Observation of room-temperature multiferroicity with strong magnetoelectric coupling in hafnia thin films

Abstract

HfO₂-based ferroelectrics have emerged as promising candidates for next-generation information devices due to their excellent compatibility with complementary metal oxide semiconductor technology. However, achieving room-temperature multiferroicity in single-phase HfO₂-based materials remains a rewarding yet challenging goal. Here, we report the discovery of room temperature multiferroicity in single-phase Cr-doped HfO₂ films. We demonstrate a direct correlation between ferroelectric and ferromagnetic orders; films with stronger ferromagnetism exhibit enhanced ferroelectricity. Crucially, the application of external magnetic fields induces a significant boost in both ferroelectric polarization and piezoresponse amplitude. A giant magnetoelectric coupling coefficient of ~100 Vcm^-1Oe^-1 is obtained, surpassing those of most previously reported single-phase multiferroic materials at room temperature. Our results not only establish Cr-doped HfO₂ films as a promising platform for exploring emergent multiferroic phenomena but also pave the way for a new class of silicon-compatible magnetoelectric devices.

Achieving single-phase room-temperature multiferroicity is a long-standing challenge. The authors discover that Si-compatible Cr-doped HfO₂ films are multiferroic with strong magnetoelectric coupling between ferroelectric and ferromagnetic orders.

Introduction

Multiferroic materials—systems that simultaneously exhibit two or more ferroic orders (ferroelectricity, (anti-)ferromagnetism, ferroelasticity) with mutual coupling —have attracted sustained interest for both fundamental condensed-matter physics and potential device applications such as nonvolatile memories, energy-efficient logic, and neuromorphic computing systems^1–3. Flourished in the last two decades, plenty of works provided multiple routes to achieving multiferroicity, with demonstration in diverse material systems including hexaferrites, rare earth orthoferrites, and van der Waals compounds^4–7. However, the realization of intrinsic single-phase multiferroics that operate at room temperature remains an enduring challenge, primarily because of the conflicting electronic and symmetry requirements: strong ferroelectric polarization typically favors closed-shell or nominal “empty” d orbitals and broken spatial inversion symmetry, whereas robust ferromagnetism relies on partially filled d orbitals and broken time reversal symmetry¹.

Recently, hafnium oxide (HfO₂)-based ferroelectrics have emerged as a transformative material platform. Since the discovery of ferroelectricity in 2011, hafnia has attracted significant attention owing to its scalability and compatibility with CMOS technology^8–12. Ferroelectricity in HfO₂-based materials arises from a metastable non-centrosymmetric orthorhombic phase stabilized by factors such as doping, oxygen vacancy, strain^13–17. In contrast to conventional perovskite oxides, where ferroelectricity is primarily governed by a cation off-centering mechanism, the ferroelectricity in HfO₂-based materials is mainly associated with oxygen anion displacements^13,18. This unconventional origin provides a unique opportunity to engineer multiferroicity in HfO₂-based systems beyond traditional ferroelectric perovskites.

Prior to the discovery of ferroelectricity, efforts to introduce ferromagnetism into dielectric HfO₂ through chemical doping or defect engineering had already been pursued^19–21. Both experimental and theoretical studies reported signatures of room temperature ferromagnetism in HfO₂ with transition-metal and rare-earth dopants or with controlled oxygen vacancies, although the microscopic origin of ferromagnetism is still under debate^19–25. On the other hand, the chemical dopants or oxygen vacancies have been shown to facilitate stabilization of the ferroelectric orthorhombic phase^13,26,27. More recently, theoretical works have proposed that the selective dopants (such as Nb, Ta and V) may enable the coexistence of ferroelectricity and ferromagnetism in doped HfO₂^28,29. These points together establish proof-of-principle routes toward realizing single-phase multiferroicity in hafnia-based systems. Nevertheless, the multiferroicity in HfO₂-based materials remains an open question.

In this work, we demonstrate room temperature multiferroicity in single-phase Cr-doped HfO₂ thin films. Cr dopants substantially enhance ferroelectricity by effectively stabilizing the orthorhombic phase, while simultaneously inducing robust ferromagnetism with a high Curie temperature exceeding 400 K. Comprehensive investigations of the ferroelectric and magnetic properties in Cr-doped HfO₂ films reveal a positive correlation between ferromagnetism and ferroelectricity. The ferroelectric polarization and piezoresponse amplitude are enhanced by applying magnetic field at room temperature, providing compelling evidence of magnetoelectric coupling between ferroelectricity and ferromagnetism. Room temperature multiferroicity discovered in HfO₂-based films therefore opens a new area to explore the magnetoelectric functionality integrated into silicon electronics.

