Theory of surface effects in binary alloys. IV. Ordering alloys with two ferromagnetic components

A theory of the surface concentration, spatial long-range order and magnetism for binary body-centered-cubic ordering alloys with ferromagnetic components is presented. It is a mean-field theory based on a model consisting of pairwise interactions between nearest neighbors only. We find that for an alloy $A_x{B}_{1-x}$ with spains $S_A$, $S_B$ and Ising exchange integrals $J_{\mathrm{AA}}$, $J_{\mathrm{AB}}$, and $J_{\mathrm{BB}}$, magnetism favors surface segregation of the $I$ component if $S_I^2{J}_{\mathrm{II}}<S_{I^{\prime }}^2{J}_{I^{\prime }{I}^{\prime }} (I,I^{\prime }=A,B)$. Results for the surface concentration and the long-range order parameters at $T=0\mathrm{}$ are presented. At finite temperatures, alloys with several bulk behaviors are studied, i.e., (i) $T_0$ (spatial order-disorder critical temperature) $<T_M$ (Curie temperature), (ii) $T_0>T_M$, and (iii) $J_{\mathrm{AB}}\ll J_{\mathrm{AA}},J_{\mathrm{BB}}$. It is found that in case (iii) there is a range of temperatures where the surface is magnetic whereas the bulk is paramagnetic. Also studied is the effect on the surface properties produced by allowing the chemical and magnetic interactions to be location dependent. It is found in general that the results are more sensitive to changes in the chemical interactions. The FeCo system is examined along these lines, and the results are compared with existing experimental data.