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Landau theory of topological defects in multiferroic hexagonal manganites

Nature Materials volume 13, pages 42–49 (2014)Cite this article

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Abstract

Topological defects in ordered states with spontaneously broken symmetry often have unusual physical properties, such as fractional electric charge or a quantized magnetic field flux, originating from their non-trivial topology. Coupled topological defects in systems with several coexisting orders give rise to unconventional functionalities, such as the electric-field control of magnetization in multiferroics resulting from the coupling between the ferroelectric and ferromagnetic domain walls. Hexagonal manganites provide an extra degree of freedom: in these materials, both ferroelectricity and magnetism are coupled to an additional, non-ferroelectric structural order parameter. Here we present a theoretical study of topological defects in hexagonal manganites based on Landau theory with parameters determined from first-principles calculations. We explain the observed flip of electric polarization at the boundaries of structural domains, the origin of the observed discrete vortices, and the clamping between ferroelectric and antiferromagnetic domain walls. We show that structural vortices induce magnetic ones and that, consistent with a recent experimental report, ferroelectric domain walls can carry a magnetic moment.

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Figure 1: Structural and magnetic angles.
Figure 2: Extraction of model parameters from ab initio calculations.
Figure 3: Structural topological defects.
Figure 4: Antiferromagnetic domain walls in hexagonal manganites.

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References

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

    Article  CAS  Google Scholar 

  2. Ramesh, R. & Spaldin, N. A. Multiferroics: Progress and prospects in thin films. Nature Mater. 6, 21–29 (2007).

    Article  CAS  Google Scholar 

  3. Khomskii, D. Trend: Classifying multiferroics: Mechanisms and effects. Physics 2, 20 (2009).

    Article  Google Scholar 

  4. Kimura, T. et al. Magnetic control of ferroelectric polarization. Nature 426, 55–58 (2003).

    Article  CAS  Google Scholar 

  5. Hur, N. et al. Electric polarization reversal and memory in a multiferroic material induced by magnetic fields. Nature 429, 392–395 (2004).

    Article  CAS  Google Scholar 

  6. Kitagawa, Y. et al. Low-field magnetoelectric effect at room temperature. Nature Mater. 9, 797–802 (2010).

    Article  CAS  Google Scholar 

  7. Van Aken, B. B., Palstra, T. T. M., Filippetti, A. & Spaldin, N. A. The origin of ferroelectricity in magnetoelectric YMnO3 . Nature Mater. 3, 164–170 (2004).

    Article  CAS  Google Scholar 

  8. Neaton, J. B., Ederer, C., Waghmare, U. V., Spaldin, N. A. & Rabe, K. M. First-principles study of spontaneous polarization in multiferroic BiFeO3 . Phys. Rev. B 71, 014113 (2005).

    Article  Google Scholar 

  9. Lebeugle, D. et al. Electric-field-induced spin flop in BiFeO3 single crystals at room temperature. Phys. Rev. Lett. 100, 227602 (2008).

    Article  CAS  Google Scholar 

  10. Chu, Y-H. et al. Electric-field control of local ferromagnetism using a magnetoelectric multiferroic. Nature Mater. 7, 478–482 (2008).

    Article  CAS  Google Scholar 

  11. Lebeugle, D., Mougin, A., Viret, M., Colson, D. & Ranno, L. Electric field switching of the magnetic anisotropy of a ferromagnetic layer exchange coupled to the multiferroic compound BiFeO3 . Phys. Rev. Lett. 103, 257601 (2009).

    Article  CAS  Google Scholar 

  12. Skumryev, V. et al. Magnetization reversal by electric-field decoupling of magnetic and ferroelectric domain walls in multiferroic-based heterostructures. Phys. Rev. Lett. 106, 057206 (2011).

    Article  CAS  Google Scholar 

  13. Fennie, C. J. Ferroelectrically induced weak ferromagnetism by design. Phys. Rev. Lett. 100, 167203 (2008).

    Article  Google Scholar 

  14. Fiebig, M., Lottermoser, Th., Fröhlich, D., Goltsev, A. V. & Pisarev, R. V. Observation of coupled magnetic and electric domains. Nature 419, 818–820 (2002).