Results

Structural characterizations

Cr-doped HfO₂ films with varying Cr concentration (x%, x = 0, 5, 10, 20) and different thicknesses (Supplementary Fig. S1) were deposited on (001)-oriented Nb:SrTiO₃ (NSTO) or SrTiO₃ (STO) substrates with a La_0.67Sr_0.33MnO₃ (LSMO) buffer layer by the pulsed laser deposition (see details in Methods). Figure 1a shows the X-ray diffraction (XRD) θ−2θ patterns of ~7.5 nm-thick Cr(x%):HfO₂ films (x = 0, 5, 10, 20). The dominant ferroelectric orthorhombic phase is identified by a diffraction peak near 30.2° corresponding to the (111) plane reflection. While undoped HfO₂ exhibits additional peaks at 2θ ~ 28.2° and 34.3°, corresponding ($\overline{1}$11) and (020) planes of the non-ferroelectric monoclinic phase. With Cr doping, the monoclinic phase is largely suppressed. The stabilization of the ferroelectric orthorhombic phase is closely associated with Cr concentration and film thickness (Supplementary Note S1). In Cr-doped HfO₂ films, distinct Laue oscillations are observed around the orthorhombic phase peaks, indicative of high crystalline quality and epitaxial growth. This conclusion is further supported by the narrow full width at half maximum (FWHM) of the orthorhombic phase peak and the smooth surface morphology (Supplementary Figs. S2 and S3).

Fig. 1. Structural characterization of Cr-doped HfO₂ films.

a XRD θ−2θ patterns of ~7.5 nm-thick Cr(x%):HfO₂ films. b Pole figure around the (111) peak of ~10 nm-thick Cr(10%):HfO₂ film at 2θ = 30.2°. c 2θ scans of 12 diffraction points (χ = 71°) extracted from pole figure, and the out-of-plane (111) plane (OOP, χ = 0°). The black and red dashed lines denote the peak positions of OOP (111) and (002) planes, respectively. d Cross-sectional HAADF-STEM image of Cr(10%):HfO₂ film (~7.5 nm), viewed along [1$\overline{1}$0] zone axis. e Plan-view HAADF-STEM image of Cr(10%):HfO₂ film viewed along [111] zone axis. The insets in (d, e) are the FFT patterns of red square regions.

To gain a deeper understanding of the phase structure of Cr(10%):HfO₂ film, the pole figure measurement was performed. Based on the XRD patterns (Fig. 1a), the Cr(10%):HfO₂ film is oriented along [111] direction; accordingly, three additional reflections, ($\overline{1}$11), (1$\overline{1}$1) and (11$\overline{1}$), are expected to appear at a chi angle χ = 71° from the out-of-plane direction, with their azimuthal angles (φ) separated by 120°. As shown in Fig. 1b, 12 clear diffraction spots are observed at the angle χ = 71°, corresponding to the projections of ($\overline{1}$11), (1$\overline{1}$1) and (11$\overline{1}$) peaks. The sharp spot at χ = 0° originates from the (001)-oriented NSTO substrate. The diffraction peaks can be grouped into four sets, highlighted in different colors (blue, green, orange, and brown). This suggests Cr(10%):HfO₂ film contains four crystallographic orthorhombic phase domains with distinct in-plane orientations, matching with the fourfold symmetry of the (001)-oriented NSTO substrate. The corresponding 2θ scans of the 12 diffraction spots (χ = 71°) are shown in Fig. 1c, which exhibit a slight shift toward larger angles compared to the reflection position of the (111) peak, indicating a small rhombohedral distortion of the orthorhombic phase structure in Cr(10%):HfO₂ film.

To further elucidate the microstructure and verify the epitaxial growth nature of Cr(x%):HfO₂ films, comprehensive high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) investigations were carried out. Figure 1d presents the cross-sectional HAADF-STEM image of the 7.5 nm-thick Cr(10%): HfO₂ film viewed along the [1$\overline{1}$0] zone axis, which reveals a well-defined interface between the Cr:HfO₂ film and LSMO buffer layer (Supplementary Fig. S4). The orthorhombic phase in Cr(10%):HfO₂ film was further confirmed by the fast Fourier transform (FFT) patterns (the inset of Fig. 1d). In addition, the microstructures of undoped HfO₂ and Cr(20%):HfO₂ films were also characterized by HAADF-STEM. As illustrated in Supplementary Fig. S4, sharp interfaces were observed between the HfO₂-based film and the LSMO layer. Undoped HfO₂ film exhibits a mixture of orthorhombic and monoclinic phases, while the Cr(20%):HfO₂ film shows an orthorhombic phase. Figure 1e shows a plan-view HAADF-STEM image of freestanding Cr(10%):HfO₂ film along the [111] zone axis, and reveals the orthorhombic domains with distinct in-plane orientations, which is in agreement with the pole figure results. For comparison, the plan-view image of the undoped HfO₂ film is shown in Supplementary Fig. S5, where the crystalline domain size is notably smaller than that of the Cr(10%):HfO₂ film. These observations indicate that Cr doping is critical for stabilizing the ferroelectric orthorhombic phase and promoting the growth of larger domains.

