  DFT calculations within the generalized Bloch theorem approach show that
interfacial Dzyaloshinskii-Moriya interactions (DMI) at both interfaces of
Graphene/Co$_n$/Pt(111) multilayer heterostructures are decoupled for $n \geq
3$. Unlike the property of magnetocrystalline anisotropy for this system, DMI
is not affected by stacking defects in the Co layer. The effect of Graphene
(Gr) is to invert the chirality of the vaccum/Co interfacial DMI, overall
reducing the DMI of the heterostructure, which is nevertheless dominated by the
strong spin-orbit coupling (SOC) of Pt. A spectral analysis in the reciprocal
space shows that DMI at both the Gr/Co and Co/Pt interfaces have the same
nature, namely SOC-split hybrid bands of $d$-orbital character. This proves
that a DMI model based on a single band, such the Rashba DMI model, is
insuficient to describe the behaviour of this family of Gr-capped $3d/5d$ metal
heterostructures.
