A two dimensional Heusler alloy model

A two dimensional version of a Heusler alloy X2MncZ1−c is presented. The Hamiltonian includes chemical interactions between nearest neighbors and magnetic interactions between first, second and third neighbors. The ground state phase diagrams at zero magnetic field and their range of stability with regard to the chemical and magnetic interactions are calculated by using the method of linear inequalities. The unit used in the calculation is a five point cluster, which allows describing an ordered alloy with the Mn atoms forming decorated ferromagnetic, antiferromagnetic, superantiferromagnetic and other more complex arrangements. Results for c = 1 / 2 and 3/4 are presented.