Room temperature ferroelectricity in Cr-doped HfO₂ films

To verify the ferroelectricity of Cr(x%):HfO₂ films, the ferroelectric polarization versus electric field (P-E) loops were measured using the positive-up-negative-down (PUND) method (Supplementary Fig. S6), which effectively eliminates non-ferroelectric contributions such as leakage current and paraelectric response. Figure 2a shows well-defined ferroelectric P-E loops for ~11.7 nm-thick Cr(x%):HfO₂ films with different Cr doping concentrations, demonstrating robust ferroelectricity. The ferroelectric polarization exhibits a non-monotonic dependence on doped Cr concentration, initially increasing and then decreasing, with a maximum remanent polarization (2P_r ~ 30 µC/cm²) at a doping level of 10%. Cr doping strongly influences not only the polarization but also the coercive field (E_c). Figure 2b, c summarize 2P_r and E_c as a function of Cr concentration for different film thicknesses, and the corresponding P-E loops are shown in Supplementary Fig. S7. Both 2P_r and E_c reach their maximum values at 10% Cr doping for different thicknesses. Such a dopant concentration dependence of polarization has been identified in different element-doped HfO₂ films, which is mainly attributed to the stabilization of the orthorhombic phase^13,30,31. Furthermore, E_c exhibits a consistent positive correlation with 2P_r values, which may reflect the intrinsic coupling between polarization dynamics and domain reversal processes in ferroelectric systems³². Importantly, the leakage current density remains nearly unchanged with varying Cr concentration (Supplementary Fig. S8), indicating the good insulating characteristics of Cr-doped HfO₂ films.

Fig. 2. Ferroelectric properties of Cr doped-HfO₂ films.

a P-E loops for 11.7 nm-thick Cr(x%):HfO₂ films (x = 0, 5, 10, 20). Cr-doping concentration dependence of b remanent polarization 2P_r and c coercive field E_c for Cr(x%):HfO₂ films with different thicknesses. d 2P_r and E_c as a function of film thickness (t) for Cr(10%):HfO₂ film. The dashed line denotes the scaling E_c ~ t^−2/3. e Phase-contrast PFM images and (f) PFM amplitude (blue) and phase (red) hysteresis loops for the Cr(10%):HfO₂ film (~9.5 nm).

Obviously, the polarization and coercive field are closely correlated with film thickness. Figure 2d summarizes the thickness dependence of 2P_r and E_c for Cr(10%):HfO₂ films, with the corresponding ferroelectric hysteresis loops shown in Supplementary Fig. S8a. The increase of polarization with decreasing film thickness may be due to the enhanced stabilization and distortion of the orthorhombic phase in thinner films^10,33. The variation of E_c with film thickness (t) approximately follows the E_c ~ t^−2/3 scaling (Janovec-Kay-Dunn law), a behavior commonly observed in ferroelectric perovskite and epitaxial HfO₂-based films^34–36. The thickness dependence of ferroelectricity in Cr-doped HfO₂ films involves a competition among various factors, such as ferroelectric phase ratio, strain relaxation and Cr doping (Supplementary Note S2)^13,30. Furthermore, the ferroelectricity of Cr-doped HfO₂ films was characterized by piezoresponse force microscopy (PFM). As shown in Fig. 2e, the phase image on Cr(10%):HfO₂ film exhibits well-defined regions with 180° phase contrast switched under positive/negative applied bias, confirming the presence of ferroelectric polarization. The corresponding amplitude image reveals clear domain walls at the boundaries between antiparallel domains (Supplementary Fig. S9), indicative of stable bipolar remanent polarization states. Notably, the unpoled regions show the same phase contrast as negatively poled regions, indicating spontaneous polarization in Cr-doped HfO₂ films. Along with phase-contrast imaging, complementary local PFM switching spectroscopy further demonstrates the robust ferroelectricity in Cr-doped HfO₂ films, as revealed by the square-like phase hysteresis loop and butterfly-shaped amplitude loop (Fig. 2f).

Room temperature ferromagnetism in Cr-doped HfO₂ films

Next, we turn to explore the ferromagnetism in Cr-doped HfO₂ films. Figure 3a, b show the room temperature in-plane (IP) and out-of-plane (OOP) magnetizations versus magnetic field (M-H) hysteresis loops of Cr(x%):HfO₂ films with different Cr doping levels, respectively. The observed ferromagnetic hysteretic behaviors demonstrate the emergence of room-temperature ferromagnetism in Cr-doped HfO₂ films, as clearly evidenced by the magnified view of the low-field region in the M-H curves (Supplementary Fig. S10). Compared with undoped HfO₂, the values of magnetization for the Cr-doped HfO₂ films are clearly enhanced by Cr doping, as shown in Supplementary Fig. S11. With increasing Cr content, the magnetizations of Cr-doped HfO₂ films initially increase and then decrease, suggesting the ferromagnetism is strongly influenced by the dopant concentration. As summarized in Fig. 3c, both saturated magnetization M_s and coercive field H_c exhibit a non-monotonic dependence on Cr doping, with the Cr(10%):HfO₂ film showing the most pronounced ferromagnetism. This non‑monotonic trend contradicts the expectation for extrinsic origins of ferromagnetism where higher concentrations of magnetic-ion clusters or induced defects would lead to a stronger ferromagnetism. Additionally, at low Cr-doping concentrations (0%, 5%, and 10%), the in-plane M_s exceeds the out-of-plane M_s, whereas a larger out-of-plane M_s is observed at a higher concentration (20%), suggesting a doping-induced change in magnetic anisotropy.

