Interpreting STM images of the MnCu/Cu(100) surface alloy

$c(2\ifmmode\times\else\texttimes\fi{}2)\mathrm{M}\mathrm{n}\mathrm{C}\mathrm{u}/\mathrm{C}\mathrm{u}(100)$ is an ordered two-dimensional surface alloy that exhibits a checkerboard arrangement of Mn and Cu atoms on the Cu(100) surface. Mn buckles outwards by 0.3 \AA{} with respect to Cu and in all previous scanning tunneling microscopy (STM) experiments only one chemical species was imaged which was assumed to be Mn. We analyze the STM results by first-principles calculations based on the density-functional theory and show that Cu rather than Mn is imaged, while indeed Mn is imaged as single Mn impurities at Cu(100). We explain this result in terms of the formation of Mn states bridging over the Cu atoms. These Mn states are characteristic for Mn in a $c(2\ifmmode\times\else\texttimes\fi{}2)\mathrm{MnCu}$ surface alloy. Missing Mn atoms break this bridging bond and the surrounding Cu atoms are imaged as depressions.