Noncollinear ferrielectricity in a van der Waals crystal

Domain: physics
Published: 2026-03-19
Editorial outcome: minor_revision

Abstract
Inspired by noncollinear magnetic dipole order, noncollinear electric dipole order is anticipated to open up rich ferroelectric physics and new opportunities for device applications. However, establishing such order in single crystals remains challenging, as electric polarization is typically locked to crystallographic axes. Here we report noncollinear ferrielectricity in the van der Waals crystal WO2Br2, arising from competition between ferroelectric and antiferroelectric phonon modes. The noncollinear dipole order of WO2Br2 is revealed by decoupling the antipolar and the polar displacement component, both of which are directly visualized by scanning transmission electron microscopy. This noncollinear dipole order enables 90° polarization flip under hydrostatic pressure through two energetically degenerate transition pathways. Moreover, ultrafast electron diffraction measurements show that optical excitation drives two distinct coherent phonon modes associated with the ferroelectric and antiferroelectric orders. This work clarifies the physics of noncollinear electric dipole order for emergent ferroelectric device applications.

Introduction
Magnetic and electric dipole order underpins functional crystalline materials. Despite distinct origins—magnetic moments from spin and orbital angular momentum, electric dipoles from charge separation—Landau phase theory supplies a unified description of their ordering1–5. Classical dipole arrangements manifest as parallel (ferroic), antiparallel (antiferroic), or collinear ferrimagnetic/ferrielectric configurations6–10. Beyond these classical paradigms, angular misalignments enable the noncollinear dipole order, and the magnetic counterpart has been extensively studied in the field of magnetic materials. This magnetic dipole configuration produces exotic spin textures and extraordinary performance such as giant magnetostriction, anomalous Hall effects and spin–orbit torque11–15, which strongly motivates the exploration of analogous noncollinear electric dipole arrangements for fascinating physics.

Progress toward noncollinear polarization phenomena has been achieved in several systems. For example, in non-Ising ferroelectric domain walls16–18, artificially designed superlattices19,20, and twisted-stacked moiré superlattices21,22, the interplay among electrostatic energy, elastic energy, polarization-gradient energy, and interfacial charge redistribution can stabilize nanoscale noncollinear polarization textures, giving rise to topological polarization structures including polar vortices and polar skyrmions. However, such textures are often closely tied to interfaces and boundary conditions. In such cases, polarization rotation at domain walls is typically confined to a finite region near the wall, whereas topological textures in superlattices depend sensitively on parameters such as the superlattice period, layer thickness, and moiré twist angle. Therefore, constructing an intrinsic, long-range-ordered noncollinear electric dipole order in a single-phase crystal remains an important goal in this field.

Unfortunately, reports of noncollinear dipole order in bulk single crystals remain scarce23–26, despite the rapid progress in noncollinear electric dipole state achieved through interfacial engineering in superlattices and domain walls. This remains highly challenging because electric polarization is often locked to the crystallographic axes, and lattices with multiple polar axes tend to relax by forming ferroelastic domains rather than stabilizing a single-phase noncollinear dipole ground state26–28, leaving this field still relatively underexplored.

Recently, noncollinear electric dipole order has been achieved in limited materials via introducing competing interactions or structural instabilities by drawing inspiration from noncollinear magnetics24–26,29–31. For instance, the competition between the Bi³⁺ lone pair electrons and the Mn³⁺ Jahn-Teller distortion in BiCuₓMn7-ₓO12 gives rise to an incommensurate helical dipole order24. Moreover, Lin et al. reported that the competition between ferroelectric and antiferroelectric modes within a single crystal could yield phonon-frustrated noncollinear electric dipole order, which is the breakthrough in this field for the search of single-crystal noncollinear ferroelectrics32. Owing to its intuitive physical basis, this strategy is considered a promising route for creating noncollinear dipole order.

Van der Waals (vdWs) layered transition-metal oxyhalides, with distorted octahedral coordination that gives rise to diverse polarization phenomena, offer a promising platform for realizing phonon-frustration-induced noncollinear dipoles33–36. In the most extensively studied NbOX2 (X = Cl, Br, I), the 4d¹ electronic configuration of Nb⁴⁺ drives uniaxial structural distortions through Peierls-type dimerization, which confines the dipole to collinear orientations37–41. In contrast, the octahedral distortion of MO2X2 (M = Mo, W) is dominated by the directional hybridization between the empty d orbitals of M⁶⁺ and the anisotropic ligand fields imposed by O²⁻ and X⁻ anions, promoting richer polarization configurations, including noncollinear arrangements, as has been theoretically demonstrated by Lin et al32.

Inspired by the pioneering theoretical prediction of phonon-frustrated noncollinear dipole order in monolayer transition-metal dioxydihalides, we revisit this system experimentally. Although their work established a fundamentally new dipolar paradigm, direct experimental evidence has remained elusive, and its impact on polarization switching as well as the tunability of the noncollinear dipole order under external stimuli has yet to be explored.

Here, we unambiguously demonstrate the noncollinear dipole order in vdWs WO2Br2 by combining single-crystal X-ray diffraction (SCXRD) for structural resolution, crystallography-targeted scanning transmission electron microscopy (STEM) for direct visualization of W-atom displacements, and theoretical calculations. Moreover, the robust room-temperature in-plane ferroelectricity is revealed via piezoresponse force microscopy (PFM). Impressively, the critical role of noncollinear electric dipoles in polarization switching is revealed through in-situ polarization-resolved second harmonic generation (SHG) under hydrostatic pressure, where a 90° polarization rotation is achieved via two energetically near-degenerate transition pathways, involving an intermediate antipolar phase and 45° polar phase respectively. Furthermore, ultrafast structural probing reveals the exotic physics arising from the noncollinear dipole order, as ultrafast electron diffraction (UED) resolves photoexcited coherent phonons associated with the ferroelectric and antiferroelectric orders. These pressure-driven polarization-rotation processes and ultrafast phonon dynamics enable an effective strategy of domain and polarization engineering for promising ferroelectric memory and high-speed optoelectronic applications.

