  A disordered alloy Ap B1-p where both A and B represent the magnetic atoms
with respective spin SA =1/2 and SB =1 and whose magnetic interaction can be
described through Ising Hamiltonian is treated using the cluster-variational
method. In this method it is assumed that the system is built out of building
block which is embedded in an effective field. Taking building block as 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 exact manner and the rest of the interaction by an effective
variational field . The magnetization M and transition temperature Tc are then
calculated for different concentration and exchange parameters (JAA, JBB and
JAB). The magnetization M exhibits different kinds of ferrimagnetic behaviour
depending on concentration and relative strength of intra- and inter-
sub-network exchange interactions. For antiferromagnetic JAB, the sub-network
magnetization saturates and aligned antiferromagnetically at low temperature.
The existence of compensation temperature Tcm, where total magnetization
reverses its direction, depends sensitively on relative values of JAA/ JAB and
JBB/ JAB and p. For B (A)-rich alloy with small JAB, the direction of net
magnetization remains same upto Tc and a maximum of M appears at intermediate T
< Tc when JBB>> JAA (JBB<< JAA).When magnitude of JAB > JAA, JBB, Tc exhibits a
maximum with p. The transition temperature is much less than the mean-field
value for all cases. The magnetic susceptibility for diverges and is
Curie-Wiess like at T >>Tc. The meta-magnetic behaviour at high magnetic field
has been found. Some of these results are in tune with experimental observation
in amorphous rare-earth-transition metal alloys.
