Spin–Orbit and Crystal‐Field Parameters for the Ground Term of Nd3+ in CaWO4

Abstract

A theoretical analysis is made of the ${}^{4}I$ ground term of Nd³⁺ in CaWO₄ to determine the spin–orbit and ($S_4$ point‐group symmetry) crystal‐field parameters for this term. The analysis is carried out by diagonalyzing the Hamiltonian ${\mathbf{H}}_E\mathrm{\hspace{0.17em}+\hspace{0.17em}}{\mathbf{H}}_X$ in the ground term where ${\mathbf{H}}_E$ is the parametrized effective spin–orbit interaction ${\mathbf{H}}_E{\mathrm{\hspace{0.17em}=\hspace{0.17em}\Sigma \lambda }}_n(\mathbf{L}·\mathbf{S}{)}^n$ developed by one of the authors and ${\mathbf{H}}_X$ is the usual crystal‐field interaction ${\mathbf{H}}_X{\mathrm{\hspace{0.17em}=\hspace{0.17em}\Sigma B}}_{\mathrm{km}}†{\mathbf{C}}_{\mathrm{km}}$ . Frequency and polarization measurements are taken of the absorptions to the ${}^4{I}_{\text{15/2}}$ and ${}^4{I}_{\text{13/2}}$ multiplets and are compared with data found in the literature in order to establish the symmetry and energy of the ground term levels. By varying the spin–orbit and crystal‐field parameters, ${\lambda }_n$ and $B_{\mathrm{km}}$ , an identification of all 26 levels for the ground term is obtained with a standard deviation between theory and experiment of 4.33 cm⁻¹. The empirical spin–orbit parameters ${\lambda }_1$ and ${\lambda }_2$ agree to within 2.5% of those predicted previously, and $g_{\Vert }$ and $g_{\perp }$ for the ground state agree to within 0.2% and 1.9% of those reported, thus further establishing the meaningfulness of the crystal‐field parameters obtained. For the ${}^{4}I$ ground term of Nd³⁺ in Na‐compensated CaWO₄ we find ${\lambda }_1{\text{\hspace{0.17em}=\hspace{0.17em}294.651, λ}}_2{\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}2.4186, λ}}_3{\text{\hspace{0.17em}=\hspace{0.17em}0.04172, B}}_{20}{\text{\hspace{0.17em}=\hspace{0.17em}548.81, B}}_{40}{\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}942.41, B}}_{44}{\text{\hspace{0.17em}=\hspace{0.17em}1004.66, B}}_{60}{\text{\hspace{0.17em}=\hspace{0.17em}−\hspace{0.17em}17.12, B}}_{64}\text{\hspace{0.17em}=\hspace{0.17em}946.84\hspace{0.17em}+\hspace{0.17em}i1.34}{\mathrm{cm}}^{\text{−1}}$ , and obtain theoretical values of $g_{\Vert }\text{\hspace{0.17em}=\hspace{0.17em}2.029}$ and $g_{\perp }\text{\hspace{0.17em}=\hspace{0.17em}2.587}$ for the ground state. Theoretical $g$ values for all the ground term levels are also calculated, and $\zeta$ and $F_2$ values for the ${\text{4f}}^3$ , Nd³⁺ configuration of 876.9 and 327.4 cm⁻¹, respectively, are obtained.