Description of the magnetic properties of linear polymetallic chains of antiferromagnetically coupled atoms : an analysis of the equation and the models used to describe magnetic susceptibility

Abstract

Experimental magnetic-susceptibility data presently available for a wide variety of compounds of copper(II). titanium(III), and oxovanadium(IV), which are thought to consist of infinite linear chains of coupled atoms, have been analysed with four equations obtained from the king and the Heisenberg models. The results lead to the emphatic conclusion that the anisotropic equationsfor the parallel and perpendicular components of the magnetic susceptibility which are obtained from the king model are quite inappropriate for the description of these compounds. In contrast, the equation for the parallel component may be used in isolation for the reasonable fitting of data, although this procedure cannot be theoretically justified. Two equations based on the isotropic Heisenberg model, which is universally applied to small finite systems. have been investigated. Unfortunately, these equations are empirical rather than analytical. One is based on the exact machine calculations of Banner and Fisher for rings of 10 and 11 coupled atoms, and the second equation is based on the present Monte-Carlo calculationson open chains of 100 and 101 atoms. Although these equations differ considerably at low temperatures, both offer a useful basis for fitting the available experimental data. In particular, the empirical equations are valuable comparative tests for the validity of moderately successful analytical equations and thus provide an improved basis for drawing structural conclusions from magnetic-susceptibility data.