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# Evidence for a single-layer van der Waals multiferroic

## Abstract

Multiferroic materials have attracted wide interest because of their exceptional static1,2,3 and dynamical4,5,6 magnetoelectric properties. In particular, type-II multiferroics exhibit an inversion-symmetry-breaking magnetic order that directly induces ferroelectric polarization through various mechanisms, such as the spin-current or the inverse Dzyaloshinskii–Moriya effect3,7. This intrinsic coupling between the magnetic and dipolar order parameters results in high-strength magnetoelectric effects3,8. Two-dimensional materials possessing such intrinsic multiferroic properties have been long sought for to enable the harnessing of magnetoelectric coupling in nanoelectronic devices1,9,10. Here we report the discovery of type-II multiferroic order in a single atomic layer of the transition-metal-based van der Waals material NiI2. The multiferroic state of NiI2 is characterized by a proper-screw spin helix with given handedness, which couples to the charge degrees of freedom to produce a chirality-controlled electrical polarization. We use circular dichroic Raman measurements to directly probe the magneto-chiral ground state and its electromagnon modes originating from dynamic magnetoelectric coupling. Combining birefringence and second-harmonic-generation measurements with theoretical modelling and simulations, we detect a highly anisotropic electronic state that simultaneously breaks three-fold rotational and inversion symmetry, and supports polar order. The evolution of the optical signatures as a function of temperature and layer number surprisingly reveals an ordered magnetic polar state that persists down to the ultrathin limit of monolayer NiI2. These observations establish NiI2 and transition metal dihalides as a new platform for studying emergent multiferroic phenomena, chiral magnetic textures and ferroelectricity in the two-dimensional limit.

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## Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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## Acknowledgements

Q.S., C.A.O. and R.C. acknowledge support from the US Department of Energy, BES under Award No. DE-SC0019126 (materials synthesis and characterization), the National Science Foundation under grant No. DMR-1751739 (optical measurements) and the STC Center for Integrated Quantum Materials, NSF grant No. DMR-1231319 (device fabrication). E.E., B.I. and N.G. acknowledge support from the US Department of Energy, BES DMSE (data taking and analysis) and Gordon and Betty Moore Foundation’s EPiQS Initiative grant no. GBMF9459 (instrumentation). J.K. and A.S.B. acknowledge NSF grant No. DMR-1904716 and the ASU Research Computing Center for high-performance computing resources. D.A. and S.P. acknowledge support by the Nanoscience Foundries and Fine Analysis (NFFA-MIUR Italy) project. P.B. and S.P. acknowledge financial support from the Italian Ministry for Research and Education through PRIN-2017 projects ‘Tuning and understanding Quantum phases in 2D materials—Quantum 2D’ (IT-MIUR grant No. 2017Z8TS5B) and ‘TWEET: Towards ferroelectricity in two dimensions’ (IT-MIUR grant No. 2017YCTB59), respectively. D.A., P.B. and S.P. also acknowledge high-performance computing systems operated by CINECA (IsC722DFmF, IsC80-Em2DvdWd, IsC88-FeCoSMO and IsB21-IRVISH projects) and computing resources at the Pharmacy Department, University of Chieti-Pescara, and thank L. Storchi for his technical support.

## Author information

Authors

### Contributions

Q.S. and R.C. conceived the project. Q.S. synthesized the NiI2 samples. Q.S. and C.A.O. performed the Raman and birefringence measurements supervised by R.C. E.E. and B.I. performed the SHG measurements supervised by N.G. T.T. and K.W. provided and characterized the bulk hBN crystals. D.A., A.S.B. and J.K. performed the first-principles calculations. P.B. and D.A. performed the MC simulations, and discussed the results with S.P. All authors contributed to the writing of the manuscript.

### Corresponding author

Correspondence to Riccardo Comin.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

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Nature thanks Masakazu Matsubara and the other, anonymous, reviewers for the peer review of this work. Peer reviewer reports are available.

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## Extended data figures and tables

### Extended Data Fig. 1 X-ray and electron diffraction of NiI2 crystals.

a, X-ray diffraction of a CVT-grown NiI2 single crystal along the c-axis. b, X-ray powder diffraction of CVT-grown NiI2. c, An optical image of a 7 nm PVD grown NiI2 flake transferred onto a SiNx membrane. d, The electron diffraction pattern of the PVD grown NiI2 flake shown in c, using a transmission electron microscope.

### Extended Data Fig. 2 Linear dichroism and birefringence-induced polarization rotation measurements in bulk NiI2.

a, Polarized microscopy image of bulk NiI2. The positions where the optical measurements were performed are labelled as Domain I-III. b, Comparison of the temperature-dependent birefringence-induced polarization rotation (top) and linear dichroism (bottom) on Domain I. c, Angular-dependent linear dichroism measurements from the three distinct domains identified in a. Radial lines indicate the crystallographic a-axes determined from the edges of the as-grown PVD sample. d, Schematics of the domains as identified from AD-LD measurements in c, denoting the local C2 axis orientation, the polar vector P and the in-plane component of the helimagnetic ordering vector Q.

