  It is experimentally well established that the Cr(001)-surface exhibits a
sharp resonance around the Fermi level. However, there is no consensus about
its physical origin. It is proposed to be either due to a single particle dz2
surface state renormalised by electron-phonon coupling or the orbital Kondo
effect involving the degenerate dxz/dyz states. In this work we examine the
electron-phonon coupling of the Cr(001)-surface by means of ab-initio
calculations in the form of density functional perturbation theory. More
precisely, the electron-phonon mass-enhancement factor of the surface layer is
investigated for the 3d states. For the majority and minority spin dz2 surface
states we find values of 0.19 and 0.16. We show that these calculated
electron-phonon mass-enhancement factors are not in agreement with the
experimental data even if we use realistic values for the temperature range and
surface Debye frequency for the fit of the experimental data. More precisely,
then experimentally an electron-phonon mass-enhancement factor of 0.70~0.10 is
obtained, which is not in agreement with our calculated values of 0.19 and
0.16. Therefore, we conclude that the experimentally observed resonance at the
Cr(001)-surface is not due to polaronic effects, but due to electron-electron
correlation effects.
