The Effect of Cubic Crystal Fields on Charge, Spin and Current Densities in Rare Earth Elements

Abstract

In this thesis the Steven’s operator equivalent method together with the methods of Racah algebra were used to obtain expressions for the atomic charge and spin den- sities for many electron configuration lN . In addition, the methods of Racah algebra were used separately to derive formulas for the orbital and spin current densities for the same configuration. Application of these formulas to the case of 4f-electronic configuration of the rare earth element group were made in both cases of free ion and crystal field hosted one. Charge and spin densities of free ions were found to obey the classical apsherical picture whereas for ions located in cubic crystal field clusters we found the spatial distributions to reflect the type of symmetry involved. The magnetocrystalline anisotropy energy was calculated making use of the charge density derived for some holmium and erbium compounds with cubic CsCl structure for which an octahedral crystal field potential is supposed. However the model calcu- lations fairly agreed with experimental results of past studies as far as hard and easy directions of magnetization are concerned. Orbital and spin contributions to the magnetic neutron scattering form factor were determined for praseodymium and holmium in a hypothetical octahedral crystal field potential. Except for states that transform according to the representation Γ4 or the group Oh , expansion terms of both contributions were found to vanish.