Paramagnetic Resonance of Trivalent Manganese in Rutile (TiO2)

Abstract

An analysis has been made of the paramagnetic resonance spectrum of ${\mathrm{Mn}}^{3+}$, $3{d}^{4}$, in rutile. The spectrum at 4.2\ifmmode^\circ\else\textdegree\fi{}K can be fitted to a spin Hamiltonian with $S=2$; ${g}_{z}=1.99(\ifmmode\pm\else\textpm\fi{}0.01)$; ${g}_{\mathrm{xy}}=2.00(\ifmmode\pm\else\textpm\fi{}0.02)$; $D=\ensuremath{-}3.4$ ${\mathrm{cm}}^{\ensuremath{-}1}$(\ifmmode\pm\else\textpm\fi{}0.1); $|E|=0.116$ ${\mathrm{cm}}^{\ensuremath{-}1}$(\ifmmode\pm\else\textpm\fi{}0.001); $a=0.13$ ${\mathrm{cm}}^{\ensuremath{-}1}$(\ifmmode\pm\else\textpm\fi{}0.02); $|{A}_{x}|=84.5(\ifmmode\pm\else\textpm\fi{}2.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$; $|{A}_{z}|=52.8(\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$; $|{A}_{c}|=80.6(\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The quartic term $a$, previously observed only in the $3{d}^{5}$ group has now also been detected for $3{d}^{4}$. The value of $a$ for ${\mathrm{Mn}}^{3+}$ exceeds that for ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ systems ($3{d}^{5}$) by factors of 60 and 4, respectively. The constants $g$, $D$, and $A$ are in good agreement with theory. From the hyperfine splitting data a value of 3.2 ${\mathrm{a}.\mathrm{u}.}^{\ensuremath{-}3}$ was obtained for $〈{r}^{\ensuremath{-}3}〉$; this is about 30% below that calculated for the free ${\mathrm{Mn}}^{3+}$ ion. The $S$-electron contribution to the hfs, $\ensuremath{\kappa}$, was derived to be +0.52. ${\mathrm{Mn}}^{3+}$ has large zero-field splittings (the outer splitting is 412 kMc/sec), fairly long relaxation times, and narrow resonance lines and may be an appropriate material for masers operating at submillimeter wavelengths.