Statistical Effects of Superexchange in Binary Mixtures with One Magnetic Component

The statistical thermodynamics of a binary solid mixture of a ferromagnetic or antiferromagnetic component $A$ and a nonmagnetic component $B$ is developed theoretically. The nearest-neighbor interaction and exchange energies and a superexchange energy between any two $A$ atoms sharing one $B$ atom as a nearest neighbor are introduced. In addition to magnetic spin ordering, long-range $A-B$ sublattice ordering of a type appropriate to a body-centered cubic lattice is considered, using the zeroth-order statistical approximation. The effects of dilution and long-range component ordering on the onset of magnetic ordering are calculated for several sets of parameter values over the whole range of mole fractions. If the super-exchange integral is large enough relative to the direct exchange integral, the curves of Curie (or Néel) temperature against mole fraction are convex upwards, and a maximum may be observed. The interaction of long-range ordering with magnetization is considered in both equilibrium (annealed) and frozen (quenched) mixtures.