Multiferroic quantum criticality


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.


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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).

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