  A combination of theoretical modelling and experiments reveals the origin of
the large perpendicular magnetic anisotropy (PMA) that appears in
nanometer-thick epitaxial Co films intercalated between graphene (Gr) and a
heavy metal (HM) substrate, as a function of the Co thickness. High quality
epitaxial Gr/Co\n/HM(111) (HM=Pt,Ir) heterostructures are grown by
intercalation below graphene, which acts as a surfactant that kinetically
stabilizes the pseudomorphic growth of highly perfect Co face-centered
tetragonal ($fct$) films, with a reduced number of stacking faults as the only
structural defect observable by high resolution scanning transmission electron
microscopy (HR-STEM). Magneto-optic Kerr effect (MOKE) measurements show that
such heterostructures present PMA up to large Co critical thicknesses of about
4~nm (20~ML) and 2~nm (10~ML) for Pt and Ir substrates, respectively, while
X-ray magnetic circular dichroism (XMCD) measurements show an inverse power law
of the anistropy of the orbital moment with Co thickness, reflecting its
interfacial nature, that changes sign at about the same critical values. First
principles calculations show that, regardless of the presence of graphene,
ideal Co $fct$ films on HM buffers do not sustain PMAs beyond around 6~MLs due
to the in-plane contribution of the inner bulk-like Co layers. The large
experimental critical thicknesses sustaining PMA can only be retrieved by the
inclusion of structural defects that promote a local $hcp$ stacking such as
twin boundaries or stacking faults. Remarkably, a layer resolved analysis of
the orbital momentum anisotropy reproduces its interfacial nature, and reveals
that the Gr/Co interface contribution is comparable to that of the Co/Pt(Ir).
