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

Abstract

A theoretical analysis is made of the I4 ground term of Nd3+ in CaWO4 to determine the spin–orbit and (S4 point-group symmetry) crystal-field parameters for this term. The analysis is carried out by diagonalyzing the Hamiltonian HE + HX in the ground term where HE is the parametrized effective spin–orbit interaction HE = Σλn(L·S)n developed by one of the authors and HX is the usual crystal-field interaction HX = ΣBkm†Ckm. Frequency and polarization measurements are taken of the absorptions to the I15/24 and I13/24 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, λn and Bkm, 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 λ1 and λ2 agree to within 2.5% of those predicted previously, and g‖ and g⊥ 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 I4 ground term of Nd3+ in Na-compensated CaWO4 we find λ1 = 294.651, λ2 = − 2.4186, λ3 = 0.04172, B20 = 548.81, B40 = − 942.41, B44 = 1004.66, B60 = − 17.12, B64 = 946.84 + i1.34 cm−1, and obtain theoretical values of g‖ = 2.029 and g⊥ = 2.587 for the ground state. Theoretical g values for all the ground term levels are also calculated, and ζ and F2 values for the 4f3, Nd3+ configuration of 876.9 and 327.4 cm−1, respectively, are obtained.