Results
Visualization of noncollinear atomic displacements in WO2Br2

Millimeter-scale, phase-pure WO2Br2 crystals were synthesized via a chemical vapor transport (CVT) method (Supplementary Fig. 1a). SCXRD patterns reveal a polar structure belonging to the non-centrosymmetric monoclinic space group Cc (No. 9) (Supplementary Table 1). The crystal is composed of two-dimensional [WO4Br2] octahedral layers interconnected through corner-sharing oxygen atoms. Halogen atoms (Br) occupy apical sites oriented along the a-axis, whereas oxygen atoms reside within the bc-plane. As illustrated in Fig. 1a, a mono-unit, defined as one unit-cell (UC) comprised of two atomic layers, exhibits alternating displacements of W atoms toward the upper-left (blue arrows) and lower-left (yellow arrows) along the c-axis. The displacements induces noncollinear ferroelectric polarization within the bc-plane, giving rise to net polarization along the c-axis and antipolar displacement along the b-axis.

Due to the inherent geometry of the monoclinic crystal system, the stacking axis a is inclined relative to the bc-plane. Consequently, the W site at fractional coordinates (x, y, z) in 1st UC would coincide with the W site at (x, -y, z+ ½) in 2nd UC if y = 0 (i.e., in the absence of a b-axis displacement) when projected along the [201] (Figs. 1a, b is the projection along this zone axis) direction. In the actual structure, an antipolar displacement along the b-axis leads to y ≠ 0, breaking the projected overlap and causing a lateral offset between the W atomic columns. Furthermore, W and Br atoms are situated in extremely close proximity along this projection. Both the two factors hamper the intuitive resolution of the noncollinear displacements, as evidenced by experimental observations (Supplementary Fig. 4). Besides, the substantial Z-contrast between heavy W (Z = 74) and light O (Z = 8) further impedes polarization analysis via octahedral core shifts. Therefore, there is not a low-index crystallographic zone axes enable unambiguous resolution of W, Br, and O atomic columns, and meanwhile avoiding stacking-induced imaging artifacts, which is a prerequisite for direct dipole visualization.

To circumvent such constraints, we strategically decoupled the b-axis antipolar and c-axis polar displacement components through crystallography-targeted analyses, thereby enabling reconstruction of the three-dimensional dipole configuration (Fig. 1d). For quantifying polar displacements along c-axis, relative positional shifts between W and Br atoms within each octahedral cage were determined via atomic-column centroid analysis projected along [010] zone axis. To resolve b-axis antipolar order, we employed multi-slice high-angle annular dark-field STEM (HAADF-STEM) simulations, guiding our selection of the [221] zone axis. Although imaging along the [221] direction remains partially constrained by stacking, simulations indicate partial spatial separation of overlapping W and Br atomic columns in few-layer WO2Br2 (Supplementary Figs. 5, 6). Additionally, surface-dominated electron scattering in thin specimens further mitigates stacking-induced average effects42,43, enabling a clear distinction of the antipolar displacements of W atoms along the b-axis.

Guided by these insights, aberration-corrected STEM was performed on mechanical-exfoliated samples to directly visualize the atomic displacements. The experimental HAADF image (Fig. 1e) exhibits exceptional agreement with [221] zone-axis simulations, permitting unambiguous identification of antipolar W-atom displacements. The HAADF signal predominantly arises from W columns due to their higher electron scattering cross-section. In this orientation, the low-density atomic column direction corresponds to the b-axis, while the high-density direction aligns with the c-axis. Within individual layers (corresponding to next-neighbor atom columns), the W displacements along the b-axis exhibit a characteristic "↑ ↓ ↑ ↓" antipolar arrangement. For multilayer configurations (n ≥ 2), the intercalation of lower-layer atoms into the voids of the upper layer results in an “↑↑↓↓↑↑” displacement pattern of W atoms when projected along the [221] zone axis, as shown in the enlarged HAADF image in Fig.1g.

FIB-prepared cross-sectional samples oriented along the [010] axis reveal the ferroelectric displacement component of W-atom displacements, as shown through HAADF imaging in Fig. 1f. The magnified analysis (Fig. 1h) highlights pronounced deviations of the W columns from the centroid of the Br-anion plane along the c-axis direction, as indicated by the arrow vectors (magnified by a factor of five relative to their actual displacement). Statistical quantification (Fig. 1i) confirms alternating ±0.23 Å displacements along b-axis, concurrent with net polarization along c-axis, with an average displacement of 0.27 Å, conclusively establishing coexisting antipolar and polar displacement along b-axis and c-axis respectively. These atomic displacements are not confined to a local region: large-area HAADF imaging also reveals uniformly distributed polar and antipolar displacements, demonstrating that the noncollinear dipole order exhibits long-range order (Supplementary Figs. 9, 10). Differential phase contrast (DPC) imaging, together with DPC simulations based on ion scattering factors (Fig. 1j and Supplementary Fig. 11), reveals asymmetric atomic-scale electric field distributions induced by ferroelectric polarization, with the asymmetry being most pronounced at the W atomic columns, in agreement with previous reports44,45. The local electric fields probed by DPC, which reflect polarization-induced charge redistribution and the associated projected electric-field gradients, when combined with the leftward polar displacement of the W atomic columns observed in HAADF-STEM images, provide further validation of the ferroelectric order along the c-axis. The spatial superposition of antipolar and polar dipole configurations results in the noncollinear dipole arrangement in WO2Br2.

