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.

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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.

Data availability

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

References

  1. 1.

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

  2. 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).

  3. 3.

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

  4. 4.

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

  5. 5.

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

  6. 6.

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

  7. 7.

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

  8. 8.

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

  9. 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).

  10. 10.

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

  11. 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).

  12. 12.

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

  13. 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).

  14. 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).

  15. 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).

  16. 16.

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

  17. 17.

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

  18. 18.

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

  19. 19.

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

  20. 20.

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

  21. 21.

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

  22. 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).

  23. 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).

  24. 24.

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

  25. 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).

  26. 26.

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

  27. 27.

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

  28. 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).

  29. 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).

  30. 30.

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

  31. 31.

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

  32. 32.

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

  33. 33.

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

  34. 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).

  35. 35.

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

  36. 36.

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

  37. 37.

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

  38. 38.

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

  39. 39.

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

  40. 40.

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

  41. 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).

  42. 42.

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

  43. 43.

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

  44. 44.

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

  45. 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).

  46. 46.

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

  47. 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).

  48. 48.

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

  49. 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).

  50. 50.

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

  51. 51.

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

  52. 52.

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

  53. 53.

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

  54. 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).

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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

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.

Correspondence to Nicola A. Spaldin.

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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

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