Fig. 3. Ferromagnetic properties of Cr-doped HfO₂ films.

a In-plane (IP) and b out-of-plane (OOP) magnetization versus magnetic field (M-H) curves for ~11.7 nm-thick Cr(x%):HfO₂ films (x = 0, 5, 10, 20) and amorphous Cr(10%):HfO₂ film, measured at 300 K. c Saturated magnetization (M_s) and coercive field (H_c) as a function of Cr-doping concentration for Cr(10%):HfO₂ film. d IP and OOP M_s and E_c measured at 300 K for different thickness Cr(10%):HfO₂ films. e IP and OOP magnetization versus temperature (M-T) curves of Cr(10%):HfO₂ film measured at zero-field-cooled (ZFC) and field-cooled (FC) modes. f Temperature dependence of M_s and H_c for Cr(10%):HfO₂ film, extracted from M-H curves at different temperatures.

As discussed above, the Cr(10%):HfO₂ film exhibits both optimized ferroelectric properties and the strongest ferromagnetism. The parallel trends of ferroelectricity and ferromagnetism with varying Cr concentration suggest a close interplay between the two ferroic orders. To further substantiate this correlation, we conducted the following two studies: (1) A non-ferroelectric amorphous Cr(10%):HfO₂ film (~11.7 nm) was synthesized, and its amorphous nature was confirmed by the XRD pattern as depicted in Supplementary Fig. S1d. Contrary to the crystallized film, room temperature ferromagnetism is absent in the amorphous film (Fig. 3a, b). (2) Magnetization measurements of thicker films (20.3 and 33.4 nm) revealed a pronounced suppression of ferromagnetism (Fig. 3d and Supplementary Fig. S12). A detailed analysis of the XRD pattern indicated that the non-ferroelectric monoclinic phase appears in these thicker films, coinciding with diminished ferroelectricity. Collectively, these results provide evidence for the coupling between ferroelectricity and ferromagnetism in Cr-doped HfO₂ films.

To further study the ferromagnetic behavior, the temperature dependence of magnetization was investigated. Figure 3e presents the temperature dependences of IP and OOP magnetizations under zero-field-cooling (ZFC) and field-cooling (FC) conditions. Notably, ferromagnetic ordering persists beyond 400 K, suggesting a high Curie temperature (T_C) for Cr-doped HfO₂ films. A kink feature observed in the ZFC M-T curves at low temperatures may indicate the presence of a spin glass state³⁷, which becomes smeared when measured at a higher magnetic field (Supplementary Fig. S13). The M-H loops of Cr(10%):HfO₂ film recorded at different temperatures reveal that both saturated magnetization M_s and coercive field H_c decrease as the temperature increases (Fig. 3f and Supplementary Fig. S14). For comparison, the IP and OOP M-H loops of undoped HfO₂ film at different temperatures were also measured (Supplementary Fig. S15). The non-zero ferromagnetic response in undoped HfO₂ film is primarily attributed to intrinsic point defects, specifically oxygen vacancies, which can induce localized magnetic moments by creating unpaired electrons or modulating the electronic structure (Supplementary Note S3)^19,20. The saturated magnetization (M_s) and remanent magnetization (M_r) values are systematically summarized in Supplementary Fig. S15e, f. The magnetization of Cr(10%):HfO₂ film consistently exceeds that of the undoped HfO₂ film across the entire measured temperature range, which demonstrates that ferromagnetism is significantly enhanced with Cr doping.

Coupling of ferroelectricity and ferromagnetism

Having established the coexistence of room-temperature ferroelectricity and ferromagnetism in Cr-doped HfO₂ films, we next investigate their magnetoelectric coupling, which fundamentally arises from the interplay between these two ferroic orders. As a characteristic probe of ferroelectricity, the ferroelectric polarization (P-E) loops of Cr-doped HfO₂ films were measured under external magnetic fields. Meanwhile, ferroelectric PbZr_0.52Ti_0.48O₃ (PZT) films without ferromagnetism were also characterized under the same conditions for comparison. Figure 4a shows the P-E loops of the Cr(10%):HfO₂ film measured without and with an in-plane magnetic field of 0.4 T. The application of a magnetic field enhances the ferroelectric polarization of Cr(10%):HfO₂ film, whereas the polarization of PZT film remains nearly unchanged (Supplementary Fig. S16a). To quantify this effect, the variation in remanent polarization (ΔP_r/P_r(H = 0), normalized by its value at 0 T) is plotted as a function of applied magnetic field, as shown in Fig. 4b (also see Supplementary Note S4). Cycling the in-plane magnetic field between 0 T and 0.4 T results in periodic variations of remanent polarization for Cr(10%):HfO₂ film. In contrast, the remanent polarization of the PZT film is insensitive to the magnetic field. At each fixed magnetic field, the P-E loops were repeatedly measured multiple times (Supplementary Figs. S17 and S18). In addition, similar polarization enhancement was observed under out-of-plane magnetic fields (Supplementary Fig. S19a). Furthermore, measurements performed under larger in-plane and out-of-plane magnetic fields of 2 T further confirm the magnetic field control of ferroelectric polarization (Supplementary Fig. S19b, c). The coercive field remains essentially unaffected by the applied magnetic field (Supplementary Fig. S19d). These results unambiguously demonstrate that ferroelectric polarization in Cr(10%):HfO₂ films is enhanced by magnetic fields, in sharp contrast to PZT films.

