Stress Effects on the Paramagnetic Resonance of Yb3+ in ThO2 and Ho2+ in CaF2

Abstract

The change of the spin-Hamiltonian parameters $g$ and $A$ has been measured for ${\mathrm{Yb}}^{3+}$ in Th${\mathrm{O}}_2$ and $\mathrm{H}_0^{}{}_{}{}^{2+}$ in Ca${\mathrm{F}}_2$ (both in cubic sites) as a function of uniaxial stress. Because of cavity geometry, the perpendicular shifts in the $g$ values were measured for stresses along the [111] direction in the former case, and along the [001] and [111] directions in the latter. The observed values were $\Delta g_{\perp }=6.18\mathrm{}\times {10}^{-6\mathrm{}}$ ${\mathrm{kg}}^{-1\mathrm{}}$ ${\mathrm{cm}}^2$, for ${\mathrm{Yb}}^{3+}$ in Th${\mathrm{O}}_2$ stressed along [111]; $\Delta g_{\perp }=1.43\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{kg}}^{-1\mathrm{}}$ ${\mathrm{cm}}^2$ and $\Delta g_{\perp }=5.3\mathrm{}\times {10}^{-5\mathrm{}}$ ${\mathrm{kg}}^{-1\mathrm{}}$ ${\mathrm{cm}}^2$, for ${\mathrm{Ho}}^{2+}$ in Ca${\mathrm{F}}_2$, stressed along the [001] and [111] directions, respectively. The change of the hyperfine interaction was related to the change in $g$ value by the usual relation, $\Delta A=A\frac{\Delta g}{g}$. The crystalline field at the impurity site was computed, using a point-charge model as a function of external stress. No allowance was made for local distortion, as compared to bulk distortion. Using Hartree-Fock radial integrals, as computed by Freeman and Watson, a theoretical value for the $g$ shifts was obtained. The dominant contribution, in the case of ${\mathrm{Yb}}^{3+}$ in Th${\mathrm{O}}_2$ was found to come from $l=2\mathrm{}$ terms in the crystalline-field potential, and very good agreement with experiment was obtained. For $\mathrm{H}_0^{}{}_{}{}^{2+}$ in Ca${\mathrm{F}}_2$, the dominant contribution for stresses along the [001]...