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

Article metrics


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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Magnetization curves of Co pairs.
Figure 2: Distance dependence and directionality of RKKY interaction.
Figure 3: Magnetization curves of Co triplets.


  1. 1

    Ruderman, M. A. & Kittel, C. Indirect exchange coupling of nuclear magnetic moments by conduction electrons. Phys. Rev. 96, 99–102 (1954).

  2. 2

    Kasuya, T. A theory of metallic ferro- and antiferromagnetism on Zener’s model. Prog. Theor. Phys. 16, 45–57 (1956).

  3. 3

    Yosida, K. Magnetic properties of Cu–Mn alloys. Phys. Rev. 106, 893–898 (1957).

  4. 4

    Baibich, M. N. et al. Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices. Phys. Rev. Lett. 61, 2472–2475 (1988).

  5. 5

    Binasch, G., Grünberg, P., Saurenbach, F. & Zinn, W. Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange. Phys. Rev. B 39, 4828–4830 (1989).

  6. 6

    Hughes, I. D. et al. Lanthanide contraction and magnetism in the heavy rare earth elements. Nature 446, 650–653 (2007).

  7. 7

    Dietl, T., Ohno, H., Matsukura, F., Cibert, J. & Ferrand, D. Zener model description of ferromagnetism in zinc-blende magnetic semiconductors. Science 287, 1019–1022 (2000).

  8. 8

    Hewson, A. C. The Kondo Problem to Heavy Fermions (Cambridge Univ. Press, 1997).

  9. 9

    Majkrzak, C. F. et al. Observation of a magnetic antiphase domain structure with long-range order in a synthetic Gd–Y superlattice. Phys. Rev. Lett. 56, 2700–2703 (1986).

  10. 10

    Grünberg, P., Schreiber, R., Pang, Y., Brodsky, M. B. & Sowers, H. Layered magnetic structures: Evidence for antiferromagnetic coupling of Fe layers across Cr interlayers. Phys. Rev. Lett. 57, 2442–2445 (1986).

  11. 11

    Parkin, S. S. P., More, N. & Roche, K. P. Oscillations in exchange coupling and magnetoresistance in metallic superlattice structures: Co/Ru, Co/Cr, and Fe/Cr. Phys. Rev. Lett. 64, 2304–2307 (1990).

  12. 12

    Parkin, S. S. P. & Mauri, D. Spin engineering: Direct determination of the Ruderman–Kittel–Kasuya–Yosida far-field range function in ruthenium. Phys. Rev. B 44, 7131–7134 (1991).

  13. 13

    Roth, L. M., Zeiger, H. J. & Kaplan, T. A. Generalization of the Ruderman–Kittel–Kasuya–Yosida interaction for nonspherical Fermi surfaces. Phys. Rev. 149, 519–525 (1966).

  14. 14

    Bruno, P. & Chappert, C. Ruderman–Kittel theory of oscillatory interlayer exchange coupling. Phys. Rev. B 46, 261–270 (1992).

  15. 15

    Simon, E., Lazarovits, B., Szunyogh, L. & Újfalussy, B. Ab-initio investigation of RKKY interactions on metallic surfaces. Phil. Mag. 88, 2667–2672 (2008).

  16. 16

    Inosov, D. S. et al. Electronic structure and nesting-driven enhancement of the RKKY interaction at the magnetic ordering propagation vector in Gd2PdSi3 and Tb2PdSi3 . Phys. Rev. Lett. 102, 046401 (2009).

  17. 17

    Lee, H. J., Ho, W. & Persson, M. Spin splitting of s and p states in single atoms and magnetic coupling in dimers on a surface. Phys. Rev. Lett. 92, 186802 (2004).

  18. 18

    Kitchen, D., Richardella, A., Tang, J.-M., Flatté, M. E. & Yazdani, A. Atom-by-atom substitution of Mn in GaAs and visualization of their hole-mediated interactions. Nature 442, 436–439 (2006).

  19. 19

    Hirjibehedin, C. F., Lutz, C. P. & Heinrich, A. J. Spin coupling in engineered atomic structures. Science 312, 1021–1024 (2006).

  20. 20

    Wahl, P. et al. Exchange interaction between single magnetic adatoms. Phys. Rev. Lett. 98, 056601 (2007).

  21. 21

    Meier, F., Zhou, L., Wiebe, J. & Wiesendanger, R. Revealing magnetic interactions from single-atom magnetization curves. Science 320, 82–86 (2008).

  22. 22

    Papanikolaou, N., Zeller, R. & Dederichs, P. H. Conceptual improvements of the KKR method. J. Phys. Condens. Matter 14, 2799–2823 (2002).

  23. 23

    Ebert, H. & Zeller, R. The SPR-TB-KKR package, <>.

  24. 24

    Gambardella, P. et al. Giant magnetic anisotropy of single cobalt atoms and nanoparticles. Science 300, 1130–1133 (2003).

  25. 25

    Wiebe, J. et al. Unoccupied surface state on Pt(111) revealed by scanning tunneling spectroscopy. Phys. Rev. B 72, 193406 (2005).

  26. 26

    Weismann, A. et al. Seeing the Fermi surface in real space by nanoscale electron focusing. Science 323, 1190–1193 (2009).

  27. 27

    Bandyopadhyay, S., Das, B. & Miller, A. E. Supercomputing with spin-polarized single electrons in a quantum coupled architecture. Nanotechnology 5, 113–133 (1994).

  28. 28

    Wiebe, J. et al. A 300 mK ultra-high vacuum scanning tunneling microscope for spin-resolved spectroscopy at high energy resolution. Rev. Sci. Instrum. 75, 4871–4879 (2004).

  29. 29

    Bode, M. et al. Chiral magnetic order at surfaces driven by inversion asymmetry. Nature 447, 190–193 (2007).

Download references


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.

Author information

L.Z., F.M. and J.W. did the experiments and the data analysis, S.L. did the first-principles calculations, E.V. did the magnetization curve modelling and J.W. wrote the paper. All authors discussed the results and commented on the manuscript.

Correspondence to Jens Wiebe.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 677 kb)

Rights and permissions

Reprints and Permissions

About this article

Further reading