Robust room-temperature in-plane ferroelectricity in WO2Br2

STEM characterizations directly resolve noncollinear displacements of W atoms, and first-principles calculations were employed to elucidate the underlying mechanism governing this unique dipole order. Based on the experimentally resolved WO2Br2 structure, our theoretical prediction identifies a high-symmetry paraelectric phase crystallizing in the C2/m space group. Phonon dispersion analysis of the paraelectric phase reveals prominent imaginary frequencies, confirming an intrinsic structural instability, as illustrated in Supplementary Fig. 12. Notably, a Γ-point phonon mode with Bu symmetry induces polar displacements (ferroelectric order, FE) along the c-axis, while a Bg mode at the A point drives antipolar distortion (antiferroelectric order, AFE) along the b-axis. In addition, the DFT energy profiles for the Γ-(FE), A+(AFE), and combined Γ-+A+ distortions show that the mixed FE+AFE distortion corresponding to the noncollinear state has a significantly lower energy minimum than either the FE-only or AFE-only structure (Supplementary Fig. 13). This indicates that, although each distortion mode individually exhibits dynamical instability, their cooperative interaction stabilizes a noncollinear ferrielectric configuration, in agreement with experimental observations. In WO2Br2, the resultant staggered (antipolar) dipole component alternates along the b-axis, while a net polar component survives along the c-axis, yielding a macroscopic polarization along c-axis.

According to theoretical calculations above, where a noncollinear arrangement of local electric dipoles gives rise to in-plane ferroelectricity, we then performed PFM measurements on mechanically exfoliated WO2Br2 flakes transferred onto Au-coated SiO2/Si substrates, with the topography of the characterized region shown in Fig. 2a. The in-plane PFM amplitude and phase images (Figs. 2b, c) clearly reveal 180° domain structures independent of the AFM morphology, in which adjacent domains exhibit comparable amplitudes together with a 180° phase contrast, and the domain walls appear as lines of reduced amplitude. To further confirm ferroelectric domain switching, we conducted point-by-point polarization-reversal measurements and recorded PFM hysteresis loops (Figs. 2d, e), in which the in-plane phase displays an approximately 180° counter-clockwise switching hysteresis and the amplitude exhibits the characteristic butterfly loop, while loops measured on the bare substrate show no hysteresis (Supplementary Fig. 15), ruling out instrumental artifacts. A visualization of the field-induced polarization reversal behavior is shown in Figs. 2f–i. When positive or negative single-point bias is applied along the appropriate direction, the written domains exhibit a phase shift of approximately 180° relative to the surrounding region (Supplementary Fig 19). A full sequence of domain writing and erasing is provided in Supplementary Fig 20. The in-plane nature of the polarization is further verified by rotating the relative angle between the probe and the sample (Supplementary Figs. 22), from which the PFM amplitude reaches a maximum when the polarization direction is perpendicular to the scan direction, decreases progressively upon rotation, and nearly vanishes when the polarization becomes parallel to the scan.

Re-orientation of polar axis in WO2Br2 under hydrostatic pressure

Given that WO2Br2 crystallizes in the non-centrosymmetric space group Cc, with structural asymmetry enabling the generation of measurable second-order nonlinear optical susceptibility, we then evaluate its second-harmonic generation (SHG) behavior for identification of crystalline orientations. Fig. 3a shows the optical image of a ~50 nm-thick WO2Br2 flake (white region), and the power-dependent SHG spectra (Supplementary Figs. 25, 26) suggests a quadratic dependence of SHG intensity on incident power, confirming the second-order nonlinearity. According to the power-dependent SHG measurements of WO2Br2 and referenced NbOI2, monolayer-equivalent WO2Br2 possesses a second-order nonlinear susceptibility χ(2) of ~120 pm/V, (Supplementary Note 2), which is comparable to top-tier 2D nonlinear optical materials such as NbOI2 and NbOCl2 39,46. The strong nonlinearity, coupled with persistent symmetry breaking, enables direct optical visualization of SHG signals of WO2Br2: 1040 nm laser excitation with power of 35 μW on WO2Br2 flake generates a visible 520 nm emission (17 nW output, conversion efficiency ~0.05%), as shown in Fig. 3b, demonstrating exceptional nonlinear conversion capabilities.

We then analyze the SHG polarization behavior of WO2Br2. Under the overall configuration, the polarization-dependent SHG intensity polar plot (Fig. 3c) displays a two-lobe pattern, where the lobe central axis coincides with the spontaneous polarization c-axis (Supplementary Fig 24), suggest that the maximum SHG response is generated when the polarization direction of pump light aligns with the c-axis (referred to the polar axis), donated as E//c, while the minimum SHG response is generated when E//b (referred to the nonpolar axis), which stems from the inherently 90° angular difference between the b-axis and c-axis stipulated by the monoclinic crystal structure of WO2Br2. This anisotropy persists under the parallel polarization configurations, while a four-lobe profiles with intensity maxima oriented at 45° relative to the crystallographic axes generated under the perpendicular configuration (Fig. 3c and Supplementary Fig 24). The high SHG efficiency and the in-plane SHG anisotropy of WO2Br2 enables precise identification of crystallographic axes.

