First-order crystal field interactions

Lam et al. (1974), Lander and Mueller (1974) and Lam and Aldred (1974) were the first to report on the properties of NpS. Their results are still valid. Comments on the unusual properties of NpS, especially the very low moments, are found in the work of Lander (1978) and Lam and Ellis (1985). The latter authors claim that hybridization and crystal-field interactions are responsible for the depression of the ordered moment. Single-crystal neutron diffraction and Mossbauer spectroscopy measurements refined the antiferromagnetic type II structure reported earlier for NpS (Blaise et al. 1992). The structure is of a multi-A type, most probably 2k. NpSe is... 

Fig. 4.13 Combined magnetic hyperfine interaction for Fe with strong electric quadrupole interaction. Top left, electric quadrupole splitting of the ground (g) and excited state (e). Top right first-order perturbation by magnetic dipole interaction arising from a weak field along the main component > 0 of the EFG fq = 0). Bottom the resultant Mossbauer spectrum is shown for a single-crystal type measurement with B fixed perpendicular to the y-rays and B oriented along...

Consider a dn configuration present in a crystal field that leaves the ground state nondegenerate except for spin. The ground state then consists of (25+ l)-spin states and the effect of the spin-orbit interaction plus the magnetic field can be computed using first- and second-order perturbation theory. If we take as the perturbation operator... 

Two ions are well-known for their highly anisotropic properties. Firstly, in the rare-earth family, Dy3+ which has a 6H15/2 ground state. The spin-orbit interaction is stronger than the crystal field effects. The ratio J /J can be of the order of 100 (Jj. = 0), gjj = 20 and gi = 0 this is practically an ideal case. Secondly, in the transition element series, the ion Co2+ is also characterized by anisotropic interactions (either in the tetrahedral or octahedral coordination), the anisotropy being however lower than in the case of Dy3+. J /J is about 0.5 for this ion. Some Fe2+ compounds also display a behavior approximating to the Ising model. 

Fig. 2 Dependence of the T2g term fine structure for the Cr ion in KMgp3. The curves are the splitting as the functions of the Ham reduction factor y calculated from the first and second order Ham theory. The open circles correspond to the energy of spinors in a static crystal field (y = 1.0), and the filled circles are observed experimental energies. The best fit is obtained for y = 0.31. AH four curves are merged into two (if y = 0 extremely strong Jahn-Teller interaction) with the separation of2 k + p)...

---