Fig. 4. Coupling of ferroelectricity and ferromagnetism in Cr-doped HfO₂ films.

a P-E loops of Cr(10%):HfO₂ film measured without and with an IP magnetic field of 0.4 T. The inset shows the enlarged view of the P-E loops. b Magnetic field induced variation of remanent polarization P_r (∆P_r(H)/P_r(H = 0), normalized by its value at 0 T) of Cr(10%):HfO₂ (upper panel) and PZT (bottom panel) films. The presented PFM amplitude curve is the result of averaging ten independent measurements (as shown in Fig.S20). c PFM amplitude loops of Cr(10%):HfO₂ measured without and with an IP magnetic field of 0.4 T. Remanent PFM amplitude at zero voltage bias is defined as A. d Variation of remanent PFM amplitude (∆A(H)/A(H = 0), normalized by its value at 0 T) of Cr(10%):HfO₂ and PZT films measured under various IP magnetic fields. Multiple measurements were performed at each fixed magnetic field. Error bars in (b, d) denote the standard deviation from the mean value. e Comparison of the magnetoelectric coupling coefficient (α_ME) of Cr-doped HfO₂ film with those of previously reported single-phase multiferroic materials at room temperature^5,38,48–58. The α_ME of Cr-doped HfO₂ film was estimated from the magnetic field-induced variations in polarization (P-E) and piezoresponse (PFM).

To further verify the coupling between ferroelectricity and ferromagnetism, the PFM technique was utilized, which offers a way to probe local magnetoelectric coupling behavior in multiferroics^38–40. Figure 4c exhibits the PFM amplitude-voltage butterfly loops of Cr(10%):HfO₂ film measured at 0 T and an in-plane magnetic field of 0.4 T. The application of the magnetic field markedly enhances the PFM amplitude for Cr(10%): HfO₂ film, whereas the response of PZT remains essentially unaffected (Supplementary Fig. S16b). These observations are well consistent with the P-E loop measurements, further demonstrating magnetoelectric coupling in Cr-doped HfO₂ films. To evaluate the magnetic field dependence, PFM amplitude loops were studied under different in-plane magnetic fields, as revealed in the Supplementary Fig. S20. For quantitative analysis, the variation in remanent piezoelectric amplitude ΔA at zero voltage was extracted (Fig. 4c and Supplementary Note S4). As shown in Fig. 4d, the variation in remanent amplitude (ΔA/A(H = 0), normalized by its value at 0 T) increases systematically with applied magnetic field in Cr(10%):HfO₂ film, while that of PZT film exhibits negligible changes. Similar field-dependent behavior was also observed in Cr(x%):HfO₂ films with other doping levels (Supplementary Figs. S20 and S21), with the strongest effect occurring at 10% doping, consistent with the enhanced ferroelectric and ferromagnetic properties at this concentration. Remarkably, Cr-doped HfO₂ films exhibit a giant magnetoelectric coupling coefficient α_ME of ~100 V cm^–1 Oe^–1 at room temperature (Supplementary Fig. S22), surpassing most previously reported single-phase multiferroics (Fig. 4e). The α_ME is estimated using two distinct methods: the changes in polarization (P-E) and piezoelectric response (PFM) under an applied magnetic field (Supplementary Note S4). The discrepancy between the two derived α_ME values is likely attributed to the inherent differences between global (P-E) and local (PFM) measurement techniques, which arise from different physical observables and boundary conditions (Supplementary Note S4). PFM measurement quantifies local magnetoelectric coupling by probing strain-mediated modulation of the piezoelectric coefficient, whereas P-E measurements reflect the global response by integrating changes in macroscopic polarization under a magnetic field. By demonstrating magnetic field control of ferroelectric polarization and piezoelectric amplitude, we confirmed robust room temperature multiferroicity in single-phase Cr-doped films.