According to our theoretical calculations, WO2Br2 is capable of undergoing a 90° polarization reorientation. Crucially, the noncollinear dipole order gives rise to nontrivial polarization-switching behavior, manifested as two nearly energy-degenerate transition pathways that proceed via distinct intermediate states, which will be discussed in the following sections. However, experimental attempts to induce this re-orientation through external electric fields (23.1 kV/cm) and uniaxial strain application along the b-axis (achieved via flexible substrate bending with 1.6% strain) in WO2Br2 both failed, where the crystal orientation was not changed (Supplementary Figs. 29, 30), indicating prohibitively high energy barriers in this interchange process between b- and c-axes. As an alternative approach, hydrostatic pressure through a diamond anvil cell (DAC) can generate gigapascal-scale stresses that induces bulk lattice deformations unattainable through conventional methods. As shown in Fig. 3d, pressure-dependent crystallographic orientation evolution in WO2Br2 was investigated under hydrostatic compression using DAC, with complete experimental details provided in the Methods section.

To mitigate anisotropic deformation caused by adhesion forces between the sample and diamond anvils that could compromise hydrostatic conditions47, we selected WO2Br2 flakes with a relatively large thickness (~100 nm) for high-pressure experiments. Optical images and polarization-resolved SHG polar plots acquired from the same location of the sample under ambient pressure (A.P.) and 6.0 GPa are presented in Supplementary Fig. 31, where 0° in SHG polar plots corresponds to the x-axis of the laboratory coordinate system. A distinct 90° reorientation is observed, where the angle of maximum SHG intensity shifts from ~46.5° (A.P.) to ~136.5° (6.0 GPa) while maintaining comparable signal intensity, eliminating the orientation ambiguity induced by SHG intensity variations. The observed rotation of SHG polar plots therefore directly demonstrates pressure-induced interchange of the b-axis and c-axis, exhibiting characteristics analogous to interconversion of ferroelastic variants. In-situ SHG intensity mapping of the sample under the configurations of both E//c and E//b revealed progressive orientation transitions under pressure, as shown in Figs. 3e-h. At ambient pressure, SHG signal across the sample exhibits uniform distribution, confirming a homogeneous single-orientation, where the SHG intensity under E//c is significantly stronger than under that E//b configuration. Under compression of 6.0 GPa, from the SHG intensity mapping with E// c, the intensity of certain locations decreases with inhomogeneous distribution, while the intensity of corresponding locations increases under E// b, providing direct evidence of reorientation of crystalline polar and nonpolar axis.

To reveal the underlying mechanism of pressure-driven reorientation of crystal axes in WO2Br2, we then carried out the first-principles calculations to evaluate the potential transition pathways. Using the climbing image nudged elastic band (CI-NEB) method, two energetically favorable transition pathways are identified (Figs. 4a, b), which exhibit double-barrier features due to the existence of metastable phases: (1) the antipolar (AP) phase pathway corresponding to metastable structures with antiparallel local dipoles along diagonal directions of [WO4Br2] octahedra, and (2) the 45° collinearly polar phase pathway (45° CP) corresponding to intermediate states with the local dipoles along identical directions, resulting in net polarization oriented at 45° relative to the initial net polarization direction. The AP and 45° CP pathway show near-degeneracy with energy barriers of 5.7 and 5.8 meV per atom respectively. Additional simulations based on the collinear dipole model (Supplementary Fig. 34) demonstrate that these nearly degenerate double-barrier energy pathways are unique features for noncollinear dipole orders. In Fig. 4b, the evolution of SHG polar plots reveals significant differences between the two pathways: SHG signals of the intermediate phase for AP path vanish due to centrosymmetric structure, while the central axis of petals in 45° CP path gradually rotates from 0° through 45° to 90° in synchronization with polarization direction changes. The energy barriers of both AP and 45° CP paths decline to the half as the compression increases to 1% (Fig. 4c), confirming the preferential pressure-driven orientation transition.

To elucidate the pressure-induced reorientation process, we conducted polarization-dependent SHG measurements at selected sample locations under varying pressures (Figs. 4d–g). Fig. 4d presents the evolution of SHG intensity with pressure along the directions of E//c (polar axis) and E//b (nonpolar axis). At ambient pressure, the SHG intensity measured along the polar axis is ~31 times higher than that along the nonpolar axis. Upon increasing the pressure to 1.1 GPa, the polar-axis SHG intensity drops sharply, whereas the nonpolar-axis intensity shows a slight increase. As a result, at 1.1 GPa the nonpolar-axis intensity becomes dominant, exceeding the polar-axis intensity by a factor of ~5. It should be noted that although the second-harmonic generation (SHG) response of a centrosymmetric antipolar phase is theoretically zero, the experimental observations reveal significant SHG intensity reduction in localized regions rather than complete disappearance (Supplementary Fig. 32). This can be attributed to two factors: (1) spatial inhomogeneity during the high-pressure phase transition, as evidenced by SHG mapping in Figs. 3e-h, and (2) limitations of the imaging system, where the use of low-NA objective lenses, which is necessary to satisfy working distance constraints, results in a relatively large laser spot size. Beyond 3.0 GPa, the SHG intensity gradually recovers, while the nonpolar axis response reaching nearly the same level as at ambient pressure by 6.0 GPa. Remarkably, beyond 1.1 GPa, the SHG signal along the nonpolar axis consistently remains stronger than that along the polar axis throughout the entire pressure range, and the SHG responses reach to 1:24 along polar and nonpolar axis under 6.0 GPa, indicating that the initial nonpolar b-axis became polar c-axis under pressure.

