  X-ray absorption spectroscopy was used to determine the valence state in
La$_2$Co$_{1-x}$Mn$_{1+x}$O$_6$ ($x\approx 0.23$) thin films. We found that in
spite of the non-stoichiometry, Co is in a divalent state while Mn ions show a
mixed valence state. The relation of this finding with the magnetic properties
of the films is discussed. X-ray magnetic circular dichroism measurements prove
that magnetic anisotropy originates from Co spin-orbit coupling and it is
strain-dependent: a strong increase of the angular contribution to the magnetic
moment is found when in-plane (out-of-plane) and cell parameters get expanded
(compressed). This behavior is reproduced by first order perturbation theory
calculations.
