Paramagnetic Resonance of Trivalent Manganese in Rutile (TiO2)

Abstract

An analysis has been made of the paramagnetic resonance spectrum of ${\mathrm{Mn}}^{3+}$, $3d^4$, in rutile. The spectrum at 4.2°K can be fitted to a spin Hamiltonian with $S=2\mathrm{}$; $g_z=1.99(\pm 0.01)$; $g_{\mathrm{xy}}=2.00(\pm 0.02)$; $D=-3.4\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$(±0.1); $\mathrm{}\left|E\right|=0.116\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$(±0.001); $a=0.13\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$(±0.02); $\left|A_x\right|=84.5(\pm 2.0)\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$; $\left|A_z\right|=52.8(\pm 0.5)\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$; $\left|A_c\right|=80.6(\pm 1.0)\times {10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$. The quartic term $a$, previously observed only in the $3d^5$ group has now also been detected for $3d^4$. The value of $a$ for ${\mathrm{Mn}}^{3+}$ exceeds that for ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ systems ($3d^5$) 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 ${\mathrm{a}.\mathrm{u}.\mathrm{}}^{-3\mathrm{}}$ was obtained for $〈r^{-3\mathrm{}}〉$; this is about 30% below that calculated for the free ${\mathrm{Mn}}^{3+}$ ion. The $S$-electron contribution to the hfs, $\kappa$, 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.