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We have studied the BiCu$_2$/Cu(111) surface alloy using low-temperaturescanning tunneling microscopy and spectroscopy. We observed standing wavescaused by scattering off defects and step edges. Different from previousstudies on similar Rashba-type surfaces, we identified multiple scatteringvectors that originate from various intraband as well as interband scatteringprocesses. A detailed energy-dependent analysis of the standing-wave patternsenables a quantitative determination of band dispersions, including the Rashbasplitting. The results are in good agreement with ARPES data and demonstratethe usefulness of this strategy to determine the band structure of Rashbasystems. The lack of other possible scattering channels will be discussed interms of spin conservation and hybridization effects. The results open newpossibilities to study spin-dependent scattering on complex spin-orbit coupledsurfaces.

Finding the Rashba-type spin-splitting from interband scattering in quasiparticle interference maps