Prediction of the quantized axis of rare-earth ions: the electrostatic model with displaced point charges

Abstract

An electrostatic model based on the effective-point-charge approach is proposed to predict the quantized axis of rare-earth ions, even in low symmetry. The effective charges of coordination atoms create an electrostatic potential interacting with the aspherical 4f electron cloud of the rare-earth ion. The quantized axis can be determined by minimizing the electrostatic energy. The effective charge displacements must be considered according to the nature of the coordination bond, which can be calculated by the atomic orbital wavefunctions for the σ- and π-bonds, respectively. Using our model, the experimentally determined magnetic easy axis of some complexes with Tb³⁺, Dy³⁺ and Er³⁺ can be very well reproduced.