Evidence for multiferroicity in single-layer CuCrSe2

Multiferroic materials, which simultaneously exhibit ferroelectricity and magnetism, have attracted substantial attention due to their fascinating physical properties and potential technological applications. With the trends towards device miniaturization, there is an increasing demand for the persistence of multiferroicity in single-layer materials at elevated temperatures. Here, we report high-temperature multiferroicity in single-layer CuCrSe2, which hosts room-temperature ferroelectricity and 120 K ferromagnetism. Notably, the ferromagnetic coupling in single-layer CuCrSe2 is enhanced by the ferroelectricity-induced orbital shift of Cr atoms, which is distinct from both types I and II multiferroicity. These findings are supported by a combination of second-harmonic generation, piezo-response force microscopy, scanning transmission electron microscopy, magnetic, and Hall measurements. Our research provides not only an exemplary platform for delving into intrinsic magnetoelectric interactions at the single-layer limit but also sheds light on potential development of electronic and spintronic devices utilizing two-dimensional multiferroics.

Despite recent advancements in 2D ferromagnetic and ferroelectric materials, achieving 2D multiferroicity that integrates both ferromagnetic and ferroelectric orders remains a formidable challenge.Even in three-dimensional (3D) materials, multiferroicity is rare, as the origins of magnetism and ferroelectricity are often mutually exclusive 2 .There are a few experimental instances of 2D multiferroicity in few-layer materials, including p-doped SnSe 28 and ε-Fe2O3 29 .However, these materials, typically thicker than 3 nm, exhibit significantly suppressed multiferroic order as their thickness decreases.Recently, Song et al. reported a type-Ⅱ multiferroic ground state in single-layer NiI2, identified through various optical techniques 30 .Nonetheless, the low transition temperature (T=21 K) and poor air stability of NiI2 pose serious impediments to its practical application.Furthermore, the all-optical characterization approach used to determine multiferroicity in single-layer NiI2 has been met with skepticism 31 , and more direct measurements such as piezo-response force microscopy (PFM) and magnetic measurements are greatly awaited.Another significant advancement in the pursuit of single-layer multiferroicity is the fabrication of one-unitcell-thick multiferroic Cr2S3 32 ; however, its 2D ferroelectric properties are attributed to interfacial modulation.Hence, the quest for a single material that exhibits intrinsic 2D multiferroicity remains a formidable challenge.
In this work, we focus on the non-van der Waals material CuCrSe2, which has garnered significant interest due to its excellent thermoelectric properties [33][34][35] .We provide compelling evidence for the multiferroicity in single-layer CuCrSe2.This material demonstrates out-of-plane polarization at room temperature, with a large coercive field, as substantiated by various techniques including second harmonic generation (SHG), PFM, cross-section high-resolution scanning transmission electron microscopy (STEM), and electrical transport measurements.Ferromagnetism with a Curie temperature of approximately 120 K was confirmed by magnetic measurements.
Further analysis reveals that the ferroelectricity in CuCrSe2 originates from the displacements of interlayer Cu atoms, leading to an orbital shift in Cr atoms of the CrSe2 layers.This orbital rearrangement of Cr atoms plays a critical role in stabilizing the ferromagnetic coupling.