Fig. 4e displays SHG polar plots at representative pressures of ambient pressure, 2.4 GPa, and 6.0 GPa in Fig. 4d, corresponding to the initial, the ongoing transition, and the fully reoriented state respectively. The characteristic two-lobed SHG pattern undergoes an angular rotation of about 90° as the pressure increases from ambient to 6.0 GPa, in excellent agreement with the theoretical prediction. These results reveal the emergence of an intermediate phase in which the SHG intensity is strongly suppressed, and consistent with a nearly vanishing macroscopic polarization, which corresponds to the AP pathway predicted by theoretical calculations.

Moreover, our experiments revealed another distinct transition pathway. Fig. 4f displays the evolution of SHG intensity along the polar and nonpolar axes throughout this transition. Although SHG attenuation is also observed below 6.0 GPa, the SHG intensity along the polar axis consistently remains stronger than that along the nonpolar axis, indicating the absence of polarization reorientation. Interestingly, at 6.0 GPa, the SHG intensities along both polar and nonpolar directions reach nearly the same level. Beyond this pressure, the intensity along polar axis decreases significantly relative to the nonpolar axis, signaling the completion of reorientation. SHG polar plots shown in Fig. 4g offer a clearer visualization of this process. At 6.0 GPa, an anomalous SHG polar plot with preserved two-lobe symmetry is observed, wherein the polar axis rotates by ~45° while maintaining substantial signal strength. This indicates the emergence of a polar intermediate phase, distinct from the centrosymmetric phase along the AP pathway. Upon 7.3 GPa, the polar axis undergoes an ~90° rotation from the angle under ambient pressure, confirming a full switching of the crystal axes. The intermediate phase maintains polar symmetry with a 45°-rotation of polar axis, in agreement with theoretically predicted 45° CP pathway. Notably, this intermediate phase exhibits enhanced SHG intensity along its own nonpolar direction (~0°) compared to pristine WO2Br2, consistent with theoretical predictions presented in Fig. 4b.

The coexistence of these two nearly degenerate transition pathways, differing by only ~0.1 meV/atom, substantiates the predicted near-degenerate energy landscape for noncollinear dipole systems and provides critical role of noncollinear dipole order during the polarization switching process. These transition paths in WO2Br2 are strongly different from the case in conventional ferroelectrics such as HfO2, where the 180°/90° polarization reversal in WO2Br2 does not require 180°/90° rotation of every local dipole32. Instead, polarization reversal can be driven through coordinated local dipole rotation across neighboring units, which constitutes a distinctive characteristic of noncollinear ferrielectricity. The coordinated behavior enables multiple switching pathways emerge during 90° polarization rotation depending on different metastable intermediate structures. Notably, the metastable phases in WO2Br2 remain stable over a relatively wide pressure range, enabling the coexistence and interconversion of multiple polarization states (as shown in Fig. 4a), which offers promising potential for applications in information storage devices.

After clarifying the two transition pathways of WO2Br2 under compression, we further investigated how the crystal structure evolves along these pathways. Raman spectroscopy serves as a sensitive probe for tracking structural evolution under hydrostatic pressure. Taking the AP transition pathway as an example, we performed in-situ Raman spectra measurements to reveal the high-pressure structural evolution of WO2Br2 (Supplementary Fig. 40). The results show that the original vibrational modes are preserved throughout compression, while novel emerging Raman modes appear at the early stage under pressure and disappear at higher pressures. Consequently, the Raman spectra obtained at 6.0 GPa closely resembles that at ambient pressure.

Further analysis of the pressure-dependent frequencies of different vibrational modes reveals that the out-of-plane vibrational mode (A′3) exhibits a monotonic blueshift with increasing pressure, while the in-plane vibrational modes (A′1, A′2, A′4) show redshift in the low-pressure region (<3.0 GPa) and blueshift at higher pressures (>3.0 GPa) (Supplementary Fig. 41). The redshift of the in-plane modes at low pressure indicates in-plane bond softening or lattice expansion50,51, consistent with the emergence of an antipolar intermediate phase. With further compression, the in-plane modes switch from redshift to blueshift, indicating the recovery of conventional pressure-induced bond stiffening and suggesting that the structure ultimately stabilizes into a noncollinear dipolar configuration. The formation of this metastable intermediate phase is mainly governed by in-plane atomic rearrangements, in agreement with the theoretically predicted transition pathway.

Consistent with the Raman spectra results, in-situ powder and single-crystal XRD under hydrostatic pressure (Supplementary Figs 35-42, Supplementary Table 5) indicate that, although WO2Br2 undergoes a space-group change (Cc to Pcc2) at 5.0 GPa, the transition does not involve a drastic structural reconstruction but rather a gradual, moderate evolution of the lattice. Taken together with the Raman and XRD analyses, WO2Br2 can still retain a noncollinear dipole configuration to a certain extent under hydrostatic pressure.

