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

Abstract

The measured $g$ values of the ground-state doublet of ${\mathrm{Ti}}^{3+}$ in methylammonium aluminum alum at 4.2 \ifmmode^\circ\else\textdegree\fi{}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 \ifmmode^\circ\else\textdegree\fi{}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 ${g}_{\ensuremath{\parallel}}=1.37\ifmmode\pm\else\textpm\fi{}0.01$, ${g}_{\ensuremath{\perp}}=1.61\ifmmode\pm\else\textpm\fi{}0.01$, and $\frac{1}{\ensuremath{\tau}}=1.88{e}^{\frac{\ensuremath{-}14.52}{T}}+390.81{e}^{\frac{\ensuremath{-}27.41}{T}}$ \ensuremath{\mu}${\mathrm{sec}}^{\ensuremath{-}1}$. The corresponding two excited doublets are at 10.5\ifmmode\pm\else\textpm\fi{}0.5 and 19.2\ifmmode\pm\else\textpm\fi{}2.0 ${\mathrm{cm}}^{\ensuremath{-}1}$, respectively. Assuming a coupling to the ${E}_{g}$ mode only, the deduced Jahn---Teller energy is 256 ${\mathrm{cm}}^{\ensuremath{-}1}$ and the effective mode frequency is 148 ${\mathrm{cm}}^{\ensuremath{-}1}$. 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 ($\overline{3}$).