Ruderman–Kittel–Kasuya–Yosida interaction1,2,3 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 devices4,5, drives ferromagnetism in heavy rare-earth elements6 as well as in diluted magnetic semiconductors7 and gives rise to complex magnetic phases such as spin glasses8. 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.
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We acknowledge financial support from SFB 668, GrK 1286 and SPP1153 of the DFG, from the ERC Advanced Grant ‘FURORE’, from the Cluster of Excellence ‘Nanospintronics’ and from the ESF EUROCORES Programme SONS under contract N. ERAS-CT-2003-980409. F.M. acknowledges financial support from the German Academic Exchange Service. We thank A. Lichtenstein, S. Schuwalow, S. Kettemann and K. Patton for discussions.
The authors declare no competing financial interests.
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Journal of Physics: Condensed Matter (2019)
Reviews of Modern Physics (2019)
Physical Review B (2019)
Frontiers in Physics (2019)
Physical Review B (2019)