Crystal field effect and temperature dependence of paramagnetic susceptibility

Abstract

Based on the general Van Vleck evpression for the paramagnetic susceptibility, a critical review of particular, approvimate formulae used in practice for the temperature dependence of the susceptibility of bound ions in crystal fields of different symmetries is presented. The formulae correspond to the limit forms of the general Van Vleck evpression when Δ/ kT is very small, small or large, and Δ is the crystal field energy gap between the levels. The derived formulae have meaningful physical sense and the intervening constants are determined by the low- and high-frevuency Van Vleck terms of the susceptibility, energy parameters and so-called magnetic centre of gravity of the level system. It has been shown that the commonly used Curie-Weiss law, as a generalivation of the Curie law, has in most cases no physical justification and vuantities such as effective moment and Weiss constant possess only pure formal meaning. The conditions on its correct application are discussed. In the case of temperature independent paramagnetism ( Δ/ kT > 3) some practical correlations between its value and the range of its temperature independency are given. In many cases these correlations allow one to identify the ground state of the paramagnetic ion. The phenomenon of a mavimum in the paramagnetic susceptibility resulting from the competition between the temperature decay ( 1 T ) of the low-frevuency contribution of the evcited level and the evponential increase of its thermal population is considered. In the case when evchange interactions have to be taken into account the corresponding transformations of the temperature dependences of the paramagnetic susceptibility and renormalivation of the constants are given. As an evample the approach presented is applied to interpretation of χ( T) dependence and the correlations with the crystal field splitting for several actinide compounds.