Short-range order in two-dimensional binary alloys

Abstract

Using variable-temperature scanning tunneling microscopy, the degree of short-range order of purely two- dimensional (2D) binary alloys on triangular lattices $[{\mathrm{Sn}}_{(1\ensuremath{-}x)}\ensuremath{-}{\mathrm{Si}}_{x},$ ${\mathrm{Pb}}_{(1\ensuremath{-}x)}\ensuremath{-}{\mathrm{Si}}_{x},$ and ${\mathrm{Pb}}_{(1\ensuremath{-}x)}\ensuremath{-}{\mathrm{Ge}}_{x},$ all showing the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}R30\ifmmode^\circ\else\textdegree\fi{}$ reconstruction onto Si(111) or Ge(111)] has been determined quantitatively via a statistical analysis of the atomic positions. The experimental data, also in comparison with Monte Carlo simulations, generally indicate that an effective nearest-neighbor repulsion between substitutional Si (Ge) adatoms explains with good accuracy the short-range-order features observed. This finding implies the occurrence of an ordered phase of the alloys for $x=0.33$ and, in the case of a 1:1 ratio of Sn(Pb) and Si(Ge) adatoms on the surface $(x=0.5),$ demonstrates that the investigated alloys are very good practical realizations of a frustrated antiferromagnetic 2D Ising system on a triangular lattice. The implications of the observed short-range order for the electronic properties of these alloys (as a function of $x)$ are discussed.