Crystal structure and chemical exfoliation of single-layer CuCrSe2
CuCrSe2 crystallizes in the R3m space group, with alternating layers of CrSe2 and Cu atoms stacked along the c-axis 36 , as denoted by the labels A, B, and C in Fig. 1a.This structure was confirmed by the x-ray diffraction measurements (see Supplementary Fig. 1).Within each CrSe2 layer, the Cr 3+ cation is octahedrally coordinated by six Se 2-ions, as illustrated in Fig. 1a.Although the unit cell of bulk CuCrSe2 comprises three Cu sheets and three CrSe2 layers, we define single-layer (1L) CuCrSe2 as consisting of two CrSe2 layers and one Cu layer, which are strongly covalently bonded to each other, as illustrated in Fig. 1b.The addition of one more CuCrSe2 layer includes one more CrSe2 layer and one Cu layer, respectively.Although the chemical formula should more accurately be denoted as CuCr2Se4, we continue to use "1L CuCrSe2" for simplicity and to avoid confusion, given that CuCrSe2 is the chemical formula of the bulk crystal.Notably, the vertical distances between Cu and Se atoms differ (d1≠d2), leading to a vertical (downward) electric polarization, PZ.This vertical polarization induces shifts in the original Cr-d orbitals in the Cr 3+ configuration, primarily eg and t2g resulting from the octahedral crystal field splitting, as depicted in Fig. 1c.Specifically, the t2g orbitals of one Cr 3+ ion experience a downward energy shift, while the eg orbitals of another undergo an upward shift.Consequently, the energy difference eg(Cr1)-t2g(Cr2) diminishes, thereby enhancing the ferromagnetic coupling within the material 37 .In this context, a single layer of CuCrSe2 is intrinsically multiferroic, as its electric polarization is intimately linked to its magnetic properties.
Additionally, single-layer CuCrSe2 exhibits significant hole doping, which effectively increases the carrier density at the Fermi level, favoring both intralayer and interlayer ferromagnetic couplings.
Through redox-controlled chemical exfoliation 38 , we selectively removed partial Cu + ions at the interface while tetraoctylammonium intercalation led to a marked increase in interlayer spacing.This process ultimately facilitated the fabrication of ultrathin 2D CuCrSe2 nanosheets from high-quality single crystals (for further details, see Methods).Figure 1d displays a typical optical image of such exfoliated CuCrSe2 nanoflakes, where the monolayer region can be distinguished by its minimal optical contrast.AFM measurements were conducted on this 1L flake, as depicted in Fig. 1e, revealing a pristine surface with a step height of approximately 1.6 nm relative to the substrate.This measured thickness corresponds to 1L CuCrSe2, which is slightly larger than the theoretical value of ~1.3 nm.Similar overestimations have been reported for many other 2D materials [39][40] .Subsequent Raman spectra were obtained for the exfoliated CuCrSe2 nanoflakes (see Supplementary Fig. 2).Analogous to CuCrS2 41 , two distinct Raman modes, E (~146.2 cm -1 ) and A1 (~237.7 cm -1 ), emerge, corresponding to in-plane and out-of-plane vibrational modes, respectively.It is noteworthy that these Raman modes are nearly undetectable in the single-layer limit.