Discussion

To illustrate the possible mechanisms underlying room temperature multiferroicity and magnetoelectric coupling in Cr-doped HfO₂ films, X-ray absorption spectroscopy (XAS) and X-ray photoelectron spectroscopy (XPS) characterizations were performed. XAS spectra provide insight into the electronic structure of Cr-doped HfO₂ films. Figure 5a displays the O K-edge XAS spectra for films with varying Cr concentration. Two prominent peaks at 536.6 eV and 540.9 eV correspond to the e_g and t_2g components of the Hf 5 d manifold, arising from crystal field splitting and associated with the hybridization of O 2p and Hf 5 d orbitals. Additional weaker peaks at higher energies originate from O 2p-Hf 6sp orbital hybridization. In case of Cr doping, the Cr 3 d and 4 s orbitals also hybridize with O 2p orbital, leading to modifications in the O K-edge spectra. For the undoped HfO₂ film, a two-fold degeneracy in the e_g component is observed, which is related to the monoclinic phase^41,42. In contrast, Cr-doped HfO2 films display only a single e_g peak, suggesting suppression of the monoclinic phase by Cr doping. This point is well consistent with the XRD results (Supplementary Fig. S1b). Furthermore, the increase in e_g peak intensity with higher Cr concentration may reflect enhanced structural distortion, as the ionic radius of Cr is smaller than that of Hf. Figure 5b shows the Cr L-edge XAS spectra of Cr-doped HfO₂ films, along with reference spectra for Cr³⁺⁴³. The spectra clearly resemble those of Cr³⁺, indicating that Cr³⁺ is the dominant oxidation state in Cr-doped films. The dominance of Cr³⁺ might arise from charge compensation via oxygen vacancies and its ionic radius (0.62 Å), which is closer to that of Hf⁴⁺ (0.76 Å) than the Cr ion with a higher valence state. Additionally, to pinpoint the source of magnetism, we performed Cr L-edge X-ray magnetic circular dichroism (XMCD) measurements on the Cr(x%):HfO₂ thin films (Supplementary Fig. S23). This provides solid evidence that the Cr ions possess a net magnetic moment and are the dominant source of the observed ferromagnetism. The ferromagnetism in Cr(x%):HfO₂ films fundamentally differs from defect-induced background magnetism, such as that induced by oxygen vacancies (Supplementary Note S5).

Fig. 5. XAS and XPS characterizations of the Cr(x%):HfO₂ films.

Normalized XAS spectra at a O K-edge and b Cr L-edge for Cr-doped HfO₂ films with varying Cr concentrations. The data are vertically offset for clarity. Referenced Cr³⁺ L-edge spectra are also presented in (b). XPS spectra of c Cr 2p and d Hf 4 f core levels. Black dot: original spectra, red line: fitted spectra. All film thicknesses are identical at 11.7 nm.

XPS was further employed to investigate the effects of Cr-doping on the valence states and defect configurations in Cr-doped HfO₂ films. Figure 5c, d present the XPS spectra of Cr 2p and Hf 4 f core levels, respectively. The Cr 2p spectrum can be deconvoluted into contributions from Cr³⁺ (2p_3/2 and 2p_1/2) and Cr⁽³⁺ⁿ⁾⁺ (2p_3/2 and 2p_1/2) species. As shown in Fig. 5c, Cr³⁺ is the dominant portion, and a noticeable fraction of Cr⁽³⁺ⁿ⁾⁺ portion is also present, consistent with the XAS results, which might be responsible for the multiferroicity of Cr-doped HfO₂ films. Similarly, Hf 4 f spectrum can be decomposed into two components: Hf⁴⁺ related to Hf–O bonding and Hf^(4-δ)+ associated with weaker bonding and reduced valence state. The O 1 s spectra further support these assignments (Supplementary Fig. S24a). With increasing Cr concentration, the relative proportions of Cr³⁺, Hf^(4-δ)+ and non-lattice O increase (Supplementary Fig. S24b). Additionally, the binding energy positions of Hf 4 f and O 1 s spectra in Cr-doped films exhibit slight shifts to the higher energy compared with undoped HfO₂, reflecting changes in oxidation state and local chemical environment. Taken together, the XAS and XPS analyses demonstrate that Cr doping alters both the electronic structure and local chemical environment of Hf. In addition, the XPS spectra of thicker Cr(10%):HfO₂ films (20.3 and 33.4 nm), which exhibit weaker ferroelectric and ferromagnetic responses, reveal a pronounced increase in the Cr⁽³⁺ⁿ⁾⁺ fraction (Supplementary Fig. S24c). This evolution may be attributed to the higher formation energy of oxygen vacancies in the monoclinic phase that becomes dominant in thicker films⁴⁴.

The coexistence of Cr³⁺/Cr⁽³⁺ⁿ⁾⁺ ions and oxygen vacancies likely plays a central role in establishing room temperature multiferroicity in Cr-doped HfO₂ thin films. Ferroelectricity arises from the stabilization of the ferroelectric orthorhombic phase facilitated by Cr doping and oxygen vacancy. Simultaneously, the Cr mixed valence states and oxygen vacancies can mediate exchange interactions, enabling long-range ferromagnetism⁴⁵. As proposed by Coey et al., the observed ferromagnetism may originate from long-range magnetic order mediated by shallow donor electrons, which form bound magnetic polarons capable of overlapping to produce a spin-split impurity band⁴⁶. The strong magnetoelectric coupling can be realized through the interplay between ferroelectricity and ferromagnetism. Polar distortions associated with ferroelectricity modify Cr-O bond lengths and angles, thereby tuning magnetic exchange interactions²⁸. Under an applied magnetic field, spin reorientation mediates Cr-O bonding changes, which in turn influence the displacement of oxygen ions and consequently modify the ferroelectric properties. In addition, the Dzyaloshinskii-Moriya (DM) interaction may provide another mechanism for magnetoelectric coupling^2,47. The inversion symmetry breaking in the non-centrosymmetric orthorhombic phase, together with the strong spin–orbit coupling from heavy Hf atoms, can induce significant antisymmetric exchange interactions between localized magnetic moments introduced by Cr dopant or oxygen vacancies. As the DM vector is intimately tied to the polar lattice distortion, an external magnetic field can indirectly affect polarization by reorienting the spin structure, thereby enhancing the ferroelectric polarization and piezoresponse in Cr-doped HfO₂ films.