FE and AFE coherent phonon dynamics in WO2Br2

In WO2Br2, the presence of ferroelectric and antiferroelectric soft phonon modes in the high-symmetry paraelectric phase drives polar displacements of W atoms along the c-axis and antipolar displacements along the b-axis, which together give rise to a noncollinear electric dipole order. This particular noncollinear dipole order in WO2Br2 provides an ideal platform for coherent control of the polar and antipolar orders separately or simultaneously. Here, we identify this concept by the combination of Raman spectra, DFT simulation and ultrafast electron diffraction (UED). The static Raman spectra in Fig. 5b displays the two A′ phonon modes with the frequency of 2.83 THz and 3.70 THz. The atomic movements and vibrational frequencies of these two phonon modes acquired by DFT simulation are shown in Figs. 5c and d. For the 2.70 THz phonon mode (i.e., A′(FE)), the collective in-phase vibration of W atoms along the c-axis together with their opposite motion relative to Br atoms along the same axis, indicates that this mode primarily modulates the ferroelectric order. In contrast, for the 3.70 THz mode, W and Br atoms vibrate out of phase along the b-axis; however, neighboring chains of W atoms oscillate in opposite directions along b-axis, demonstrating that this mode mainly modulates the antiferroelectric order (i.e., A′(AFE)). Polarization-resolved Raman spectra also reveal that these two A′ modes exhibit a phase difference close to 90° (Supplementary Figs. 42c, d), which further supports that they are associated with the polar and nonpolar axes respectively.

With femtosecond laser pump, we monitor the coherent phonon modes by the intensity change of Bragg reflections. Both the A′(FE) and A′(AFE) phonon mode are coherently excited as shown in Figs. 5e-f and Figs. 5g-h (Supplementary Fig 48). The long lifetime of these coherent phonon modes indicates the primary ferroelectric and antiferroelectric modes. Therefore, the concept of coherent control of the ferroelectric and antiferroelectric dipole orders separately and simultaneously, which is the unique feature of noncollinear ferroelectricity of WO2Br2, has been identified. This coherent excitation regime sheds light on the ultrafast control of the exotic physics in noncollinear ferroelectricity, such as the dipole-based skyrmions32, for applications in high-speed optoelectronic devices52. Such experimental explorations toward ultrafast switching of macroscopic orders32,53,54 and metastable states55–57 are expected.

In summary, we have theoretically and experimentally established the phonon-frustration driven noncollinear electric dipole order and room-temperature ferroelectricity in the layered crystal WO2Br2. Hydrostatic pressure enables a nontrivial crystal axes 90° switching, and ultrafast structural probes reveal the distinctive coherent phonon dynamics associated with the noncollinear dipole state. Atomic-scale HAADF-STEM microscopy directly visualized the antipolar W atoms arrangement along the b-axis and polar alignment along the c-axis. PFM measurements and hysteresis loops confirmed macroscopic ferroelectric properties. Under hydrostatic compression, WO2Br2 exhibits coexistence of two distinct pathways during 90° polarization switching: one involving intermediate phases with vanishing polarity and another maintaining polarity with 45°-rotation of polar axis relative to the pristine state, which is the direct consequence of noncollinear dipole order in WO2Br2. This pressure-driven 90° rotation further offers an effective route for domain and domain-wall engineering. Ultrafast electron diffraction measurements additionally demonstrate excitation of coherent phonon modes associated with ferroelectric and antiferroelectric modes upon photoexcitation. This work deepens the understanding of noncollinear ferroelectric physics and opens a practical pathway for polarization-state control and domain engineering in ferroelectric memory devices.

Methods
Materials synthesis
High-purity WO2Br2 single crystals were synthesized through CVT method. The chemical reactants W, WO3 and Br2 were thoroughly mixed in a molar ratio of 1:2:6 and sealed into an evacuated quartz tube (10-5 torr). The tubes were heated in a two-zone furnace, and the reaction region and crystal growth region were kept at 450 ℃ and 300 ℃ for 5 days, respectively. Finally, the reddish-brown plate-like crystals can be obtained at the growth region.

Structure characterizations
Single-crystal X-ray diffraction was performed on a Bruker D8 QUEST diffractometer equipped with Mo Kα radiation. The diffraction data were collected at room temperature by the ω- and φ-scan methods. The crystal structure was solved and refined using APEX3 program. Absorption corrections were performed using the multi-scan method (SADABS). The atomic structure is visualized using the VESTA software58. The samples for STEM characterization were prepared via mechanical exfoliation and dry transfer. WO2Br2 crystals were first exfoliated using 3M Scotch tape to expose cleavage planes, followed by picking up the exfoliated flakes with a polydimethylsiloxane (PDMS) film to obtain nanosheets. The thickness of the nanosheets was pre-screened via optical microscope (BX53M, Olympus) to select suitable samples. For in-plane STEM observation, selected nanosheets were transferred onto porous silicon nitride TEM grids using standard dry transfer methods. For cross-sectional observation, nanosheets were initially transferred onto SiO2/Si substrates. After determining their crystallographic orientation via polarization-dependent SHG, thin lamellae were milled using a focused ion beam-scanning electron microscopy (FIB-SEM) system via a standard lift-out process, transferred onto TEM grids, and polished to electron transparency. HAADF-STEM and DPC imaging were performed using a probe-corrected JEOL ARM-200F TEM (200 kV) for in-plane specimens and an FEI Titan Themis G2 double-aberration-corrected TEM (300 kV) for cross-sectional specimens. For basal-plane imaging, a collection angle of 68-200 mrad and a convergence semiangle of 29.2 mrad were employed. Cross-sectional characterization utilized a collection angle of 52-200 mrad and a convergence semiangle of 25 mrad. Beam current was maintained below 30 pA for all experiments to minimize radiation damage. Electron diffraction patterns were simulated using the software Recipro59, while multi-slice STEM images were generated using QSTEM60.