Out-of-plane ferroelectricity in ultrathin CuCrSe2
As previously noted, the occupation of Cu + ions in CuCrSe2 induces a spontaneous electric polarization.This structural asymmetry is detectable through nonlinear optical techniques such as SHG [42][43] .For our experiments, we employed a 1064 nm picosecond laser as the excitation source based on the backscattering geometry and observed a robust emission peak centered at 532 nm, as shown in in Fig. 2a.This wavelength is precisely half of the incident wavelength, thereby underscoring the symmetry-breaking nature of the CuCrSe2 lattice.Subsequent polarization-dependent SHG measurements in the parallel-polarized configuration yielded a six-fold symmetry pattern, as shown in Fig. 2b.This result is consistent with the crystalline structure of CuCrSe2 and fits well with the cosine square formula.In summary, the SHG response of CuCrSe2 nanoflakes confirms its intrinsic non-centrosymmetric nature, fulfilling the basic criterion for ferroelectricity.
To validate the presence of room-temperature out-of-plane ferroelectricity in ultrathin CuCrSe2 flakes, we conducted a comprehensive set of PFM measurements.
The experimental schematic for our PFM setup is illustrated in Fig. 2c, where a silicon chip served as a conductive substrate to mitigate charge accumulation.Typically, applying a minor voltage to the AFM tip induces uniform dipole moment orientation in ferroelectric materials under the influence of a vertical electric field 44 .We recorded offfield phase and amplitude loops for bilayer CuCrSe2, single-layer CuCrSe2, and the silicon substrate, as depicted in Fig. 2d-f.For both the bilayer and single-layer CuCrSe2 flakes, we observed a distinct hysteresis in the phase loop accompanied by a 180° phase switch, along with a well-defined butterfly-shaped amplitude evolution.In contrast, no piezo-response signal was detected for the bare silicon substrate.The local PFM switching spectra corroborate the out-of-plane ferroelectricity inherent in this system.Moreover, the coercive voltage is found to lie in the range of 4-5 V, which exceeds that of many conventional 2D ferroelectrics like In2Se3 (1.5 V) 45 , SnS (2.0 V) 46 , and MoS2/WS2 heterobilayer (3.0 V) 47 .This suggests that CuCrSe2 possesses a more stable ferroelectric state characterized by a higher energy barrier separating the two distinct polarization states.In addition, compared with conventional layered 2D ferroelectrics, the emergence of room-temperature ferroelectricity in non van der Waals CuCrSe2 broadens the spectrum of ferroelectric materials.
To rule out alternative mechanisms that could generate ferroelectric artifacts, such as Cu + ion migration, we analyzed the direct current voltage (VDC) dependent phase curve 48 .The results are summarized in Fig. 2g.In an intrinsic ferroelectric material, when the maximum sweeping VDC surpasses the coercive voltage, the switching threshold voltage remains largely consistent, exhibiting only minor variations.
Conversely, when the maximum VDC falls below the coercive voltage, polarization switching is inhibited, and the PFM loops vanish.This behavior precisely aligns with our observations for 1L CuCrSe2, as shown in Fig. 2g.In contrast to ion-mediated piezo-responses observed in materials like TiO2 thin films 49 , CuCrSe2 exhibits structure-mediated spontaneous polarization.In essence, this confirms the material's robust 2D ferroelectricity, surviving to the single-layer limit.
We corroborate the ferroelectric properties via PFM domain writing and reading experiments.For a 1L CuCrSe2 nanoflake on a silicon substrate, we selected a flat region (Fig. 1e) and poled the area with opposite biases of +10 V and -10 V, in accordance with the pattern depicted in Fig. 2h.After domain writing, a distinct "boxin-box" pattern emerges in both the PFM amplitude (Fig. 2i) and phase images (Fig. 2j), revealing a marked 180° phase contrast between the two domains (as further verified in Supplementary Fig. 3).Notably, this domain pattern remains clearly identifiable even after one day and one week (see Supplementary Fig. 4), substantiating the non-volatile nature of the material's ferroelectricity.Furthermore, the antiparallel charge polarization manifests as a discernible contrast in both the electrostatic force microscopy (EFM) amplitude (Fig. 2k) and phase images (Fig. 2l).

