Abstract
Multiferroics are compounds in which at least two ferroic orders coexist, typically ferroelectricity and some form of magnetism. While magnetic order can arise in both insulating and metallic compounds, ferroelectricity is in principle only allowed in insulators, although ferroelectric metals have been proposed and several two-dimensional systems have been reported to behave in this way. However, their combination with and coupling to magnetic order have not been realized thus far. Here we show the coexistence of ferroelectricity and magnetism in an oxide-based two-dimensional electron gas. We report a modulation of the Ti–O polar displacements depending on the ferroelectric polarization direction, and a voltage-induced hysteresis of the sheet resistance that is reminiscent of the ferroelectric polarization loop. The transport properties of the electron gas display an anomalous Hall effect and magnetoresistance that can both be modulated and cycled by switching the remanent polarization, demonstrating a magnetoelectric coupling. Our findings provide new opportunities in quantum matter that stem from the interplay between ferroelectricity, ferromagnetism, metallicity and Rashba spin–orbit coupling.
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Data availability
The data that support the findings of this study are available at https://doi.org/10.5281/zenodo.7551336.
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Acknowledgements
We thank A. Barthélémy, N. Bergeal, V. Garcia, Y. Dagan, G. Tuvia and B. Kalisky for useful discussions and L.M. Vicente-Arche for the data in Extended Data Fig. 6c,d. This project received funding from the ERC advanced grant ‘FRESCO’ no. 833973, the French ANR through project ‘CONTRABASS’, the ERA-NET QUANTERA European Union’s Horizon H2020 project ‘QUANTOX’ under grant agreement no. 731473 and the Ministero dell’Istruzione, dell’Università e della Ricerca for the PRIN project ‘TOP-SPIN’ (grant no. PRIN 20177SL7HC). M. S. and Y. C. acknowledge financial support from PNRR MUR project PE0000023-NQSTI. DFT calculations took advantage of HPC resources of CRIANN through projects 2020005 and 2007013 and of CINES through DARI project A0080911453.
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M.B. conceived the study and supervised it with MS. Y.C. and M.S. prepared the samples, collected the reflection high-energy electron diffraction data and imaged the samples by atomic force microscopy. Preliminary transport measurements were carried out by D.S. and M.D.A. J.B. performed the complete set of polarization and magnetotransport measurements with help from S.V. The analysis was carried out by J.B. with the help of M.B., S.V., D.S. and M.S. C.P., M.S. and J.B. performed the XAS and XMCD experiment and analysed the data. M.S. performed the atomic multiplet calculations. J.V. carried out DFT calculations. M.B., M.S. and J.B. wrote the paper with input from all authors.
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Nature Physics thanks Xiaoshan Xu, Zhicheng Zhong and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Extended data
Extended Data Fig. 1
(a) RHEED intensity as function of time during the preparation of a LAO/ETO//Ca-STO heterostructure. (b) AFM image of the sample after growth. Each terrace is separated from its neighbours by a 4 Å high step.
Extended Data Fig. 2
Current vs voltage loop at 2 K.
Extended Data Fig. 3
Remanent polarization loop at 2 K.
Extended Data Fig. 4
a,b, Two R vs VG cycles as in Fig. 3b measured consecutively. They are virtually identical, evidencing that the resistance is modulated by ferroelectricity rather than by irreversible effects occurring on the first cycle in standard STO 2DEGs.
Extended Data Fig. 5
(a) Raw transverse resistance measured at 6 K in the Pup state. (b) Same data after antisymmetrization. (c) AHE after the subtraction of a linear slope. (d) Same as in (c) after smoothing.
Extended Data Fig. 6
Hall effect (a) and field derivative of the Hall effect (b) for a LAO/ETO//Ca-STO sample. Hall effect (c) and field derivative of the Hall effect (d) for a AlOx//STO sample. The inverted-V shape and V shape of the data in (b) and (d), respectively, indicate a non-linear component in the Hall signal, but with a sign opposite in LAO/ETO//Ca-STO compared to AlOx//STO. While in AlOx//STO (and in standard LAO/STO 2DEGs) this non-linearity is well explained by standard two-electronic bands contributions, the non-linear component in LAO/ETO//Ca-STO has a different origin, only visible when a magnetic layer is present19, and thus ascribed to anomalous Hall effect.
Extended Data Fig. 7
Comparison of the field dependence of the AHE (left axis) and the XMCD at the Eu M5 edge (right axis), both measured at 2 K and with the magnetic field perpendicular to the plane.
Extended Data Fig. 8
Low magnetic field comparison of the AHE signal at 2 K for both remanent polarization state, after rescaling the Pup signal to match the amplitude of the Pdn signal at high magnetic field.
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Bréhin, J., Chen, Y., D’Antuono, M. et al. Coexistence and coupling of ferroelectricity and magnetism in an oxide two-dimensional electron gas. Nat. Phys. 19, 823–829 (2023). https://doi.org/10.1038/s41567-023-01983-y
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DOI: https://doi.org/10.1038/s41567-023-01983-y
