Paramagnetic Resonance and Relaxation of the Jahn—Teller Complex[Ti(H2O)6]3+

The measured $g$ values of the ground-state doublet of ${\mathrm{Ti}}^{3+}$ in methylammonium aluminum alum at 4.2 °K and below are shown to be incompatible with static crystal field theory. The measured spin-lattice relaxation rates in the range 1.45-2. 85 °K can be described by either a two-Orbach process or a ${\mathrm{T}}^9$ Raman process. A dynamic Jahn—Teller model due to Ham, which includes the interaction between an $E_g$ vibrational mode and the ${}_{}{}^2{}_{}{}^{}T_2^{}{}_{}{}^{}$ electronic state, gives theoretical results which agree with both the measured $g$ values and the two-Orbach relaxation process. Consequently, the agreement with the Raman process would appear to be fortuitous The measured $g$ values and the two-Orbach process are described by $g_{\parallel }=1.37\mathrm{}\pm 0.01$, $g_{\perp }=1.61\mathrm{}\pm 0.01$, and $\frac{1}{\tau }=1.88\mathrm{}{e}^{\frac{-14.52\mathrm{}}{T}}+390.81\mathrm{}{e}^{\frac{-27.41\mathrm{}}{T}}$ μ${\sec }^{-1\mathrm{}}$. The corresponding two excited doublets are at 10.5±0.5 and 19.2±2.0 ${\mathrm{cm}}^{-1\mathrm{}}$, respectively. Assuming a coupling to the $E_g$ mode only, the deduced Jahn—Teller energy is 256 ${\mathrm{cm}}^{-1\mathrm{}}$ and the effective mode frequency is 148 ${\mathrm{cm}}^{-1\mathrm{}}$. The ferroelectric transition from a structure with space group Pa3 to either space group $P{2}_1$ or $\mathrm{Pca}{2}_1$ has a negligible effect on the EPR spectra, which in spite of the transition possess symmetry ($\overline{3}$).