    Article  CAS  Google Scholar 

  15. Yakel, H. L., Koehler, W. C., Bertaut, E. F. & Forrat, E. F. On the crystal structure of the manganese(III) trioxides of the heavy lanthanides and yttrium. Acta Crystallogr. 16, 957–962 (1963).

    Article  CAS  Google Scholar 

  16. Katsufuji, T. et al. Dielectric and magnetic anomalies and spin frustration in hexagonal RMnO3 (R = Y, Yb, and Lu). Phys. Rev. B 64, 104419 (2001).

    Article  Google Scholar 

  17. Fennie, C. J. & Rabe, K. M. Ferroelectric transition in YMnO3 from first principles. Phys. Rev. B 72, 100103 (2005).

    Article  Google Scholar 

  18. Dela Cruz, C. et al. Strong spin-lattice coupling in multiferroic HoMnO3: Thermal expansion anomalies and pressure effect. Phys. Rev. B 71, 060407 (2005).

    Article  Google Scholar 

  19. Lee, S. et al. Giant magneto-elastic coupling in multiferroic hexagonal manganites. Nature 451, 805–808 (2008).

    Article  CAS  Google Scholar 

  20. Adem, U. et al. Scaling behavior of the magnetocapacitance of YbMnO3 . J. Phys.: Condens. Matter 21, 496002 (2009).

    CAS  Google Scholar 

  21. Goltsev, A. V., Pisarev, R. V., Lottermoser, T. & Fiebig, M. Structure and interaction of antiferromagnetic domain walls in hexagonal YMnO3 . Phys. Rev. Lett. 90, 177204 (2003).

    Article  CAS  Google Scholar 

  22. Hanamura, E., Hagita, K. & Tanabe, Y. Clamping of ferroelectric and antiferromagnetic order parameters of YMnO3 . J. Phys. Condens. Matter 15, L103–L109 (2003).

    Article  CAS  Google Scholar 

  23. Hanamura, E. & Tanabe, Y. Ferroelectric and antiferromagnetic domain wall. J. Phys. Soc. Jpn. 72, 2959–2966 (2003).

    Article  CAS  Google Scholar 

  24. Choi, T. et al. Insulating interlocked ferroelectric and structural antiphase domain walls in multiferroic YMnO3 . Nature Mater. 9, 253–258 (2010).

    Article  CAS  Google Scholar 

  25. Chae, S. C. et al. Self-organization, condensation, and annihilation of topological vortices and antivortices in a multiferroic. Proc. Natl Acad. Sci. USA 107, 21366–21370 (2010).

    Article  CAS  Google Scholar 

  26. Jungk, T., Hoffmann, Á., Fiebig, M. & Soergel, E. Electrostatic topology of ferroelectric domains in YMnO3 . Appl. Phys. Lett. 97, 012904 (2010).

    Article  Google Scholar 

  27. Lilienblum, M., Soergel, E. & Fiebig, M. J. Manipulation of ferroelectric vortex domains in hexagonal manganites. J. Appl. Phys. 110, 052007 (2011).

    Article  Google Scholar 

  28. Mostovoy, M. Multiferroics: A whirlwind of opportunities. Nature Mater. 9, 188–190 (2010).

    Article  CAS  Google Scholar 

  29. Kumagai, Y. & Spaldin, N. Structural domain walls in polar hexagonal manganites. Nature Commun. 4, 1540 (2013).

    Article  Google Scholar 

  30. Chaikin, P. M. & Lubensky, T. C. Principles of Condensed Matter Physics (Cambridge Univ. Press, 1995).

    Book  Google Scholar 

  31. Kaski, K., Grant, M. & Gunton, J. D. Domain growth in the clock model. Phys. Rev. B 31, 3040–3047 (1985).

    Article  CAS  Google Scholar 

  32. Grest, G. S., Anderson, M. P. & Srolovitz, D. J. Domain-growth kinetics for the Q-state Potts model in two and three dimensions. Phys. Rev. B 38, 4752–4760 (1988).

    Article  CAS  Google Scholar 

  33. Fong, D. D. et al. Ferroelectricity in ultrathin perovskite films. Science 304, 1650–1653 (2004).

    Article  CAS  Google Scholar 

  34. Matsumoto, T. & Okamoto, M. J. Effects of electron irradiation on the ferroelectric 180° in-plane nanostripe domain structure in a thin film prepared from a bulk single crystal of BaTiO3 by focused ion beam. J. Appl. Phys. 109, 014104 (2011).