Extraction of atomic displacements and vector mapping
Polar atomic displacements in WO2Br2 along the [010] direction were quantified using a custom Python workflow based on template matching. Initial templates for W, Br1, and Br2 motifs were selected as 50×50-pixel windows from the HAADF-STEM image (Supplementary Fig. 10a). To reduce noise, each template was refined by averaging high cross-correlation regions, producing noise-reduced reference patterns. These templates were used for normalized cross-correlation across the entire image to obtain initial atomic coordinates. Sub-pixel accuracy was achieved by refining atomic positions using two-dimensional Gaussian peak fitting. The polar displacement vector for each unit cell was calculated as the offset of the W atom relative to the midpoint of its surrounding Br atoms, representing the local polar distortion. The resulting displacement field was visualized by overlaying arrow vectors magnified by a factor of five (Supplementary Fig. 10b). For WO2Br2 imaged along the [221] direction, antipolar displacements were extracted using the CalAtom software61. Atomic coordinates (Fig. 1e) were identified by applying an intensity threshold to locate atomic maxima, followed by sub-pixel localization using center-of-mass calculations. The mean y-coordinate of each atomic row was taken as the local reference center, and atomic displacements were computed relative to this reference. The column-averaged antipolar shift for each atomic column was obtained by averaging these displacements, forming a single data point in Fig. 1i.

PFM measurements
The exfoliated crystals were directly transferred onto SiO2/Si substrates coated with a 50 nm gold film for PFM characterization. PFM images were acquired in contact mode using a Bruker Dimension Icon atomic force microscope. Measurements were performed with a platinum/iridium-coated silicon tip (SCM-PIT, Bruker) with a radius of 20 nm and a spring constant of ~3.0 N m⁻¹. The driving frequency and amplitude for PFM imaging were set to the in-plane contact resonance frequency (~760 kHz) and 2000 mV, respectively. PFM switching spectroscopy was conducted by applying a triangular-wave voltage (±6 V) to the tip while monitoring the PFM phase and amplitude under a 2000 mV drive voltage.

Optical characterization
SHG and Raman spectroscopy measurements were performed using a custom-built spectroscopic system (detailed in Supplementary Fig. 23). The SHG signal was excited by a 1034-nm fibre-based femtosecond laser (Femto-10, Huaray), with its polarization purified via a Glan-Thompson prism (GTP-10, LBTEK). Polarization-resolved SHG spectroscopy employed a shared half-wave plate configuration62: an achromatic half-wave plate (SAHWP05M-700, Thorlabs) rotated the polarization of both the incident laser and the emitted signal. Switching between parallel and perpendicular polarization configurations was achieved by adjusting the angle of a polarizer in the signal collection path. The SHG signal was collected using a spectrometer (Shamrock 500i, Andor). For Raman spectroscopy, a 523-nm laser (Samba 04-01, Cobolt) was used as the excitation source. The laser beam was purified and filtered using a Bragg bandpass filter (BPF-532, OptiGrate) and two notch filter (BNF-532, OptiGrate) to resolve Raman peaks across low-to-high wavenumber regions.

Hydrostatic pressure measurements
For spectroscopic measurements, appropriately sized samples were transferred onto the surface of a DAC via a dry transfer method. During in-situ single crystal and powder XRD testing, single-crystal samples or fine powders were selectively sieved for optimal particle size, and loaded into the high-pressure chamber using a microtip. The high-pressure chamber was sealed with a stainless-steel gasket containing a central aperture of 120 μm, while low-fluorescence silicone oil served as the pressure-transmitting medium. Ruby particles with diameters ranging from 10–20 μm were precisely positioned within the DAC using a microtip for subsequent pressure calibration. Unit cell parameter refinements were performed using the GSAS Ⅱ software63.

In millimetre-scale sample high-pressure experiments, WO2Br2 flakes were stacked within a cylindrical platinum sample chamber prior to hermetic sealing. High-pressure experiments were performed by ultrahard tungsten carbide anvils assembly in a 10 MN Walker-type LVP (the State Key Laboratory of Superhard Materials, Jilin University). The pressure was increased to 8.0 GPa first over around 30 h, and then released slowly over the course of approximately 30 h.

DFT calculations
Density functional theory (DFT) calculations were performed by Vienna ab initio Simulation Package (VASP)64 and a plane-wave pseudopotential code, QUANTUM ESPRESSO65. The exchange-correlation function was Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA)66. Optimized norm-conserving pseudopotentials were adopted to treat the electron-ion interactions. In the geometry optimization and self-consistent field calculations of monolayer WO2Br2, the plane-wave kinetic energy cut-off was 140 Ry and the k-point mesh was 4×8×1. A convergence threshold of 10-10 Ry was used for the self-consistent cycle. The convergence thresholds of energy and force for the structural relaxation were 10-6 Ry/Bohr and 10-5 Ry/Bohr, respectively. The computed in-plane lattice parameters are 7.6 and 3.9 Å, matching well with the experimental structure (7.7 and 3.9 Å). The SHG susceptibility was calculated using a denser k-point mesh of 12×24×1 and 280 bands (including 80 valence bands) for convergence67. Spin-orbit coupling (SOC) effects were incorporated into the theoretical modelling of SHG. CI-NEB calculations for 1×2×1 supercell was performed using 9 images to obtain the transition path with the minimum energy and saddle points. Limited by the restriction of lattice relaxation using the CI-NEB method, the lattice parameter of the supercell was fixed to the average of two in-plane lattices, which is 7.7 Å. The k-point mesh was set to 4×4×1 accordingly. A blueshift of bandgap about 0.14 eV due to the lattice parameter modulation is considered in the computed SHG polar plots in Fig. 4. The phonons were computed by the density functional perturbation theory (DFPT)68.

