Model of Exchange-Inversion Magnetization

A thermodynamic theory is given of a class of magnetic crystals which transform from ferromagnetic to antiferromagnetic states as the temperature is varied. Applications are suggested to ${\mathrm{Mn}}_{2-x}{\mathrm{Cr}}_x\mathrm{Sb}$ and to crystals having the nickel arsenide type structure. It is shown that the exchange magnetoelastic energy is often important in such transformations and leads to an additional interaction energy of the form ${\left({\mathrm{S}}_A·{\mathrm{S}}_B\right)}^2$ in the effective spin Hamiltonian. It is suggested that one of the exchange constants goes linearly through zero near a critical value of some lattice coordinate characterizing the transition. There are important differences in the behavior of compact and noncompact antiferromagnetic lattices, under the assumption of nearest-neighbor interactions between sublattices. A triangular array is treated, such as might arise in crystal structures of the NiAs type.