Stabilizing the magnetic moment of single holmium atoms by symmetry


Single magnetic atoms, and assemblies of such atoms, on non-magnetic surfaces have recently attracted attention owing to their potential use in high-density magnetic data storage and as a platform for quantum computing1,2,3,4,5,6,7,8. A fundamental problem resulting from their quantum mechanical nature is that the localized magnetic moments of these atoms are easily destabilized by interactions with electrons, nuclear spins and lattice vibrations of the substrate3,4,5. Even when large magnetic fields are applied to stabilize the magnetic moment, the observed lifetimes remain rather short5,6 (less than a microsecond). Several routes for stabilizing the magnetic moment against fluctuations have been suggested, such as using thin insulating layers between the magnetic atom and the substrate to suppress the interactions with the substrate’s conduction electrons2,3,5, or coupling several magnetic moments together to reduce their quantum mechanical fluctuations7,8. Here we show that the magnetic moments of single holmium atoms on a highly conductive metallic substrate can reach lifetimes of the order of minutes. The necessary decoupling from the thermal bath of electrons, nuclear spins and lattice vibrations is achieved by a remarkable combination of several symmetries intrinsic to the system: time reversal symmetry, the internal symmetries of the total angular momentum and the point symmetry of the local environment of the magnetic atom.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Magnetic sublevels of atoms with a total angular momentum J.
Figure 2: Magnetic behaviour of Ho atoms (J = 8) adsorbed on Pt(111).
Figure 3: Lifetimes of adsorbed Ho atoms as function of external parameters.


  1. 1

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

    ADS  CAS  Article  Google Scholar 

  2. 2

    Heinrich, A. J., Gupta, J. A., Lutz, C. P. & Eigler, D. M. Single-atom spin-flip spectroscopy. Science 306, 466–469 (2004)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Hirjibehedin, C. F. et al. Large magnetic anisotropy of a single atomic spin embedded in a surface molecular network. Science 317, 1199–1203 (2007)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Balashov, T. et al. Magnetic anisotropy and magnetization dynamics of individual atoms and clusters of Fe and Co on Pt(111). Phys. Rev. Lett. 102, 257203 (2009)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Loth, S., Etzkorn, M., Lutz, C. P., Eigler, D. M. & Heinrich, A. J. Measurement of fast electron spin relaxation times with atomic resolution. Science 329, 1628–1630 (2010)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Khajetoorians, A. A. et al. Itinerant nature of atom-magnetization excitation by tunneling electrons. Phys. Rev. Lett. 106, 037205 (2011)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Loth, S., Baumann, S., Lutz, C. P., Eigler, D. M. & Heinrich, A. J. Bistability in atomic-scale antiferromagnets. Science 335, 196–199 (2012)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Khajetoorians, A. A. et al. Current-driven spin dynamics of artificially constructed quantum magnets. Science 339, 55–59 (2013)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Fransson, J. Spin inelastic electron tunneling spectroscopy on local spin adsorbed on surface. Nano Lett. 9, 2414–2417 (2009)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Schuh, T. et al. Magnetic anisotropy and magnetic excitations in supported atoms. Phys. Rev. B 84, 104401 (2011)

    ADS  Article  Google Scholar 

  11. 11

    Bleaney, B. & Stevens, K. W. H. Paramagnetic resonance. Rep. Prog. Phys. 16, 108–159 (1953)

    ADS  Article  Google Scholar 

  12. 12

    Schuh, T. et al. Magnetic excitations of rare earth atoms and clusters on metallic surfaces. Nano Lett. 12, 4805–4809 (2012)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Wybourne, B. G. Spectroscopic Properties of Rare Earths Ch. 4.4, 166 (Wiley, 1965)

    Google Scholar 

  14. 14

    Coey, J. M. D. Magnetism and Magnetic Materials 114 (Cambridge Univ. Press, 2009)

    Google Scholar 

  15. 15

    Richter, M., Oppeneer, P., Eschrig, H. & &Johansson, B. Calculated crystal-field parameters of SmCo5 . Phys. Rev. B 46, 13919–13927 (1992)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Wiesendanger, R. Spin mapping at the nanoscale and atomic scale. Rev. Mod. Phys. 81, 1495–1550 (2009)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Rusponi, S. et al. The remarkable difference between surface and step atoms in the magnetic anisotropy of two-dimensional nanostructures. Nature Mater. 2, 546–551 (2003)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Zhou, L. et al. Strength and directionality of surface Ruderman-Kittel-Kasuya-Yosida interaction mapped on the atomic scale. Nature Phys. 6, 187–191 (2010)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Zhang, L., Miyamachi, T., Tomanić, T., Dehm, R. & Wulfhekel, W. A compact sub-Kelvin ultrahigh vacuum scanning tunneling microscope with high energy resolution and high stability. Rev. Sci. Instrum. 82, 103702 (2011)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996)

    ADS  CAS  Google Scholar 

  21. 21

    Hafner, J. Ab-initio simulations of materials using VASP: density-functional theory and beyond. J. Comput. Chem. 29, 2044–2078 (2008)

    CAS  Article  Google Scholar 

  22. 22

    Lüders, M., Ernst, A., Temmerman, W. M., Szotek, Z. & Durham, P. J. Ab initio angle-resolved photoemission in multiple-scattering formulation. J. Phys. Condens. Matter 13, 8587–8606 (2001)

    ADS  Article  Google Scholar 

  23. 23

    Zeller, R. & Dederichs, P. H. Electronic structure of impurities in Cu, calculated self-consistently by Korringa-Kohn-Rostoker Green's-function method. Phys. Rev. Lett. 42, 1713–1716 (1979)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Perdew, J. P. & Zunger, A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048–5079 (1981)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Anisimov, V. I., Zaanen, J. & Andersen, O. K. Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B 44, 943–954 (1991)

    ADS  CAS  Article  Google Scholar 

Download references


We acknowledge funding by the German Science Foundation (DFG) grant number Wu 349/4-2, the DFG priority programme SPP 1538 Spin Caloric Transport and the DFG Collaborative Research Centre SFB 762 Functionality of Oxide Interfaces. The calculations were performed at the Rechenzentrum Garching of the Max Planck Society.

Author information




W.W. conceived the experiments, and T. Miyamachi, T.S., T. Märkl, A.S. and C.B. carried them out. The data were analysed by T. Miyamachi, T.S., T. Märkl, C.B., T.B. and W.W. Group theory of the crystal field was performed by T.S., T.B., C.B. and W.W. Master equations were analysed by C.K., S.A., M.M. and G.S. Ab initio calculations were performed by M.H., M.G., S.O., W.H., I.M. and A.E. The manuscript was written by T.B. and W.W. Figures were prepared by T. Miyamachi. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Wulf Wulfhekel.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-3, Supplementary Tables 1-2 and Supplementary References. (PDF 1146 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Miyamachi, T., Schuh, T., Märkl, T. et al. Stabilizing the magnetic moment of single holmium atoms by symmetry. Nature 503, 242–246 (2013).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing