Skip to main content

Thank you for visiting nature.com. 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.

  • Letter
  • Published:

Measuring the Dzyaloshinskii–Moriya interaction in a weak ferromagnet

Abstract

Magnetism—the spontaneous alignment of atomic moments in a material—is driven by quantum mechanical exchange interactions that operate over interatomic distances. Some magnetic interactions cause1,2, or are caused by3,4, a twisting of arrangements of atoms. This can lead to the magnetoelectric effect, predicted to play a prominent role in future technology, and to the phenomenon of weak ferromagnetism, governed by the so-called Dzyaloshinskii–Moriya interaction5,6,7,8. Here we determine the sign of the latter interaction in iron borate (FeBO3) by using synchrotron radiation. We present a novel experimental technique based on the interference between two X-ray scattering processes, where one acts as a reference wave. Our experimental results are validated by state-of-the-art ab initio calculations. Together, our experimental and theoretical approaches are expected to open up new possibilities for exploring, modelling and exploiting novel magnetic and magnetoelectric materials.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Atomic and magnetic order in FeBO3.
Figure 2: A schematic view of the experiment carried out on FeBO3.
Figure 3: The major experimental results and simulations for FeBO3.

Similar content being viewed by others

References

  1. Eerenstein, W., Mathur, N. D. & Scott, J. F. Multiferroic and magnetoelectric materials. Nature 442, 759–765 (2006).

    Article  ADS  Google Scholar 

  2. Cheong, S-W. & Mostovoy, M. Multiferroics: A magnetic twist for ferroelectricity. Nature Mater. 6, 13–20 (2007).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Dzialoshinskii, I. E. Thermodynamic theory of ‘weak’ ferromagnetism in antiferromagnetic substances. Sov. Phys. JETP 5, 1259–1262 (1957).

    MATH  Google Scholar 

  6. Dzyaloshinsky, I. A thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958).

    Article  ADS  Google Scholar 

  7. Moriya, T. New mechanism of anisotropic superexchange interaction. Phys. Rev. Lett. 4, 228–230 (1960).

    Article  ADS  Google Scholar 

  8. Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98 (1960).

    Article  ADS  Google Scholar 

  9. Kitzerow, H-S. & Bahr, C. (eds) Chirality in Liquid Crystals (Springer, 2001).

    Book  Google Scholar 

  10. Blundell, S. Magnetism in Condensed Matter (Oxford Univ. Press, 2001).

    Google Scholar 

  11. White, R. M. Quantum Theory of Magnetism (Springer, 2007).

    Book  Google Scholar 

  12. Matarrese, L. W. & Stout, J. W. Magnetic anisotropy of NiF2 . Phys. Rev. 94, 1792–1793 (1954).

    Article  ADS  Google Scholar 

  13. Maleyev, S. V. Spin chirality and polarized neutrons. Physica B 350, 26–32 (2004).

    Article  ADS  Google Scholar 

  14. Okorokov, A. I. et al. The spin chirality in MnSi single crystal probed by small angle scattering with polarized neutrons. Physica B 350, e323–e326 (2004).

    Article  Google Scholar 

  15. Johnson, R. D. et al. X-ray imaging and multiferroic coupling of cycloidal magnetic domains in ferroelectric monodomain BiFeO3 . Phys. Rev. Lett. 110, 217206 (2013).

    Article  ADS  Google Scholar 

  16. Dmitrienko, V. E., Ovchinnikova, E. N., Kokubun, J. & Ishida, K. Dzyaloshinskii–Moriya interaction: How to measure its sign in weak ferromagnets?. JETP Lett. 92, 383–387 (2010).

    Article  ADS  Google Scholar 

  17. Blume, M. in Resonant Anomalous X-Ray Scattering (eds Materlik, G., Sparks, C. S. & Fischer, K.) 95–515 (North-Holland, 1994).

    Google Scholar 

  18. De Bergevin, F. & Brunel, M. Diffraction of X-rays by magnetic materials. I. General formulae and measurements on ferro- and ferrimagnetic compounds. Acta Crystallogr. A 37, 314–324 (1981).

    Article  ADS  Google Scholar 

  19. Dmitrienko, V. E., Ishida, K., Kirfel, A. & Ovchinnikova, E. N. Polarization anisotropy of X-ray atomic factors and ‘forbidden’ resonant reflections. Acta Crystallogr. A 61, 481–493 (2005).

    Article  ADS  Google Scholar 

  20. Lovesey, S. W., Balcar, E., Knight, K. S. & Rodríguez, J. F. Electronic properties of crystalline materials observed in X-ray diffraction. Phys. Rep. 411, 233–289 (2005).

    Article  ADS  Google Scholar 

  21. Solovyev, I. V., Lichtenstein, A. I. & Terakura, K. Is Hunds second rule responsible for the orbital magnetism in solids?. Phys. Rev. Lett. 80, 5758–5761 (1998).

    Article  ADS  Google Scholar 

  22. Shorikov, A. O., Lukoyanov, A. V., Korotin, M. A. & Anisimov, V. I. Magnetic state and electronic structure of the δ and α phases of metallic Pu and its compounds. Phys. Rev. B 72, 024458 (2005).

    Article  ADS  Google Scholar 

  23. Mazurenko, V. V. & Anisimov, V. I. Weak ferromagnetism in antiferromagnets: α-Fe2O3 and La2CuO4 . Phys. Rev. B 71, 184434 (2005).

    Article  ADS  Google Scholar 

  24. Yildirim, T., Harris, A. B., Aharony, A. & Entin-Wohlman, O. Anisotropic spin Hamiltonians due to spin–orbit and Coulomb exchange interactions. Phys. Rev. B 52, 10239–10267 (1995).

    Article  ADS  Google Scholar 

  25. Solovyev, I., Hamada, N. & Terakura, K. Crucial role of the lattice distortion in the magnetism of LaMnO3 . Phys. Rev. Lett. 76, 4825–4828 (1996).

    Article  ADS  Google Scholar 

  26. Katsnelson, M. I., Kvashnin, Y. O., Mazurenko, V. V. & Lichtenstein, A. I. Correlated band theory of spin and orbital contributions to Dzyaloshinskii–Moriya interactions. Phys. Rev. B 82, 100403 (2010).

    Article  ADS  Google Scholar 

  27. Brown, S. D. et al. The XMaS beamline at ESRF: Instrumental developments and high resolution diffraction studies. J. Synchrotron Radiat. 8, 1172–1181 (2001).

    Article  Google Scholar 

  28. Collins, S. P. et al. Diamond beamline I16 (materials and magnetism). AIP Conf. Proc. 1234, 303–306 (2009).

    ADS  Google Scholar 

  29. Joly, Y. X-ray absorption near-edge structure calculations beyond the muffin-tin approximation. Phys. Rev. B 63, 125120 (2001).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The work of V.V.M. is supported by the grant program of the President of Russian Federation MK-5565.2013.2, the contracts of the Ministry of Education and Science of Russia No. 14.A18.21.0076 and 14.A18.21.0889. V.E.D. is grateful for the grant of the Presidium RAS No. 24 ‘Diffraction of synchrotron radiation in multiferroics and chiral magnetics’. M.I.K. acknowledges financial support by FOM (The Netherlands). We thank the staff of ESRF BM-28 for expert assistance, and Y. Shvyd’ko for the loan of the FeBO3 crystal.

Author information

Authors and Affiliations

Authors

Contributions

V.E.D. and E.N.O. proposed the project. G.B., S.P.C. and G.N. carried out experimental work at BM-28. S.P.C. carried out experimental work at I16. Y.O.K., V.V.M., A.I.L., M.I.K. performed ab initio calculations. V.E.D. carried out FDMNES calculations. G.B. performed least-squares fitting of model functions to experimental data. G.N. carried out multiple scattering simulations. S.P.C., V.E.D. and V.V.M. wrote the majority of the text.

Corresponding author

Correspondence to S. P. Collins.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 970 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dmitrienko, V., Ovchinnikova, E., Collins, S. et al. Measuring the Dzyaloshinskii–Moriya interaction in a weak ferromagnet. Nature Phys 10, 202–206 (2014). https://doi.org/10.1038/nphys2859

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/nphys2859

This article is cited by

Search

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