Paramagnetic Resonance of ${\mathrm{Tb}}^{3+}$ Ions in CaW${\mathrm{O}}_4$ and Ca${\mathrm{F}}_2$

The paramagnetic resonance absorption spectra of ${\mathrm{Tb}}^{+++}$ ions in single crystals of CaW${\mathrm{O}}_4$ and Ca${\mathrm{F}}_2$ have been studied at 4.2°K over a wide range of frequencies from 4 to 50 kMc/sec. The observed spectra fit a simple spin Hamiltonian $\mathcal{H}=g_{\parallel }\beta Hcos\theta S_z+{\Delta }_x{S}_x+{\Delta }_y{S}_y+A{S}_z{I}_z$. Because the zero-field splittings in these crystals fall in the microwave region, direct measurement of the parameters in the Hamiltonian was possible and these were in excellent agreement with those obtained from the high-frequency measurements. In CaW${\mathrm{O}}_4$, the parameters are $g_{\parallel }=17.777\mathrm{}\pm 0.005$, $\Delta ={({{\Delta }_x}^2+{{\Delta }_y}^2)}^{\frac{1}{2}}=8.131\mathrm{}\pm 0.006$ kMc/sec and $A=6.284\mathrm{}\pm 0.005$ kMc/sec. In Ca${\mathrm{F}}_2$, there are two sets of spectra, one having axial symmetry about the cubic axes, and the other having axial symmetry about the body diagonals of the cube. The spectra with symmetry about the cubic axes are interpreted as resulting from ${\mathrm{Tb}}^{3+}$ ions which have a charge-compensating ${\mathrm{F}}^{-}$ ion occupying the nearest neighbor interstitial site. The spectra with symmetry about the body diagonals can arise from ${\mathrm{Tb}}^{3+}$ ions which have either (a) a charge-compensating ${\mathrm{F}}^{-}$ ion occupying the next-nearest interstitial site, or (b) a charge-compensating ${\mathrm{O}}^{--}$ ion occupying the site of one of the eight ${\mathrm{F}}^{-}$ ions surrounding the paramagnetic ion. Our measurements do not allow us to distinguish between these two possibilities. The parameters in the spin Hamiltonian are, respectively: $g_{\parallel }=17.77\mathrm{}\pm 0.02$, $\Delta =5.134\mathrm{}\pm 0.006$ kMc/sec, and $A=6.26\mathrm{}\pm 0.01$ kMc/sec; $g_{\parallel }=17.28\mathrm{}\pm 0.01$, $\Delta =31.67\mathrm{}\pm 0.02$ kMc/sec, and $A=6.10\mathrm{}\pm 0.01$ kMc/sec.