In this theoretical investigation we demonstrate that the adsorption of spatially extended two-dimensional (2D) π systems such as graphene and hexagonal boron nitride on the ferromagnetic fcc Co(111) surface leads to a specific behavior of the in-plane and interlayer Co-Co magnetic exchange interactions. More specifically, for both systems the magnetic exchange coupling within the first Co layer is enhanced, while the one between the first and the second Co layer is not modified, in contrast to the magnetic interlayer softening induced by organic molecules. Importantly, the in-plane magnetic hardening effect is mainly due to the hybridization between the p z states of the 2D π system and the d states of the Co surface.The ability to prepare high-quality two-dimensional (2D) materials on semiconductor and metal surfaces has opened the path to investigate a variety of fundamental physical properties of such systems, of which graphene [1] is the most prominent example. Among these are the study of a two-dimensional gas of massless Dirac fermions [2], the observation of the quantum Hall effect and Berry phase [3], the prediction of a quantum spin Hall effect [4], and perfect spin filters [5], but also many other interesting physical properties that are reviewed in detail in Refs. [6,7].With the prospect of future spintronics applications, of special interest are the studies of graphene on transitionmetal substrates such as Fe, Co, Ni, and Au that have been the focus of several recent experimental and theoretical investigations [8][9][10][11][12][13][14][15][16]. For instance, the weak hybridization between the graphene π orbitals and the d states of the Au atoms in the case of a graphene-Au-Ni(111) system induces an experimentally measurable Rashba effect into the graphene electronic structure [8,11]. Furthermore, the adsorption of graphene on more reactive substrates such as Co (0001), Co/Ir(111), and Fe/Ir(111) leads to a strong π -d hybridization and consequently to the creation of a new hybrid material whose properties can be considerably different than those of the separated components [9,10,14,17].In this Rapid Communication we explore how the adsorption of spatially extended two-dimensional (2D) π systems such as graphene and hexagonal boron nitride (hBN) on fcc Co(111) modifies the magnetic properties of this substrate. It is important to note that finite-size small π -conjugated systems such as molecules adsorbed on ferromagnetic surfaces can significantly change the magnetic properties of the substrate. For example, experimentally and theoretically it was shown that the deposition of phenalenyl-like molecules on a Co(111) surface reduces the interlayer magnetic exchange coupling between the first and second Co layer, known as interlayer magnetic softening [18,19]. Furthermore, theoretical simulations demonstrated that the paracyclophane molecule chemisorbed on a Fe/W(110) surface locally enhances the magnetic exchange coupling of the metal atoms below the molecule * r.friedrich@fz-juelich.de † n.atodiresei@...