Magnetic properties of paramagnetically doped crystals Fe3+, Nd3+ and Ho3+ in various compounds

In this work we calculate the energy levels, wave functions and transition probabilities for a number of compounds whose crystal field parameters have been determined. We introduce a convergence criterion in the diagonalization of the Hamilton matrices dependent upon a self consistency test on the eigenvectors. This assures us of numerically accurate wave functions.First we calculated energy level and susceptibility differences in (Nd³⁺)PbMoO₄ dependent on the multiplicative constants θ_n, used with the published A_l^m to determine the crystal field parameters B_l^m, (B_l^m = θ_nA_l^M). Calculated energy levels as a function of external magnetic field strength and orientation are compared with experimental results for three different sets of published crystal field parameters, B_l^m, for (Fe³⁺)TiO₂. The ground state energy levels, and wave functions, have been calculated for the non-Kramers Ho³⁺ ion in the crystals PbMoO₄, LaCl₃ and HoCl₃. Easily distinguishable variations in the temperature dependence of the X_zz component of the susceptibility are found as a function of the host crystal. It is pointed out that susceptibility calculations, based upon measured crystal field parameters, in conjunction with subsequent susceptibility measurements, provide a good check on the validity of the crystal field parameters.