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:

Multiferroic quantum criticality

Abstract

The zero-temperature limit of a continuous phase transition is marked by a quantum critical point, which can generate physical effects that extend to elevated temperatures. Magnetic quantum criticality is now well established, and has been explored in systems ranging from heavy fermion metals to quantum Ising materials. Ferroelectric quantum critical behaviour has also been recently demonstrated, motivating a flurry of research investigating its consequences. Here, we introduce the concept of multiferroic quantum criticality, in which both magnetic and ferroelectric quantum criticality occur in the same system. We develop the phenomenology of multiferroic quantum criticality and describe the associated experimental signatures, such as phase stability and modified scaling relations of observables. We propose several material systems that could be tuned to multiferroic quantum criticality utilizing alloying and strain as control parameters. We hope that these results stimulate exploration of the interplay between different kinds of quantum critical behaviours.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Fig. 1: Phenomenology and identification of multiferroic quantum criticality.
Fig. 2: Crystal structure of EuTiO3.
Fig. 3: Tuning criticality in EuTiO3 by alloying.
Fig. 4: Near-bicriticality in strained EuTiO3.

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Sachdev, S. Quantum Phase Transitions 2nd edn (Cambridge Univ. Press, Cambridge, 2011).

    Book  Google Scholar 

  2. Lake, B., Tennant, D. A., Frost, C. D. & Nagler, S. E. Quantum criticality and universal scaling of a quantum antiferromagnet. Nat. Mater. 4, 329–334 (2005).

    Article  CAS  Google Scholar 

  3. Coldea, R. et al. Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry. Science 327, 177–180 (2010).

    Article  CAS  Google Scholar 

  4. Custers, J. et al. The break-up of heavy electrons at a quantum critical point. Nature 424, 524–527 (2003).

    Article  CAS  Google Scholar 

  5. Gegenwart, P., Si, Q. & Steglich, F. Quantum criticality in heavy-fermion metals. Nat. Phys. 4, 186–197 (2008).

    Article  CAS  Google Scholar 

  6. Rowley, S. E. et al. Ferroelectric quantum criticality. Nat. Phys. 10, 367–372 (2014).

    Article  CAS  Google Scholar 

  7. Khmelnitskii, D. E. & Shneerson, V. L. Low temperature displacement-type phase transition in crystals. Sov. Phys. Solid State 13, 687 (1971).

    Google Scholar 

  8. Roussev, R. & Millis, A. J. Theory of the quantum paraelectric–ferroelectric transition. Phys. Rev. B 67, 014105 (2003).

    Article  Google Scholar 

  9. Edge, J. M., Kedem, Y., Aschauer, U., Spaldin, N. A. & Balatsky, A. V. Quantum critical origin of the superconducting dome in SrTiO3. Phys. Rev. Lett. 115, 247002 (2015).

    Article  Google Scholar 

  10. Stucky, A. et al. Isotope effect in superconducting n-doped SrTiO3. Sci. Rep. 6, 37582 (2016).

    Article  CAS  Google Scholar 

  11. Rischau, C. W. et al. A ferroelectric quantum phase transition inside the superconducting dome of Sr1−xCaxTiO3−δ. Nat. Phys. 13, 643–648 (2017).

    Article  CAS  Google Scholar 

  12. Spaldin, N. A. & Fiebig, M. The renaissance of magnetoelectric multiferroics. Science 309, 391–392 (2005).

    Article  CAS  Google Scholar 

  13. She, J.-H., Zaanen, J., Bishop, A. R. & Balatsky, A. V. Stability of quantum critical points in the presence of competing orders. Phys. Rev. B 82, 165128 (2010).

    Article  Google Scholar 

  14. Morice, C., Chandra, P., Rowley, S. E., Lonzarich, G. & Saxena, S. S. Hidden fluctuations close to a quantum bicritical point. Phys. Rev. B 96, 245104 (2017).

    Article  Google Scholar 

  15. Chandra, P., Lonzarich, G. G., Rowley, S. E. & Scott, J. F. Prospects and applications near ferroelectric quantum phase transitions: a key issues review. Rep. Progr. Phys. 80, 112502 (2017).

