Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Formation of a topological non-Fermi liquid in MnSi


Fermi liquid theory provides a remarkably powerful framework for the description of the conduction electrons in metals and their ordering phenomena, such as superconductivity, ferromagnetism, and spin- and charge-density-wave order. A different class of ordering phenomena of great interest concerns spin configurations that are topologically protected, that is, their topology can be destroyed only by forcing the average magnetization locally to zero1. Examples of such configurations are hedgehogs (points at which all spins are either pointing inwards or outwards) and vortices. A central question concerns the nature of the metallic state in the presence of such topologically distinct spin textures. Here we report a high-pressure study of the metallic state at the border of the skyrmion lattice in MnSi, which represents a new form of magnetic order composed of topologically non-trivial vortices2. When long-range magnetic order is suppressed under pressure, the key characteristic of the skyrmion lattice—that is, the topological Hall signal due to the emergent magnetic flux associated with the topological winding—is unaffected in sign or magnitude and becomes an important characteristic of the metallic state. The regime of the topological Hall signal in temperature, pressure and magnetic field coincides thereby with the exceptionally extended regime of a pronounced non-Fermi-liquid resistivity3,30. The observation of this topological Hall signal in the regime of the NFL resistivity suggests empirically that spin correlations with non-trivial topological character may drive a breakdown of Fermi liquid theory in pure metals.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Temperature and field dependence of the resistivity, ρxx , and Hall resistivity, ρxy , of MnSi over a wide range.
Figure 2: Hall resistivity, ρxy , and magnetoresistance, ρxx , for low fields at various pressures.
Figure 3: Phase diagrams of MnSi.


  1. Chaikin, P. & Lubensky, T. Principles of Condensed Matter Physics Chs 9, 10 (Cambridge Univ. Press, 1995)

    Book  Google Scholar 

  2. Mühlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009)

    ADS  Article  Google Scholar 

  3. Pfleiderer, C., Julian, S. R. & Lonzarich, G. G. Non-Fermi liquid nature of the normal state of itinerant-electron ferromagnets. Nature 414, 427–430 (2001)

    CAS  ADS  Article  Google Scholar 

  4. Janoschek, M. et al. Fluctuation-induced first-order phase transition in Dzyaloshinskii-Moriya helimagnets. Phys. Rev. B (in the press); preprint available at (2012)

  5. Landau, L. D. & Lifshitz, E. M. Course of Theoretical Physics Vol. 8, Sec. 52 (Pergamon, 1980)

    Google Scholar 

  6. Yu, X. Z. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010)

    CAS  ADS  Article  Google Scholar 

  7. Yu, X. Z. et al. Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. Nature Mater. 10, 106–109 (2011)

    CAS  ADS  Article  Google Scholar 

  8. Münzer, W. et al. Skyrmion lattice in the doped semiconductor Fe1–x Co x Si. Phys. Rev. B 81, 041203 (2010)

    ADS  Article  Google Scholar 

  9. Seki, S., Yu, X., Ishiwata, S. & Tokura, Y. Observation of skyrmions in a multiferroic material. Science 336, 198–201 (2012)

    CAS  ADS  Article  Google Scholar 

  10. Adams, T. et al. Long-wavelength helimagnetic order and skyrmion lattice phase in Cu2OSeO3 . Phys. Rev. Lett. 108, 237204 (2012)

    CAS  ADS  Article  Google Scholar 

  11. Pfleiderer, C. et al. Partial order in the non-Fermi liquid phase of MnSi. Nature 427, 227–231 (2004)

    CAS  ADS  Article  Google Scholar 

  12. Pfleiderer, C., Böni, P., Keller, T., Rößler, U. K. & Rosch, A. Non-Fermi liquid metal without quantum criticality. Science 316, 1871–1874 (2007)

    CAS  ADS  Article  Google Scholar 

  13. Uemura, Y. J. et al. Phase separation and suppression of critical dynamics at quantum transitions of itinerant magnets: MnSi and (Sr1–x Ca x )RuO3 . Nature Phys. 3, 29–35 (2007)

    CAS  ADS  Article  Google Scholar 

  14. Lonzarich, G. G. & Taillefer, L. Effect of spin fluctuations on the magnetic equation of state of ferromagnetic or nearly ferromagnetic metals. J. Phys. C 18, 4339–4371 (1985)

    CAS  ADS  Article  Google Scholar 

  15. Tewari, S., Belitz, D. & Kirkpatrick, T. R. Blue quantum fog: chiral condensation in quantum helimagnets. Phys. Rev. Lett. 96, 047207 (2006)

