Complete Theory of Paramagnetism in Transition Metal Ions IV. The d² and d⁸ Electron Configurations in Cubic (O_h and T_d), Tetragonal (D_4h), and Trigonal (D_3d) Symmetry

Abstract

On the basis of the diagonalization of the complete Coulomb repulsion, ligand field, spin‐orbit interaction, and Zeeman effect matrices, the magnetic properties were calculated for the octahedral and tetrahedral d2 and d8 electron systems. In addition, the corresponding tetragonally and trigonally distorted systems were likewise studied. Irreducible tensor operator (Racah) methods were used in both weakfield and intermediate‐field coupling, and complete agreement of the results was achieved. The magnetization was evaluated by direct numerical differentiation of the energies, followed by Boltzmann averaging, and no assumptions limiting the applicability to high temperatures and small magnetic fields were introduced. Plots are presented giving the effective magnetic moment μeff as function of the ligand field parameter 10 Dq in Oh and Td symmetry for a fixed set of values of B, C, ζ, and k. In D4h and D3d symmetry, similar plots are furnished which present μeff as function of the parameter Dt or D. Here 10Dq as well as K = Ds/Dt = Dσ/Dτ assume fixed values. The H‐dependence of μeff is found to be minor. The effect of a variation in the parameter values B, C, ζ, and k is likewise studied. The results may be employed in an accurate comparison of experimental magnetic and spectroscopic data with theory.