STEM measurements
Having demonstrated the robust out-of-plane ferroelectricity in CuCrSe2, we further elucidate the underlying physical origins through STEM investigations.As suggested by prior theoretical calculations 37 , both bulk and single-layer CuCrSe2 possess two stable ferroelectric configurations: P1 and P2.These configurations can be switched between each other through electrical field poling, as depicted in Fig. 3b.The principal distinction between the P1 and P2 polarization states lies in the occupancy of interlayer Cu atom sites, which are designated as "Cu-1" and "Cu-2", respectively 50 .Intriguingly, we are able to capture both tetrahedron sites using cross-section high-resolution STEM in different regions of the CuCrSe2 sample along the [100] zone axis, as illustrated in Fig. 3a and Fig. 3c.Here the sample shows high chemical homogeneity, as evidenced by the energy-dispersive spectroscopy (EDS) mapping in Fig. 3d, clearly revealing the Cu, Cr and Se element distributions.Each of these asymmetric configurations gives rise to a spontaneous polarization.Thus, the ferroelectric nature of CuCrSe2 can be comprehensively understood via the traditional double-well potential model 51 .This model also explains the relatively high energy barrier for ferroelectric switching (Fig. 3b), which allows the ferroelectric state to be stable at room temperature.When Cu atoms transition from the "Cu-1" site to the adjacent "Cu-2" site, the charge center has vertical displacements without a corresponding movement in the CrSe2 layers.Therefore, CuCrSe2 exhibit the out-of-plane ferroelectric switching behavior.
The data indicate a pronounced increase in magnetization below 120 K under a modest external magnetic field (H=50 Oe), signifying a phase transition from a paramagnetic to ferromagnetic state with a Curie temperature (Tc) of approximately 120 K.In the ZFC magnetization curve, a noticeable cusp is evident after its divergence from the FC curve.This feature can be attributed to the fact that the applied external magnetic field is less than the material's coercive field.Meanwhile, such a phenomenon might be ascribed to the residual antiferromagnetic coupling in the sample.Additionally, fielddependent magnetization measurements (Fig. 4b) for CuCrSe2 films reveal a distinct magnetic hysteresis loop below the Tc.At a temperature of 2 K, the coercive field is approximately 600 Oe, indicative of a robust ferromagnetic ordering.
We further performed Hall measurements on ultrathin CuCrSe2 flakes to validate its intrinsic ferromagnetism.As displayed in Fig. 4d, the single-layer sample exhibits anomalous Hall effect (AHE) with a large hysteresis window, indicating that the magnetic order can persist down to monolayer with a strong in-plane magnetic anisotropy 52 .For bilayer and quadrilayer CuCrSe2, the AHE is still observed but with a slightly decreased coercive field.We noticed that only linear Hall effect exists in the trilayer (see Supplementary Fig. 8), which indicates an odd-even-layer-dependent ferromagnetism in CuCrSe2.
Although bulk CuCrSe2 exhibits an antiferromagnetic ground state owing to interlayer antiferromagnetic coupling 53 , single-layer CuCrSe2 favors a ferromagnetic state.As elucidated in Fig. 1b and 1c, the Cu + ions contribute not only to vertical polarization but also induces an orbital shift in Cr atoms.This orbital shift effectively augments the ferromagnetic coupling between the adjacent Cr layers of CrSe2 in singlelayer CuCrSe2 structure.Consequently, this leads to the emergence of a naturally occurring multiferroic state in this material.

Discussion
In summary, we have verified the presence of intrinsic 2D multiferroicity in singlelayer CuCrSe2 using a comprehensive suite of experimental techniques, including SHG, PFM, STEM, and magnetic measurements.Importantly, the transition temperatures for both ferroelectricity and ferromagnetism are notably high, exceeding room temperature and 120 K, respectively.These findings represent a seminal advancement in achieving intrinsic 2D multiferroicity in a single-layer material at comparatively elevated temperatures, thus paving the way for the potential development of advanced multiterminal spintronic chips and magnetoelectric devices.

Methods
Growth of CuCrSe2 single crystals.Single crystals of CuCrSe2 were synthesized using a chemical vapor transport (CVT) method starting from polycrystalline powders.Polycrystalline CuCrSe2 was prepared by a solid-state reaction in which a stoichiometric mixture of high purity Cu, Cr, and Se powders was sealed in an evacuated quartz tube and sintered at 1050 ℃ for 40 h.The furnace was then heated to 1200 ℃ and kept for several minutes, followed with rapid quenching to obtain pure phase of CuCrSe2.The polycrystalline CuCrSe2 was then grinded into fine powder and sealed in an evacuated quartz tube together with a small amount of CrCl3 as a transport agent.The tube was heated on a two-zone tube furnace in a temperature gradient of 1050 ˚C at the hot end and 800 ˚C at the cold end for 200 hours.Rapid quenching with cold water was also employed and single crystals of CuCrSe2 were obtained.
Preparation of CuCrSe2 nanosheets.CuCrSe2 nanosheets were exfoliated from bulk CuCrSe2 single crystals using a redox-controlled electrochemical exfoliation method.Specifically, a CuCrSe2 crystal was anchored between two titanium plates, serving as the cathode, while a platinum electrode was employed as the anode.The electrolyte for