0.014$ and $\delta =7.97\mathrm{}\pm 0.10$ ${\mathrm{cm}}^{-1\mathrm{}}$. The value of $\delta =7.97\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ resulted in a new value for the spin-orbit coupling constant of $\lambda =87\mathrm{}\pm 1$ ${\mathrm{cm}}^{-1\mathrm{}}$. Finally, we obtain the temperature-independent value of ${\chi }_{\perp }$ in good agreement with the experimental results.