    ADS  Article  Google Scholar 

  16. Binz, B., Vishwanath, A. & Aji, V. Theory of the helical spin crystal: a candidate for the partially ordered state of MnSi. Phys. Rev. Lett. 96, 207202 (2006)

    CAS  ADS  Article  Google Scholar 

  17. Rößler, U. K., Bogdanov, A. N. & Pfleiderer, C. Spontaneous skyrmion ground states in magnetic metals. Nature 442, 797–801 (2006)

    ADS  Article  Google Scholar 

  18. Kirkpatrick, T. R. & Belitz, D. Columnar fluctuations as a source of non-Fermi-liquid behavior in weak metallic magnets. Phys. Rev. Lett. 104, 256404 (2010)

    CAS  ADS  Article  Google Scholar 

  19. Ritz, R. et al. Giant generic topological Hall resistivity in MnSi under pressure. Phys. Rev. B (submitted)

  20. Lee, M., Onose, Y., Tokura, Y. & Ong, N. P. Hidden constant in the anomalous hall effect of high-purity magnet MnSi. Phys. Rev. B 75, 172403 (2007)

    ADS  Article  Google Scholar 

  21. Neubauer, A. et al. Topological Hall effect in the A phase of MnSi. Phys. Rev. Lett. 102, 186602 (2009)

    CAS  ADS  Article  Google Scholar 

  22. Lee, M., Kang, W., Onose, Y., Tokura, Y. & Ong, N. Unusual Hall effect anomaly in MnSi under pressure. Phys. Rev. Lett. 102, 186601 (2009)

    ADS  Article  Google Scholar 

  23. Thessieu, C., Pfleiderer, C., Stepanov, A. N. & Flouquet, J. Field dependence of the magnetic quantum phase transition in MnSi. J. Phys. Condens. Matter 9, 6677–6687 (1997)

    CAS  ADS  Article  Google Scholar 

  24. Pfleiderer, C., Reznik, D. & Pintschovius, L. &. Haug, J. Magnetic field and pressure dependence of small angle neutron scattering in MnSi. Phys. Rev. Lett. 99, 156406 (2007)

    CAS  ADS  Article  Google Scholar 

  25. Belitz, D. & Kirkpatrick, T. R. Fluctuation-driven quantum phase transitions in clean itinerant ferromagnets. Phys. Rev. Lett. 89, 247202 (2002)

    CAS  ADS  Article  Google Scholar 

  26. Conduit, G. J., Green, A. G. & Simons, B. D. Inhomogeneous phase formation on the border of itinerant ferromagnetism. Phys. Rev. Lett. 103, 207201 (2009)

    CAS  ADS  Article  Google Scholar 

  27. Smith, R. P. et al. Marginal breakdown of the Fermi-liquid state on the border of metallic ferromagnetism. Nature 455, 1220–1223 (2008)

    CAS  ADS  Article  Google Scholar 

  28. Neubauer, A. et al. Ultra-high vacuum compatible image furnace. Rev. Sci. Instrum. 82, 013902 (2011)

    CAS  ADS  Article  Google Scholar 

  29. Pfleiderer, C., McMullan, G. J., Julian, S. R. & Lonzarich, G. G. Magnetic quantum phase transition in MnSi under hydrostatic pressure. Phys. Rev. B 55, 8330–8338 (1997)

    CAS  ADS  Article  Google Scholar 

  30. Doiron-Leyraud, N. et al. Fermi-liquid breakdown in the paramagnetic phase of a pure metal. Nature 425, 595–599 (2003)

    CAS  ADS  Article  Google Scholar 

Download references


We wish to thank P. Böni, K. Everschor, M. Garst, M. Janoschek, S. Mayr and A. Rosch for discussions and support. R.R., M.H., A.B., M.W. and C.F. acknowledge financial support through the TUM Graduate School. Financial support through DFG TRR80 and DFG FOR960 as well as ERC-AdG (291079 TOPFIT) are gratefully acknowledged.

Author information

Authors and Affiliations



R.R. and C.P. developed the experimental set-up; R.R. performed the transport measurements; M.H. and M.W. performed magnetization measurements; C.F. wrote the software for analysing the data; A.B. grew the single-crystal samples and characterized them; R.R. and C.P. analysed the experimental data; C.P. supervised the experimental work; C.P. proposed this study and wrote the manuscript; all authors discussed the data and commented on the manuscript.

Corresponding authors

Correspondence to R. Ritz or C. Pfleiderer.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, which gives details of the experimental methods and includes additional data in support of the results. Also included are Supplementary Figures 1-3, Supplementary Table 1 and additional references. (PDF 461 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ritz, R., Halder, M., Wagner, M. et al. Formation of a topological non-Fermi liquid in MnSi. Nature 497, 231–234 (2013).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

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.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing