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.

  • Article
  • Published:

Metamagnetic texture in a polar antiferromagnet

Nature Physics volume 15, pages 671–677 (2019)Cite this article

Subjects

Abstract

The notion of a simple ordered state implies homogeneity. If the order is established by a broken symmetry, the elementary Landau theory of phase transitions shows that only one symmetry mode describes this state. At the exact points of phase coexistence, domain states composed of large regions of different phases can be stabilized by long-range interactions. In uniaxial antiferromagnets, so-called metamagnetism is an example of such behaviour where antiferromagnetic and field-induced, spin-polarized paramagnetic/ferromagnetic states coexist at a jump-like transition in the magnetic phase diagram. Here, by combining experiments with theoretical analysis, we show that a different type of mixed state between antiferromagnetism and ferromagnetism can be created in certain non-centrosymmetric materials. In small-angle neutron scattering experiments, we observe a field-driven spin state in the layered antiferromagnet Ca3Ru2O7, which is modulated on a scale between 8 and 20 nm and has both antiferromagnetic and ferromagnetic parts. We call this state a metamagnetic texture and attribute its appearance to the chiral twisting effects of the asymmetric Dzyaloshinskii–Moriya exchange. The observation can be understood as an extraordinary coexistence—in one thermodynamic state—of spin orders that belong to different symmetries. The complex nature of this metamagnetic state is demonstrated experimentally by measurements of anomalies in electronic transport that reflect the spin polarization in the metamagnetic texture; determination of the magnetic orbital moments, which support the existence of strong spin–orbit effects, is a pre-requisite for the mechanism of twisted magnetic states in this material. Our findings provide an example of a rich and largely unexplored class of textured states. Such textures mediate between different ordering modes near phase coexistence, and produce extremely rich phase diagrams.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Fig. 1: Bulk properties of Ca3Ru2O7 measured with the magnetic field along the b axis on the same single crystal.
Fig. 2: SANS patterns.
Fig. 3: Metamagnetic textures in Ca3Ru2O7.
Fig. 4: Schematics of metamagnetic texture in Ca3Ru2O7 and temperature-field phase diagrams.

Similar content being viewed by others

Data availability

The data that support the plots within this paper can be downloaded at https://doi.org/10.17617/3.23. The datasets for the SANS experiments on D33 are available from the Institute Laue–Langevin data portal (https://doi.org/10.5291/ILL-DATA.5-42-462)49.

References

  1. Becquerel, J. & van den Handel, J. Le métamagnétisme. J. Phys. Radium 10, 10–13 (1939).

    Article  Google Scholar 

  2. Becquerel, J. Le métamagnétisme. In Reunion d’ étude sur le magnétisme. Généralités et magnéto-optique. Strasbourg, 21–25 Mai 1939 97–139 (Institut International de Coopération Intellectuelle, 1940).

  3. Stryjewski, E. & Giordano, N. Metamagnetism. Adv. Phys. 26, 487–650 (1977).

    Article  ADS  Google Scholar 

  4. Néel, L. Les métamagnétiques ou substances antiferromagnétiques à champ seuil. Nuovo Cimento 6, 942–960 (1957).

    Article  Google Scholar 

  5. Bar’yakhtar, V. G., Bogdanov, A. N. & Yablonskii, D. A. The physics of magnetic domains. Usp. Fiz. Nauk 156, 47–92 (1988).

    Article  Google Scholar 

  6. Dzyaloshinskii, I. E. Theory of helicoidal structures in antiferromagnets. 1. Nonmetals. Sov. Phys. JETP 19, 960–971 (1964).

    Google Scholar 

  7. Levanyuk, A. P. Incommensurate Phases in Dielectrics (eds Blinc, R. & Levanyuk, A. P.) (North Holland, 1986).

  8. Cummins, H. Z. Experimental studies of structurally incommensurate crystal phases. Phys. Rep. 185, 211–409 (1990).

    Article  ADS  Google Scholar 

  9. De Gennes, P. G. Short range order effects in the isotropic phase of nematics and cholesterics. Mol. Cryst. Liquid Cryst. 12, 193–214 (1971).

    Article  Google Scholar 

  10. Wright, D. C. & Mermin, N. D. Crystalline liquids: the blue phases. Rev. Mod. Phys. 61, 385–432 (1989).

    Article  ADS  Google Scholar 

  11. Meiboom, S., Sethna, J. P., Anderson, P. W. & Brinkman, W. F. Theory of the blue phase of cholesteric liquid crystals. Phys. Rev. Lett. 46, 1216–1219 (1981).

    Article  ADS  Google Scholar 

  12. Nakanishi, O., Yanase, A., Hasegawa, A. & Kataoka, M. The origin of the helical spin density wave in MnSi. Solid State Commun. 35, 995–998 (1980).

    Article  ADS  Google Scholar 

  13. Bak, P. & Jensen, M. H. Theory of helical magnetic structures and phase transitions in MnSi and FeGe. J. Phys. C 13, L881–L885 (1980).

    Article  ADS  Google Scholar 

  14. Bogdanov, A. N. New localized solutions of the nonlinear field equations. JETP Lett. 62, 247–251 (1995).

    ADS  MathSciNet  Google Scholar 

  15. Bogdanov, A. N., Rößler, U. K., Wolf, M. & Müller, K.-H. Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnets. Phys. Rev. B 66, 214410 (2002).

    Article  ADS  Google Scholar 

  16. Bogdanov, A. N. & Yablonskii, D. A. Thermodynamically stable ‘vortices’ in magnetically ordered crystals. The mixed state of magnets. Zh. Eksp. Teor. Fiz. 95, 178–182 (1989).

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Jungwirth, T. et al. The multiple directions of antiferromagnetic spintronics. Nat. Phys. 14, 200–203 (2018).

    Article  Google Scholar 

  21. Gomonay, O., Baltz, V., Brataas, A. & Tserkovnyak, Y. Antiferromagnetic spin textures and dynamics. Nat. Phys. 14, 213–216 (2018).

    Article  Google Scholar 

  22. Duine, R. A., Lee, K.-J., Parkin, S. S. P. & Stiles, M. D. Synthetic antiferromagnetic spintronics. Nat. Phys. 14, 217–219 (2018).

    Article  Google Scholar 

  23. Yoshida, Y. et al. Crystal and magnetic structure of Ca3Ru2O7. Phys. Rev. B 72, 054412 (2005).

    Article  ADS  Google Scholar 

  24. Bao, W., Mao, Z. Q., Qu, Z. & Lynn, J. W. Spin valve effect and magnetoresistivity in single crystalline Ca3Ru2O7. Phys. Rev. Lett. 100, 247203 (2008).

    Article  ADS  Google Scholar 

  25. Liu, G. Q. Mott transition and magnetic anisotropy in Ca3Ru2O7. Phys. Rev. B 84, 235137 (2011).

    Article  ADS  Google Scholar 

  26. Yoshida, Y. et al. Quasi-two-dimensional metallic ground state of Ca3Ru2O7. Phys. Rev. B 69, 220411(R) (2004).

    Article  ADS  Google Scholar 

  27. Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).

    Article  ADS  Google Scholar 

  28. McCall, S., Cao, G. & Crow, J. E. Impact of magnetic fields on anisotropy in Ca3Ru2O7. Phys. Rev. B 67, 094427 (2003).

    Article  ADS  Google Scholar 

  29. Cao, G. et al. Orbitally driven behaviour: Mott transition, quantum oscillations and colossal magnetoresistance in bilayered Ca3Ru2O7. New J. Phys. 6, 159 (2004).

    Article  ADS  Google Scholar 

  30. Fobes, D., Peng, J., Qu, Z., Liu, T. J. & Mao, Z. Q. Magnetic phase transitions and bulk spin-valve effect tuned by in-plane field orientation in Ca3Ru2O7. Phys. Rev. B 84, 014406 (2011).

    Article  ADS  Google Scholar 

  31. Dewhurst, C. D. et al. The small-angle neutron scattering instrument D33 at the Institut Laue Langevin. J. Appl. Cryst. 49, 1–14 (2015).

    Article  Google Scholar 

  32. Ke, X., Peng, J., Tian, W., Hong, T. & Mao, Z. Q. Commensurate-incommensurate magnetic phase transition in the Fe-doped bilayer ruthenate Ca3Ru2O7. Phys. Rev. B 89, 220407(R) (2014).

    Article  ADS  Google Scholar 

  33. Zhu, M. et al. Tuning the competing phases of bilayer ruthenate Ca3Ru2O7 via dilute Mn impurities and magnetic field. Phys. Rev. B 95, 144426 (2017).

    Article  ADS  Google Scholar 

  34. Zheludev, A. et al. Field-induced incommensurate-to-commensurate transition in Ba2CuGe2O7. Phys. Rev. B 57, 2968–2978 (1998).

    Article  ADS  Google Scholar 

  35. Agrestini, S. et al. Nature of the magnetic order in Ca3Co2O6. Phys. Rev. Lett. 101, 097202 (2008).

    Article  ADS  Google Scholar 

  36. Gao, S. et al. Spiral spin-liquid and the emergence of a vortex-like state in MnSc2S4. Nat. Phys. 13, 157–161 (2017).

    Article  Google Scholar 

  37. Jensen, J. & Mackintosh, A. R. Rare Earth Magnetism (Clarendon, 1991).

  38. Levanyuk, A. P. Thermodynamical theory of phase-transitions with appearance of an incommensurate superstructure in ferroelectrics NaNO2 and SC(NH2)2. Fiz. Tverd. Tela 18, 1927–1932 (1976).

    Google Scholar 

  39. Stefanovskii, E. P. Exchange-relativistic modulated magnetic-structures in multisublattice rhombic antiferromagnets. Fiz. Tverd. Tela 28, 3452–3456 (1986).

    Google Scholar 

  40. Yablonskii, D. A. & Medvedeva, L. I. Classification of magnetic structures in compounds with the Fe2P-structure. Physica B 167, 125–132 (1990).

    Article  ADS  Google Scholar 

  41. Aizu, K. Investigation of incommensurate phases of the ‘Twiny’ gradient form as compared with incommensurate phases of the simple gradient form. J. Phys. Soc. Jpn 58, 4501–4510 (1989).

    Article  ADS  Google Scholar 

  42. Zavorotnev, Yu. D. & Medvedyeva, L. I. Long-period incommensurate structures in crystals with a triangular arrangement of magnetic ions. J. Magn. Magn. Mater. 248, 402–412 (2002).

    Article  ADS  Google Scholar 

  43. Zavorotnev, Yu. D. & Medvedeva, L. I. Characteristics of irreducible vectors rotating in superstructures with two one-component order parameters. Crystallogr. Rep. 47, 1003–1006 (2002).

    Article  ADS  Google Scholar 

  44. Milward, G. C., Calderon, M. J. & Littlewood, P. B. Electronically soft phases in manganites. Nature 433, 607–611 (2005).

    Article  ADS  Google Scholar 

  45. Bar’yakhtar, V. G., Stefanovskij, E. P. & Yablonskii, D. A. Theory of magnetic structure and electric polarization of Cr2BeO4 system. Pisma Zh. Eksp. Teor. Fiz. 42, 258–260 (1985).

    Google Scholar 

  46. Ronning, F. et al. Electronic in-plane symmetry breaking at field-tuned quantum criticality in CeRhIn5. Nature 548, 313–317 (2017).

    Article  ADS  Google Scholar 

  47. Tolédano J. C. & Tolédano P. The Landau Theory of Phase Transitions (World Scientific, 1987).

  48. Koepernik, K. & Eschrig, H. Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme. Phys. Rev. B 59, 1743 (1999).

    Article  ADS  Google Scholar 

  49. Sokolov, D. A. & Cubitt, R. Probing the Magnetic Field Driven Modulated Structure and Exotic Magnetism in Ca 3 Ru 2 O 7 (Institut Laue–Langevin, 2018); https://doi.org/10.5291/ILL-DATA.5-42-462

Download references

Acknowledgements

We thank U. Nitzsche for technical support with FPLO. N.K. acknowledges the support from JSPS KAKENHI (nos JP17H06136 and JP18K04715) and JST-Mirai Program (no. JPMJMI18A3) in Japan. D.A.S. thanks C. Geibel for the critical reading of the manuscript and constructive comments. Access to NG7 SANS was provided by the Center for High Resolution Neutron Scattering, a partnership between the National Institute of Standards and Technology and the National Science Foundation under agreement no. DMR-1508249. We thank J. Krzywon and Y. Qiang for technical support during the SANS experiment at NIST. This work is partly based on experiments performed at the Swiss spallation neutron source SINQ, Paul Scherrer Institute, Villigen, Switzerland. Certain commercial equipment, instruments, or materials are identified in this article to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

Author information

Authors and Affiliations

  1. Max Planck Institut für Chemische Physik fester Stoffe, Dresden, Germany

    D. A. Sokolov, T. Helm, H. Borrmann, U. Burkhardt & A. P. Mackenzie

  2. National Institute for Materials Science, Tsukuba, Japan

    N. Kikugawa

  3. Institut Laue–Langevin, Grenoble, France

    R. Cubitt

  4. Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, Villigen, Switzerland

    J. S. White

  5. Université Grenoble Alpes, CEA, INAC-MEM, Grenoble, France

    E. Ressouche

  6. NIST Center for Neutron Research National Institute of Standards and Technology, Gaithersburg, MD, USA

    M. Bleuel

  7. Department of Materials Science and Engineering, University of Maryland, College Park, MD, USA

    M. Bleuel

  8. ESRF, Grenoble, France

    K. Kummer

  9. Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St Andrews, St Andrews, UK

    A. P. Mackenzie

  10. Leibniz-Institut für Festkörper- und Werkstoffforschung, IFW, Dresden, Germany

    U. K. Rößler

Authors
  1. D. A. Sokolov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Kikugawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Helm
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. Borrmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. U. Burkhardt
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. R. Cubitt
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. J. S. White
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. E. Ressouche
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. M. Bleuel
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. K. Kummer
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. A. P. Mackenzie
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. U. K. Rößler
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

U.K.R. conceived the project. U.K.R., A.P.M. and D.A.S. supervised the project. N.K. and D.A.S. grew single crystals. D.A.S oriented and characterized samples. H.B. and U.B. analysed the crystal structure. T.H. performed the electrical transport measurements and analysed the Hall effect data. K.K. performed XMCD measurements. D.A.S., R.C., J.S.W. and M.B. performed SANS measurements. D.A.S. and E.R. carried out neutron diffraction experiments. U.K.R. carried out density functional theory calculations and developed the Landau–Ginzburg-type free-energy theory. D.A.S. and U.K.R wrote the manuscript with contributions from all co-authors.

Corresponding author

Correspondence to D. A. Sokolov.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–8 and Supplementary references 1–17.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sokolov, D.A., Kikugawa, N., Helm, T. et al. Metamagnetic texture in a polar antiferromagnet. Nat. Phys. 15, 671–677 (2019). https://doi.org/10.1038/s41567-019-0501-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-019-0501-0

This article is cited by

Search

Advanced 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