Model calculations of phase diagrams of magnetic alloys on the body-centered-cubic lattice

A comparative study of a model of binary (AB) alloys on the body-centered-cubic lattice, one species (A) being magnetic and the other (B) being nonmagnetic, is presented. Allowing for nearest-neighbor and next-nearest-neighbor interactions as well as nearest-neighbor magnetic-exchange interactions, a variety of phases occurs as is familiar from the Fe-Al phase diagram: both paramagnetic and ferromagnetic A2(α), B2(Fe-Al), and ${\mathrm{DO}}_3$(${\mathrm{Fe}}_3$Al) phases, with order-disorder phase transitions as well as transitions between different ordered phases; some of these transitions being of second order and some of first order. The statistical mechanics of the model is treated both by the molecular-field approximation, the Kikuchi cluster-variation method in the tetrahedron approximation, and the Monte Carlo method. We find that the molecular-field approximation yields a qualitatively wrong phase diagram which substantially overestimates the stability of the ordered phases, in contrast to previous work suggesting that it yields a reliable description of the Fe-Al problem. On the other hand, the cluster-variation phase diagram is in rather close agreement with the (presumably most accurate) Monte Carlo results, the transition temperatures being too high by only a few percent. It is shown that the crystallographic order induces a staggered magnetization in the ferromagnetic B2 and ${\mathrm{DO}}_3$ phases. Consequences for work on related problems and experiments are briefly discussed.