    Article  Google Scholar 

  35. Fiebig, M., Lottermoser, T. & Pisarev, R. V. Spin-rotation phenomena and magnetic phase diagrams of hexagonal RMnO3 . J. Appl. Phys. 93, 8194–8196 (2003).

    Article  CAS  Google Scholar 

  36. Sato, T. J. et al. Unconventional spin fluctuations in the hexagonal antiferromagnet YMnO3 . Phys. Rev. B 68, 014432 (2003).

    Article  Google Scholar 

  37. Ueland, B., Lynn, J. W., Laver, M., Choi, Y. J. & Cheong, S-W. Origin of electric-field-induced magnetization in multiferroic HoMnO3 . Phys. Rev. Lett. 104, 147204 (2010).

    Article  CAS  Google Scholar 

  38. Geng, Y., Lee, N., Choi, Y. J., Cheong, S-W. & Wu, W. Collective magnetism at multiferroic vortex domain walls. Nano Lett. 12, 6055–6059 (2012).

    Article  CAS  Google Scholar 

  39. Sugie, H., Iwata, N. & Kohn, K. J. Magnetic ordering of rare earth ions and magnetic-electric interaction of hexagonal RMnO3 (R = Ho, Er, Yb or Lu). J. Phys. Soc. Jpn. 71, 1558–1564 (2002).

    Article  CAS  Google Scholar 

  40. Gonze, X. et al. First-principles computation of material properties: The ABINIT software project. Comput. Mater. Sci. 25, 478–492 (2002).

    Article  Google Scholar 

  41. Gonze, X. et al. A brief introduction to the ABINIT software package. Z. Kristallogr. 220, 558–562 (2005).

    CAS  Google Scholar 

  42. Torrent, M., Jollet, F., Bottin, F., Zerah, G. & Gonze, X. Implementation of the projector augmented-wave method in the ABINIT code: Application to the study of iron under pressure. Comput. Mater. Science 42, 337–351 (2008).

    Article  CAS  Google Scholar 

  43. Perdew, J. P. & Wang, Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 45, 13244–13249 (1992).

    Article  CAS  Google Scholar 

  44. Amadon, B., Jollet, F. & Torrent, M. γ and β cerium: LDA+U calculations of ground-state parameters. Phys. Rev. B 77, 155104 (2008).

    Article  Google Scholar 

  45. Liechtenstein, A. I., Anisimov, V. I. & Zaanen, J. Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators. Phys. Rev. B 52, R5467–R5470 (1995).

    Article  CAS  Google Scholar 

  46. Smith, A. E. et al. Mn3+ in trigonal bipyramidal coordination: A new blue chromophore. J. Am. Chem. Soc. 131, 17084–17086 (2009).

    Article  CAS  Google Scholar 

  47. King-Smith, R. D. & Vanderbilt, D. Theory of polarization of crystalline solids. Phys. Rev. B 47, 1651–1654 (1993).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We are grateful to S-W. Cheong for discussions of the stripe state. S.A. and M.M. were supported by the ZIAM Groningen under award MSC06-20 and by FOM grant 11PR2928. K.T.D. acknowledges fellowship support from the International Center of Materials Research. We acknowledge support from the Center for Scientific Computing from the CNSI, MRL, an NSF MRSEC grant (DMR-1121053) and Hewlett Packard. N.A.S. was supported by the ETH Zürich.

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Authors and Affiliations

  1. Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG, Groningen, The Netherlands

    Sergey Artyukhin & Maxim Mostovoy

  2. Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA

    Sergey Artyukhin

  3. Materials Research Laboratory, University of California, Santa Barbara, California 93106-5121, USA

    Kris T. Delaney

  4. Materials Theory, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland

    Nicola A. Spaldin

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  1. Sergey Artyukhin
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Correspondence to Maxim Mostovoy.

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Artyukhin, S., Delaney, K., Spaldin, N. et al. Landau theory of topological defects in multiferroic hexagonal manganites. Nature Mater 13, 42–49 (2014). https://doi.org/10.1038/nmat3786

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