### Extended Data Fig. 3 Wavelength-dependent Second Harmonic Generation of NiI2.

Rotational anisotropy SHG (RA-SHG), fits to nonlinear tensor elements and their temperature dependence on a single domain CVT grown bulk NiI2 using a–c, 826 nm laser, and d–f, 991 nm laser. The RA-SHG traces obtained with 826 nm can only be fit with a combination of electric dipole (ED) and magnetic dipole (MD) radiation, whereas the RA-SHG traces obtained with 991 nm only exhibit ED component. g, h, RA-SHG on PVD grown bulk NiI2 samples shows the same signatures as the CVT grown samples. i, SHG imaging of the PVD sample at 15 K. The red circle shows the single domain region where the RA-SHG was taken.

### Extended Data Fig. 4 Temperature-dependent polarized Raman spectra of bulk NiI2.

a, Raman data in the cross-polarized XY channel from 30 K to 300 K. b, Comparison of the cross-polarized (XY) and parallel-polarized (XX) channels at high and low temperature. c, Circularly polarized Raman spectra at 30 K on domain I and domain II regions for σ+/σ incident polarization (top) and the net ROA (σ+σ) (bottom).

### Extended Data Fig. 5 Angular Resolved Polarized Raman Spectroscopy (ARPRS) in cross-polarized (XY) configuration.

a, b, The ARPRS polar plots of the 31 cm−1 and 37 cm−1 modes appearing in the multiferroic phase. Neither agrees with a pure phonon or magnon mode, suggesting they may be consistent with electromagnons. c, d, The 80 cm−1 peak is composed of two phonons below TN,2, one at 79.9 cm−1 and the other at 80.2 cm−1. These closely-spaced phonon modes display out-of-phase modulation with respect to the incident linear polarization and both display an Eg symmetry with respect to the high-temperature $$R\bar{3}m$$ phase. e, f, The 120.8 cm−1 and 168.8 cm−1 are magnon modes. Red lines: ARPRS fits to the Raman tensors for different mode symmetries.

### Extended Data Fig. 6 Bulk photovoltaic effect (BPE) in bulk NiI2.

a, Optical image of the BPE device. A PVD grown bulk-like NiI2 flake was transferred across a sapphire gap, bridging two gold pads as electrodes. The electric field was applied between the electrodes and in a direction nearly parallel to the a-axis, while the magnetic field was applied perpendicular to the electric field in plane. b, The electric field dependence of the photocurrent at 30 K, in the multiferroic phase and at 100 K, in the paramagnetic phase, reveals the presence of a polarization-induced internal electric field the multiferroic phase. c, The position dependence of the photocurrent along the dashed line in a, under zero bias shows a major contribution of the photocurrent from the NiI2 between the electrodes. d, The temperature dependence of the zero-bias photocurrent shows a strong enhancement in the multiferroic phase. e, The external magnetic field increased the zero-bias photocurrent by 10–15%, which we ascribe to an increase of the electric polarization from magnetoelectric coupling. Linearly polarized 532 nm light (0.3 mW power) was used in the BPE measurement.

### Extended Data Fig. 7 Cross-polarization images of the bulk, 1- and 2-layer NiI2.

Temperature-dependent histogram plots of the polarization contrast images for a, bulk, c, 1-layer region and e, 2-layer region. The upper-left images in b, d, f show optical images of bulk, 1- and 2-layer NiI2 flakes, respectively. Subsequent images depict the temperature-dependent polarization contrast images for key temperatures. The raw cross-polarization images at various temperatures across the multiferroic transition provide signatures of the domain dynamics, explaining the spatial inhomogeneity of the transition temperature identified through polarization rotation measurements. The domain texture vanishes in d, 1-layer near 20 K, and in f, 2-layer near 35 K, consistent with polarization rotation measurements (Fig. 2d).

### Extended Data Fig. 8 Temperature dependent Second Harmonic Generation imaging of the single-layer NiI2 crystals.

a, b, Optical images of the region where the SHG imaging was performed. c, Integrated SHG counts on three single-layer NiI2 crystals show a transition around 20 K, which is consistent with the polarization rotation measurement. d, Temperature dependent SHG imaging of the rectangular region in a using 780 nm excitation. e, Temperature dependent SHG imaging of the region in b using 991 nm laser. Colorbar: SHG counts.

### Extended Data Fig. 9 Temperature dependent Raman Spectroscopy of two- and three-layer NiI2 in cross-polarized (XY) configuration.

The soft modes at around 38 cm−1 in a, 2-layer and b, 3-layer built up below 25 K and 35 K respectively, which are consistent with the transition temperature measured from polarization rotation and SHG.

### Extended Data Fig. 10 Atomic Force Microscopy and additional polarization rotation measurements on few-layer NiI2 crystals.

a–c, Wide-field optical images of one- to four-layer NiI2 samples used in the optical measurements. d–h, Corresponding AFM maps of the region shown in the optical images. i–k, Temperature dependent polarization rotation measurements on one- to four-layer samples in different domain regions.

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Song, Q., Occhialini, C.A., Ergeçen, E. et al. Evidence for a single-layer van der Waals multiferroic. Nature 602, 601–605 (2022). https://doi.org/10.1038/s41586-021-04337-x

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