To gain deeper insights into the underlying mechanism of magnetoelectric coupling in single-phase multiferroic Cr-doped HfO₂ films, we performed density functional theory (DFT) calculations (Supplementary Note S6). Compared with undoped HfO₂, the energy difference between orthorhombic and monoclinic phases is reduced in Cr doped HfO₂ (Supplementary Fig. S25 and Table S1), indicating that Cr doping facilitates the stabilization of the ferroelectric orthorhombic phase. Intriguingly, our calculations reveal that the energy values of ferromagnetic and antiferromagnetic orders are very close. This suggests that the two orders could coexist in large supercells with a disordered distribution of Cr atoms, potentially leading to a ferrimagnetic ground state in the Cr-doped HfO₂ system. The partial density of states (PDOS) shows a significant overlap of Cr 3 d and O 2p orbitals, and the band structures are mainly composed of Cr 3 d and O 2p components near the Fermi level (Supplementary Figs. S26 and S27), indicating the strong orbital hybridization between Cr 3 d and O 2p. The magnetic reorientation induces a redistribution of electronic charge due to this strong p-d orbital hybridization (Supplementary Fig. S28), which subsequently modulates the ferroelectric polarization, demonstrating that the Cr-doped HfO₂ system can possess strong magnetoelectric coupling.

In summary, we demonstrate the room temperature multiferroicity in single-phase Cr-doped HfO₂ thin films. With the introduction of Cr dopant, the ferroelectric phase is stabilized with enhanced ferroelectricity. Concurrently, intrinsic room temperature ferromagnetism emerges, which is positively correlated with ferroelectricity. More importantly, the strong magnetoelectric coupling between these two ferroic orders is verified, with a giant coupling coefficient of 10 ~ 100 Vcm^–1Oe^–1, which is superior to that of the majority of single-phase multiferroic materials. The discovery of room-temperature multiferroicity in HfO₂-based materials marks a significant advance, opening new opportunities for integrating magnetoelectric functionality into silicon-based electronics.

Methods

Thin-film growth

HfO₂ targets with different Cr-doping concentrations were prepared by spark plasma sintering (SPS) system using high-purity HfO₂ (99.99%) and Cr₂O₃ (99.99%) powders. Cr-doped HfO₂ thin films were grown on (001)-oriented Nb-doped SrTiO₃ (NSTO, 0.7 wt%) and SrTiO₃ (STO) substrates with a La_0.67Sr_0.33MnO₃ (LSMO) buffer layer by the pulsed laser deposition (PLD). Specifically, the thin LSMO buffer layer (~3 u.c.) was first deposited on (001) NSTO substrate using a KrF excimer laser (λ = 248 nm) with 1 Hz frequency and 1.3 J/cm² energy density, at 650 °C under an oxygen pressure of 20 Pa. The Cr-doped HfO₂ layer was then deposited at 825 °C under an oxygen pressure of 13 Pa with a frequency of 2 Hz. Following deposition, the films were cooled to room temperature at a cooling rate of 10 °C/min in a 1000 Pa oxygen atmosphere. For the preparation of freestanding films used in plan-view HAADF-STEM measurements, a thicker LSMO buffer layer (~25 nm) was grown to serve as a sacrificial layer. Finally, circular Au top electrodes with 20 ~ 100 μm diameters were prepared by magnetron sputtering and patterned using lift-off lithography for subsequent ferroelectric characterization.

Structural characterizations

The phase structure and thickness of the films were probed by X-ray diffraction (XRD, Rigaku Smartlab 9 kW) with Cu K_α1 radiation (λ = 1.5406 Å) in θ−2θ scanning, X-ray rocking curves (RC) and X-ray reflectivity (XRR) modes. Pole figure and corresponding 2θ scans were obtained using the χ-φ pole figure measuring method. The surface morphology of Cr(x%):HfO₂ films (x = 0, 5, 10, 20) was examined by atomic force microscope (AFM, Asylum Research MFP-3D Infinity). The atomic lattice structures of films were investigated by high-angle annular dark-field high-resolution transmission electron microscopy (HAADF-HRTEM, JEM-ARM200F, JEOL).

