Nature of interfacial Dzyaloshinskii-Moriya interactions in graphene/Co/Pt(111) multilayer heterostructures

Density-functional theory calculations utilizing the generalized Bloch theorem show that interfacial Dzyaloshinskii-Moriya interactions (DMI) at both interfaces of graphene/${\mathrm{Co}}_n$/Pt(111) multilayer heterostructures are decoupled for $n\ensuremath{\ge}3$. Unlike the property of magnetocrystalline anisotropy, DMI in this system is not strongly 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 reciprocal space shows that DMI at both the Gr/Co and Co/Pt interfaces have similar contributions from the strongly hybridized SOC-split $d$ bands. Our analysis proves that the DMI in this family of Gr-capped $3d/5d$ metal heterostructures displays richer physics than what is expected from the prediction of single-band models, such as the Rashba DMI model.