    Article  CAS  Google Scholar 

  16. Oliver, G. T. & Schofield, A. J. Quantum multicriticality. Preprint at https://arxiv.org/abs/1506.03021 (2015).

  17. Katsura, H., Nagaosa, N. & Balatsky, A. V. Spin current and magnetoelectric effect in noncollinear magnets. Phys. Rev. Lett. 95, 057205 (2005).

    Article  Google Scholar 

  18. Cheong, S.-W. & Mostovoy, M. Multiferroics: a magnetic twist for ferroelectricity. Nat. Mater. 6, 13–20 (2007).

    Article  CAS  Google Scholar 

  19. Dzyaloshinskii, I. E. & Mills, D. L. Intrinsic paramagnetism of ferroelectrics. Philos. Mag. 89, 2079–2082 (2009).

    Article  CAS  Google Scholar 

  20. Juraschek, D. M., Fechner, M., Balatsky, A. V. & Spaldin, N. A. Dynamical multiferroicity. Phys. Rev. Mat. 1, 014401 (2017).

    Google Scholar 

  21. Abrikosov, A. A., Gorkov, L. P. & Dzyaloshinski, I. E. Methods of Quantum Field Theory in Statistical Physics (Dover, Mineola, 1975).

  22. Zhu, L., Garst, M., Rosch, A. & Si, Q. Universally diverging Grüneisen parameter and the magnetocaloric effect close to quantum critical points. Phys. Rev. Lett. 91, 066404 (2003).

    Article  Google Scholar 

  23. Rushchanskii, K. Z., Spaldin, N. A. & Ležaić, M. First principles prediction of oxygen octahedral rotations in perovskite-structure EuTiO3. Phys. Rev. B 85, 104109 (2012).

    Article  Google Scholar 

  24. Goian, V. et al. Antiferrodistortive phase transition in EuTiO3. Phys. Rev. B 86, 054112 (2012).

    Article  Google Scholar 

  25. McGuire, T. R., Shafer, M. W., Joenk, R. J., Alperin, H. A. & Pickart, S. J. Magnetic structure of EuTiO3. J. Appl. Phys. 37, 981–982 (1966).

    Article  CAS  Google Scholar 

  26. Kamba, S. et al. Magnetodielectric effect and optic soft mode behavior in quantum paraelectric EuTiO3 ceramics. EPL 80, 27002 (2007).

    Article  Google Scholar 

  27. Das, N. Quantum critical behavior of a magnetic quantum paraelectric. Phys. Lett. A 376, 2683–2687 (2012).

    Article  CAS  Google Scholar 

  28. Rushchanskii, K. Z. et al. A multiferroic material to search for the permanent electric dipole moment of the electron. Nat. Mater. 9, 649–654 (2010).

    Article  CAS  Google Scholar 

  29. Guguchia, Z., Shengelaya, A., Keller, H., Köhler, J. & Bussmann-Holder, A. Tuning the structural instability of SrTiO3 by Eu doping: the phase diagram of Sr1−xEuxTiO3. Phys. Rev. B 85, 134113 (2012).

    Article  Google Scholar 

  30. Schlom, D. G. et al. Strain tuning of ferroelectric thin films. Annu. Rev. Mater. Res. 37, 589–626 (2007).

    Article  CAS  Google Scholar 

  31. Fennie, C. J. & Rabe, K. M. Magnetic and electric phase control in epitaxial EuTiO3 from first principles. Phys. Rev. Lett. 97, 267602 (2006).

    Article  Google Scholar 

  32. Lee, J. H. et al. A strong ferroelectric ferromagnet created by means of spin-lattice coupling. Nature 466, 954–958 (2010).

    Article  CAS  Google Scholar 

  33. Kleemann, W. et al. Multiglass order and magnetoelectricity in Mn2+ doped incipient ferroelectrics. Eur. Phys. J. B 71, 407 (2009).

    Article  CAS  Google Scholar 

  34. Dubrovin, R. M., Kizhaev, S. A., Syrnikov, P. P., Gesland, J.-Y. & Pisarev, R. V. Unveiling hidden structural instabilities and magnetodielectric effect in manganese uoroperovskites AMnF3. Phys. Rev. B 98, 060403 (2018).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  36. Ishiwata, S. et al. Perovskite manganites hosting versatile multiferroic phases with symmetric and antisymmetric exchange strictions. Phys. Rev. B 81, 100411 (2010).