Ferroelectric characterizations

The macroscopic ferroelectric properties of the Au/Cr(x%):HfO₂/LSMO/NSTO capacitors were measured by a semiconductor parameter analyzer (4200A-SCS, Keithley). Ferroelectric P-E hysteresis loops of Cr(x%): HfO₂ films (x = 0, 5, 10, 20) were characterized by positive-up-negative-down (PUND) mode under triangular electric pulses with a frequency of 10 kHz. For magnetoelectric coupling measurements, P-E loops of ~10.6 nm-thick Cr(10%):HfO₂ film and referenced ~80.0 nm-thick PZT film (with ~25 nm-thick LSMO buffer layer as bottom electrode) were measured by PUND mode under in-plane or out-of-plane magnetic field cycled between 0 T and 0.4 T/2 T. Multiple P−E loops were measured in each fixed magnetic field to ensure reproducibility.

Magnetization characterizations

The temperature and magnetic field dependences of magnetization were measured by a superconducting quantum interference device (SQUID, MPMS3). For zero field cooling (ZFC) measurements, samples were cooled from 400 K to 2 K without a magnetic field; whereas for field cooling (FC) measurements, samples were cooled down to 2 K under a magnetic field of 2 T. Then, the M-T curves were measured upon warming from 2 K to 400 K under different magnetic fields (500 Oe, 1000 Oe and 1500 Oe).

PFM measurements

Amplitude-voltage butterfly and phase-voltage hysteresis loops of the films were measured using piezoresponse force microscopy (PFM, Asylum Research MFP-3D Infinity, Oxford) to enhance measurement sensitivity. All PFM measurements were performed using non-magnetic Pt-coated conductive tips (Multi75E-G, Budget Sensors) with a resonance frequency of 75 kHz and a spring constant of 3 nN/nm. For single-point PFM amplitude and phase hysteresis loop characterizations, a combined voltage waveform was applied to the conductive tip: a triangular-square waveform with a maximum amplitude of 12 V served as the DC bias for polarization switching, while an AC driving bias of 1.2 V at a frequency of 310 kHz was superimposed to detect the local piezoelectric response. The resonant quality factor (Q) was approximately 120. The bottom electrode of the sample was grounded throughout. In-plane magnetic fields of 0, 1000, 2000, 3000, and 4000 Oe were sequentially applied using a variable field module (VFM3, Asylum Research) to investigate the magnetic-field-dependent response, and the corresponding amplitude-voltage butterfly loops were recorded. For each magnetic field condition, five consecutive loops were acquired, and the average of the middle three loops was used to minimize experimental uncertainties. The universality of magnetoelectric coupling in the films was further evaluated by measuring the magnetoelectric response at multiple spatially distinct regions.

XPS and XAS characterizations

High-resolution spectra of O 1 s, Cr 2p and Hf 4 f core levels of Cr(x%):HfO₂ films (x = 0, 5, 10, 20) were studied by X-ray photoelectron spectroscopy (XPS, Kratos AXIS SUPRA + , Japan). Prior to measurements, in-situ argon ion etching was performed to remove surface contaminants such as carbon, nitrogen, and hydroxy, ensuring the collection of intrinsic signals from the films. The C 1 s peak at 284.8 eV was used as a reference marker to calibrate all measured spectra. The O K-edge and Cr L-edge X-ray absorption spectroscopy (XAS) of Cr(x%): HfO₂ films were measured at Beamline MCD-A in National Synchrotron Radiation Laboratory (NSRL, Hefei Light Source, China).

First-principles calculations

First-principles calculations were performed using the Vienna ab initio simulation package (VASP) with a plane-wave basis, based on density functional theory (DFT). Electron-ion interactions were described via the projector augmented-wave (PAW) method. For exchange-correlation interactions, the Perdew–Burke–Ernzerhof (PBEsol) functional within the generalized gradient approximation (GGA) was employed. The cutoff energy of the plane-wave basis was set to 550 eV, and a Γ-centered 4×4×2 k-point grid was adopted for sampling in the $2\times 2\times 1$ (48-atom) supercell. A Hubbard U correction with an effective value of 3 eV was employed to account for the strong on-site Coulomb repulsion associated with the localized Cr 3 d orbitals. All structures were fully relaxed until the force on each atom was less than 1 meV Å^–1 and the total energy difference of the supercell between two adjacent steps was less than 10^–6eV. An oxygen vacancy was introduced in the vicinity of the trivalent Cr³⁺ ions to maintain charge neutrality for the 12.5 at.% Cr³⁺ doping system. The spontaneous polarization was determined via the Berry phase method.

Author contributions

X.G.L. and S.C.S. conceived the idea and the project plan. H.Y.Z. prepared samples. H.Y.Z. and H.F.B. performed ferroelectric and magnetic characterizations and analyzed the data with help from Y.C.T., Y.X.L., Z.J.S., W.J.P., Z.Y.G., K.C., and Y.W.Y. Q.H.Z. performed TEM for freestanding films. D.H.Z. conducted the theoretical calculations under the supervision of Y.R.Y. H.Y.Z., H.F.B., S.C.S., Y.W.Y., and X.G.L. co-wrote the manuscript with feedback from all the authors.

Peer review

Peer review information

Nature Communications thanks Jan-Chi Yang and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The data generated in this study are provided in the Supplementary Information/Source Data file. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-72456-y.