Strength and directionality of surface Ruderman-Kittel-Kasuya-Yosida interaction mapped on the atomic scale

Ruderman-Kittel-Kasuya-Yosida interaction is an indirect magnetic coupling between localized spins in a non-magnetic host mediated by conduction electrons. In diluted systems it is often the dominating magnetic interaction and has played a key part in the development of giant magnetoresistance devices, drives ferromagnetism in heavy rare-earth elements as well as in diluted magnetic semiconductors and gives rise to complex magnetic phases such as spin glasses. For bulk systems, an isotropic and continuous model of Ruderman-Kittel-Kasuya-Yosida interaction is often sufficient. However, it can be misleading in magnetic nanostructures consisting of separate magnetic atoms adsorbed on the surface of a non-magnetic material. Here, an atomically precise map of the magnetic coupling between individual adatoms in pairs is measured and directly compared with first-principles calculations, proving that Ruderman-Kittel-Kasuya-Yosida interaction is strongly directional. By investigating adatom triplets of different shapes we demonstrate that the map can serve to tailor the magnetism of larger nanostructures.