CLUSTER-VARIATIONAL TREATMENT OF DISORDERED MIXED SPIN ISING MODEL

Abstract

A disordered alloy ApB1-pwhere both A and B represent magnetic atoms with respective spins SA= 1/2 and SB= 1 and whose magnetic interaction can be described by the Ising Hamiltonian is treated using the cluster-variational method. In this method, it is assumed that the system is built out of a "building block" which is embedded in an effective field. Taking the "building block" as a 4-atom cluster, the approximate free energy of the alloy is then obtained by treating the interactions between spins within the cluster of all possible configurations in an exact manner and the rest of the interaction by an effective variational field. The magnetization M and the transition temperature Tcare then calculated for different concentration and exchange parameters (JAA, JBBand JAB). The magnetization M exhibits different kinds of ferrimagnetic behavior depending on the concentration and the relative strengths of the intra- and inter-sub-network exchange interactions. For antiferromagnetic JAB, the sub-network magnetization saturates and is aligned antiferromagnetically at low temperature. The existence of the compensation temperature, Tcm, where the total magnetization reverses its direction, and depends sensitively on the relative values of JAA/JABand JBB/JABand p. For B (A)-rich alloy with small JAB, the direction of the net magnetization remains unchanged up to Tc, and a maximum in M appears at intermediate T < Tcwhen JBB≫ JAA(JBB≪ JAA). When |JAB| > JAA, JBB, Tcexhibits a maximum with p. The transition temperature is much less than the mean-field value in all cases. The magnetic susceptibility diverges as T tends to Tcand is Curie-Wiess like at T ≫ Tc. The meta-magnetic behavior has been found at high magnetic fields. Some of these results are in tune with the experimental observations in the amorphous rare-earth transition metal alloys.