  We report on a systematic study of the structural, magnetic properties and
the anomalous Hall effect, in the Heusler alloy Co2FeAl (CFA) epitaxial films
on MgO(001), as a function of film thickness. It was found that the epitaxial
CFA films show a highly ordered B2 structure with an in-plane uniaxial magnetic
anisotropy. An analysis of the electrical transport properties reveals that the
lattice and magnon scattering contributions to the longitudinal resistivity.
Independent on the thickness of films, the anomalous Hall resistivity of CFA
films is found to be dominated by skew scattering only. Moreover, the anomalous
Hall resistivity shows weakly temperature dependent behavior, and its absolute
value increases as the thickness decreases. We attribute this temperature
insensitivity in the anomalous Hall resistivity to the weak temperature
dependent of tunneling spin-polarization in the CFA films, while the thickness
dependence behavior is likely due to the increasing significance of interface
or free surface electronic states.
