Surface-induced disorder in body-centered-cubic alloys

Abstract

We present Monte Carlo simulations of surface-induced disordering in a model of a binary alloy on a bcc lattice which undergoes a first-order bulk transition from the ordered DO3 phase to the disordered A2 phase. The data are analyzed in terms of an effective interface Hamiltonian for a system with several order parameters in the framework of the linear renormalization approach due to Br\'ezin, Halperin, and Leibler. We show that the model provides a good description of the system in the vicinity of the interface. In particular, we recover the logarithmic divergence of the thickness of the disordered layer as the bulk transition is approached, we calculate the critical behavior of the maxima of the layer susceptibilities, and demonstrate that it is in reasonable agreement with the simulation data. Directly at the (110) surface, the theory predicts that all order parameters vanish continuously at the surface with a nonuniversal, but common critical exponent ${\ensuremath{\beta}}_{1}.$ However, we find different exponents ${\ensuremath{\beta}}_{1}$ for the order parameter $({\ensuremath{\psi}}_{2},{\ensuremath{\psi}}_{3})$ of the DO3 phase and the order parameter ${\ensuremath{\psi}}_{1}$ of the B2 phase. Using the effective interface model, we derive the finite size scaling function for the surface order parameter and show that the theory accounts well for the finite size behavior of $({\ensuremath{\psi}}_{2},{\ensuremath{\psi}}_{3}),$ but not for that of ${\ensuremath{\psi}}_{1}.$ The situation is even more complicated in the neighborhood of the (100) surface, due to the presence of an ordering field which couples to ${\ensuremath{\psi}}_{1}.$