The Effect of Anisotropy Direct and Indirect Interactions in some Rare Earth Elements

Abstract

In this thesis different connections between free energy of the magnetic crystal and the Hamiltonian of the rare earth is established, Anisotropy energy transform form dependence on the direction cosines to dependence on the spherical angle ( , ∅ ) to formula defines the anisotropy Constants. equation connect between anisotropy constant and anisotropy coefficient has be found . Application of these formulas to case of heavy rare earth was done . The crystal field parameters have been calculated for rare earth elements by means of point charge model. Anisotropy constant was calculated for Terbium (Tb) using the exception value of the Steven operators and values of crystal filed obtained. Anisotropy coefficients was found using the formulism connection. The result obtained has good agree with the experimental data.