Energy-Level Scheme for Nd3+ in LiYF4

Crystal‐field parameters appropriate for $S_4$ symmetry were fit to existing data on the ${}^4{I}_{\text{9/2}}$ and ${}^4{I}_{\text{11/2}}$ sublevel splittings of LiYF₄:Nd³⁺. Intermediate coupling wavefunctions obtained previously from fits to the CaWO₄:Nd³⁺ spectrum were used. Although ground‐state EPR data were not available in this system, the symmetries of the levels were uniquely assignable from group‐theoretical considerations and the available polarization data. The parameter values found are (in cm⁻¹): $B_0^2\text{\hspace{0.17em}=\hspace{0.17em}482.7}$ , $B_0^4\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}1452.5}$ , $B_0^6\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}122.1}$ , $B_4^4\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}1222.0}$ , $B_4^6\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}981.9}$ , $B_4^{\text{′4}}\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}0.3}$ , and $B_4^{\text{′6}}\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}0.2}$ . The rms deviation of this fit was 10. We calculate ground‐state $\mathrm{g\parallel }$ and $\mathrm{g\perp }$ values of 0.483 and 2.571, respectively. The crystal‐field parameters found here are compared with those of CaWO₄:Nd³⁺ and those of the “mirror” ion Er³⁺ in LiYF₄:Er³⁺. We conclude that simple geometrical considerations as to the algebraic signs of the crystal‐field components in these systems may be misleading.