Angular Dependence of Zeeman Spectra of Gd 3 + in Ca F 2 at Cubic Sites

摘要: The optical Zeeman spectra of $^{6}P_{\frac{5}{2}}$ and $^{6}P_{\frac{7}{2}}$ multiplets ${\mathrm{Gd}}^{3+}$ in Ca${\mathrm{F}}_{2}$ at a site cubic symmetry show pronounced angular variation with rotation the sample magnetic field. This occurs even when initial final sublevels are rotationally invariant. phenomenon may be explained by considering that $^{8}S_{\frac{7}{2}}$ ground state, split only 0.149 ${\mathrm{cm}}^{\ensuremath{-}1}$ crystal field, is described fields greater than about 4 kG projection quantum number ${J}_{z}$ referred to field axis; excited states most conveniently basis along fourfold ax is. calculation dependence patterns on orientation, therefore, ${\mathrm{require}}^{\mathrm{S}}$ transformation common Cartesian reference frame. accomplished matrix ${{R}_{{{J}_{z}}^{\ensuremath{'}}{J}_{z}}}^{J}$ acting ground-state basis, or crystal-field Hamiltonian for from numbers (irreducible representations) assigned order increasing energy: $^{2}\ensuremath{\Gamma}_{6}$, $^{4}\ensuremath{\Gamma}_{8}$, $^{2}\ensuremath{\Gamma}_{7}$ $^{2}\ensuremath{\Gamma}_{7}$. measured $g$ factors 1.61\ifmmode\pm\else\textpm\fi{}0.06 1.76\ifmmode\pm\else\textpm\fi{}0.1 levels, respectively.