    Article  Google Scholar 

  37. Fedorova, N. S. et al. Relationship between crystal structure and multiferroic orders in orthorhombic perovskite manganites. Phys. Rev. Mat. 2, 104414 (2018).

    Google Scholar 

  38. Ramesh, R. & Spaldin, N. A. Multiferroics: progress and prospects in thin films. Nat. Mater. 6, 21–29 (2007).

    Article  CAS  Google Scholar 

  39. Friedemann, S. et al. Quantum tricritical points in NbFe2. Nat. Phys. 14, 62–67 (2018).

    Article  CAS  Google Scholar 

  40. Miyake, K., Schmitt-Rink, S. & Varma, C. M. Spin-fluctuation-mediated even-parity pairing in heavyfermion superconductors. Phys. Rev. B 34, 6554 (1986).

    Article  CAS  Google Scholar 

  41. Scalapino, D. J., Loh, E. Jr. & Hirsch, J. E. D-wave pairing near a spin-density-wave instability. Phys. Rev. B 34, 8190 (1986).

    Article  CAS  Google Scholar 

  42. Kim, J. W. et al. Observation of a multiferroic critical end point. Proc. Natl Acad. Sci. USA 106, 15573–15576 (2009).

    Article  CAS  Google Scholar 

  43. Chandra, P., Coleman, P., Continentino, M. A. & Lonzarich, G. G. Quantum annealed criticality. Preprint at https://arxiv.org/abs/1805.11771 (2018).

  44. Peiderer, C. Why first order quantum phase transitions are interesting. J. Phys. Condens. Matter 17, S987 (2005).

    Article  Google Scholar 

  45. Morales, A., Zupancic, P., Léonard, J., Esslinger, T. & Donner, T. Coupling two order parameters in a quantum gas. Nat. Mater. 17, 686–690 (2018).

    Article  CAS  Google Scholar 

  46. Basov, D. N., Averitt, R. D. & Hsieh, D. Towards properties on demand in quantum materials. Nat. Mater. 16, 1077–1088 (2017).

    Article  CAS  Google Scholar 

  47. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).

    Article  CAS  Google Scholar 

  48. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).

    Article  CAS  Google Scholar 

  49. Dudarev, S. L., Botton, G. A., Savrasov, S. Y., Humphreys, C. J. & Sutton, A. P. Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA + U study. Phys. Rev. B 57, 1505 (1998).

    Article  CAS  Google Scholar 

  50. Togo, A. & Tanaka, I. First principles phonon calculations in materials science. Scr. Mater. 108, 1–5 (2015).

    Article  CAS  Google Scholar 

  51. Blinc, R. Soft Modes in Ferroelectrics and Antiferro-electrics (North-Holland, Amsterdam, 1974).

  52. Zhang, L., Zhong, W.-L. & Kleemann, W. A study of the quantum effect in BaTiO3. Phys. Lett. A 276, 162–166 (2000).

    Article  CAS  Google Scholar 

  53. Landau, D. P. & Binder, K. A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge Univ. Press, Cambridge, 2014).

  54. Bergqvist, L., Eriksson, O., Kudrnovskỳ, J., Drchal, Va, Korzhavyi, P. & Turek, I. Magnetic percolation in diluted magnetic semiconductors. Phys. Rev. Lett. 93, 137202 (2004).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge helpful discussions with G. Aeppli, T. Donner, K. Dunnett, C. Ederer, A. Edström, T. Esslinger, N. Fedorova, C. Gattinoni, Q. Meier, A. Morales, R. Pisarev and P. Zupancic. This work is supported by ETH-Zurich (A.N., A.C. and N.A.S.), the US DOE BES E3B7, the Villum Foundation and the Knut and Alice Wallenberg Foundation (A.V.B.). Calculations were performed at the Swiss National Supercomputing Centre (project ID p504).

Author information

Authors and Affiliations

Authors

Contributions

N.A.S. conceived the concept. N.A.S., A.V.B., A.C. and A.N. devised the analysis. A.N. carried out the calculations. A.N. and N.A.S. wrote the manuscript with contributions from all authors.

Corresponding author

Correspondence to Nicola A. Spaldin.

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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Narayan, A., Cano, A., Balatsky, A.V. et al. Multiferroic quantum criticality. Nature Mater 18, 223–228 (2019). https://doi.org/10.1038/s41563-018-0255-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-018-0255-6

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