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Introduction
The microscopic understanding of the emergence of the macroscopic magnetic order is one of the earliest successes of quantum mechanics. In magnetism, Hund’s coupling promotes the formation of the ions local magnetic moment, while the exchange interaction establishes how such moments align with respect to each other. The magnetic anisotropy couples the local moments with the lattice, selecting their preferential direction of alignment. These three ingredients alone give rise to a multitude of magnetic states with sharply different static and dynamical properties, going from conventional ferromagnets, to various types of antiferromagnets, to more complex magnetic textures such as vortexes and skyrmions1,2. Crucially, in conventional magnetism, the exchange interaction and the magnetic anisotropy set the relevant length scales of a system and ultimately determine the dynamical response to an external perturbation.
It has been recently reported that the chemisorption of molecules on 3 d metallic ferromagnetic layers can strongly modify the surface magnetic anisotropy and the exchange interaction, opening new routes for the manipulation of magnetic properties3, 4, 5–6. Such interfaces have been studied for years, with an almost-exclusive focus on the effects induced on the molecular layer7, 8, 9, 10, 11–12. Remarkably, at the opposite side of the interface the molecules promote specific surface orbital engineering, with their p-orbitals binding to selected d metallic orbitals. This coupling induces radical modifications of the magnetocrystalline field in close proximity to the surface13,14. It has been shown that these hybridization effects can alter key magnetic properties of the 3 d layer, resulting in the enhancement of the coercive fields for the in-plane magnetization rotation5,15, the activation of new mechanisms for the in- to out-of-plane switching13 and others12.
Significant theoretical efforts have been devoted to understanding the interfacial effects in such systems and their possible propagation inside the ferromagnetic layer. Research has proceeded mainly via density functional theory (DFT) modeling of the effects induced by the proximity of a single molecule, with extrapolation to the entire surface3,4,13, 14, 15–16. This approach has successfully confirmed the enhancement of the local magnetic anisotropy4,13,16 and the alteration of the exchange interactions16 for the surface hybridized 3 d atoms. Nevertheless, all theoretical reports have limited their...




