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Interatomic force laws that evade dynamic measurement

A Publisher Correction to this article was published on 09 January 2019

This article has been updated


Measurement of the force between two atoms is performed routinely with the atomic force microscope. The shape of this interatomic force law is now found to directly regulate this capability: rapidly varying interatomic force laws, which are common in nature, can corrupt their own measurement.

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Fig. 1: Frequency-modulation force spectroscopy.
Fig. 2: Inflection point test for assessing the ill-posedness of force measurements.

Change history

  • 09 January 2019

    In the version of this Comment originally published, equation (4) was incorrect; see the correction notice for details. This has now been corrected in the online versions of the Comment.


  1. Garcia, R. & Perez, R. Surf. Sci. Rep. 47, 197–301 (2002).

    Article  CAS  Google Scholar 

  2. Giessibl, F. J. Rev. Mod. Phys. 75, 949–983 (2003).

    Article  CAS  Google Scholar 

  3. Dürig, U. Appl. Phys. Lett. 76, 1203–1205 (2000).

    Article  Google Scholar 

  4. Giessibl, F. J. Appl. Phys. Lett. 78, 123–125 (2001).

    Article  CAS  Google Scholar 

  5. Sader, J. E. & Jarvis, S. P. Appl. Phys. Lett. 84, 1801–1803 (2004).

    Article  CAS  Google Scholar 

  6. Lantz, M. A. et al. Science 291, 2580–2583 (2001).

    Article  CAS  Google Scholar 

  7. Sugimoto, Y. et al. Nature 446, 64–67 (2007).

    Article  CAS  Google Scholar 

  8. Gross, L., Mohn, F., Moll, N., Liljeroth, P. & Meyer, G. Science 325, 1110–1114 (2009).

    Article  CAS  Google Scholar 

  9. Gross, L. et al. Science 324, 1428–1431 (2009).

    Article  CAS  Google Scholar 

  10. Welker, J. & Giessibl, F. J. Science 336, 444–449 (2012).

    Article  CAS  Google Scholar 

  11. Weymouth, A. J., Hofmann, T. & Giessibl, F. J. Science 343, 1120–1122 (2014).

    Article  CAS  Google Scholar 

  12. Ternes, M., Lutz, C. P., Hirjibehedin, C. F., Giessibl, F. J. & Heinrich, A. J. Science 319, 1066–1069 (2008).

    Article  CAS  Google Scholar 

  13. Kawai, S. et al. Science 351, 957–961 (2016).

    Article  CAS  Google Scholar 

  14. Albrecht, T. R., Grütter, P., Horne, D. & Rugar, D. J. Appl. Phys. 69, 668–673 (1991).

    Article  Google Scholar 

  15. Giessibl, F. J. Phys. Rev. B 56, 16010–16015 (1997).

    Article  CAS  Google Scholar 

  16. Phillips, D. L. J. ACM 9, 84–97 (1962).

    Article  Google Scholar 

  17. Tikhonov, A. N. & Arsenin, V. Y. Solutions of Ill Posed Problems (Winston, Washington, 1977).

  18. Hansen, P. C. Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (SIAM, Philadelphia, 1998).

  19. Vogel, C. R. Computational Method for Inverse Problems (SIAM, Philadelphia, 2002).

  20. Welker, J., Illek, E. & Giessibl, F. J. Beilstein J. Nanotechnol. 3, 238–248 (2012).

    Article  CAS  Google Scholar 

  21. Sader, J. E., Hughes, B. D., Huber, F. & Giessibl, F. J. Preprint at (2017).

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We acknowledge support from the Australian Research Council Centre of Excellence in Exciton Science (CE170100026), the Australian Research Council Grants Scheme and Deutsche Forschungsgemeinschaft within SFB 689, project A9, and CRC 1277, project A02. The referees are thanked for their comments.

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J.E.S. supervised the project. F.H. and F.J.G. performed initial measurements on the Cu–Cu atomic system in which an anomaly between the matrix and Sader–Jarvis methods was observed. This was communicated to J.E.S. who explored with B.D.H. various theories to explain the anomaly. J.E.S. identified ill-posedness in the inverse problem, formulated the inflection point test and performed all calculations. F.H. and F.J.G. devised and performed further measurements using the Cu–CO system to validate the inflection point test. All authors analysed the data and contributed to the writing of the paper.

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Correspondence to John E. Sader.

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Sader, J.E., Hughes, B.D., Huber, F. et al. Interatomic force laws that evade dynamic measurement. Nature Nanotech 13, 1088–1091 (2018).

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