UED characterization
For the MeV femtosecond electron diffraction system, the 400 nm, 30 fs and 400 Hz laser pulse (Vitara and Legend Elite Duo HE, Coherent) is split into the pump and the probe pulse. The pump pulse excites the sample and the probe pulse is frequency tripled in nonlinear crystals before illuminating a photocathode for electron pulse generation. After being accelerated by an intense radio-frequency field to relativistic velocity (~0.989c), the electron pulse goes through a double-bend achromatic lens for pulse compression and jitter removal. The spot size of the electron pulse on the sample is ~150 μm FWHM, around five times smaller than the size of the pump laser, ensuring a homogeneous photoexcitation. The diffraction pattern is imaged by a phosphor screen (P43) and recorded by an electron-multiplying charge-coupled device (Andor iXon Ultra 888C). The overall temporal resolution of the MeV UED system is ~50 fs. Further details for the system can be found in our previous work69. Single crystal WO2Br2 nanofilms are prepared via mechanical exfoliation from the bulk crystal and transferred to TEM Si3N4 windows for femtosecond electron diffraction experiments. The samples with the thickness of ~ 30 nm are characterized by optical microscopy and TEM.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "I read carefully the response provided by the authors. I appreciate the efforts in the response file. I would enthusiastically recommend this work for publication once the authors have considered the following final remark:\nOn the non collinear dipole order engineering : considering a discussion on other bulk materials in which non collinear electric dipole ordering can be artificially established, as discussed in the response document, in the introduction section would enrich the manuscript and highlight the novelty of the work in my opinion.", "reviewer_2": "The authors have addressed the reviewers’ comments thoroughly, and the manuscript is now in very good shape. I believe it is ready for publication in Nature Communications as is.", "reviewer_3": "The Authors have adequately addressed the points I raised in the first review round. They have fixed a number of problems and improved the presentation of the results. The paper can now be recommended for publication."}, "author_response": "Response to the reviewers’ comments\n(Research Article, NCOMMS-26-006885A)\nDear the reviewers,\nWe would like to thank you for reviewing our manuscript and providing us the\ninsightful comments on our work. We have revised the manuscript accordingly based\non your suggestions/comments. Below are the detailed point-by-point responses. The\nreply to reviewers is highlighted in blue, and the changes to our manuscript are\nhighlighted in red. The corresponding changes are also highlighted in yellow in the\nmain text and Supplementary Information.\nReferee #1 (Remarks to the Author):\nGeneral comment R1:\nI read carefully the response provided by the authors. I appreciate the efforts in the\nresponse file. I would enthusiastically recommend this work for publication once the\nauthors have considered the following final remark:\nOn the non collinear dipole order engineering: considering a discussion on other bulk\nmaterials in which non collinear electric dipole ordering can be artificially established,\nas discussed in the response document, in the introduction section would enrich the\nmanuscript and highlight the novelty of the work in my opinion.\nResponse: We thank the reviewer for this insightful and constructive comment. We\nhave incorporated the requested discussion into the Introduction to enrich the context\nof noncollinear dipole-order engineering and to better highlight the novelty of our work.\nThe added text is as follows:\nPage 2, line80:\nProgress toward noncollinear polarization phenomena has been achieved in several\nsystems. For example, in non-Ising ferroelectric domain walls16,17, artificially designed\nsuperlattices18,19, and twisted-stacked moiré superlattices20,21, the interplay among\nelectrostatic energy, elastic energy, polarization-gradient energy, and interfacial charge\nredistribution can stabilize nanoscale noncollinear polarization textures, giving rise to\ntopological polarization structures including polar vortices and polar skyrmions.\nHowever, such textures are often closely tied to interfaces and boundary conditions. In\nsuch cases, polarization rotation at domain walls is typically confined to a finite region\nnear the wall, whereas topological textures in superlattices depend sensitively on\nparameters such as the superlattice period, layer thickness, and moiré twist angle.\nTherefore, identifying an intrinsic, long-range-ordered noncollinear electric dipole state\nin a single-phase crystal remains an important goal in this field.\nUnfortunately, reports of noncollinear dipole order in bulk single crystals remain\nscarce22–25, despite the rapid progress enabled by interfacial engineering in superlattices\nand domain walls.\nReferee #2 (Remarks to the Author):\nGeneral comment R2:\nThe authors have addressed the reviewers’ comments thoroughly, and the manuscript is\nnow in very good shape. I believe it is ready for publication in Nature Communications\nas is.\nResponse: We sincerely thank the reviewer for their positive and encouraging feedback.\nWe are pleased to hear that the manuscript is now in very good shape, and we appreciate\nthe time and effort the reviewer put into evaluating our work.\nReferee #3 (Remarks to the Author):\nGeneral comment R3:\nThe Authors have adequately addressed the points I raised in the first review round.\nThey have fixed a number of problems and improved the presentation of the results.\nThe paper can now be recommended for publication.\nResponse: We sincerely thank the reviewer for the constructive feedback and for\nacknowledging the improvements made in the manuscript. We are glad that the\nrevisions have addressed the points raised in the first round of review, and we appreciate\nthe reviewer’s positive assessment of this article. We are confident that these changes\nhave enhanced the clarity and quality of the results, and we are grateful for the\nreviewer’s valuable input in this process."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed all the points raised in this final stage. I can now recommend this work for publication as is."}, "author_response": "Response to the reviewers’ comments\n(Research Article, NCOMMS-26-006885A)\nDear the reviewers,\nWe would like to thank you for reviewing our manuscript and providing us the\ninsightful comments on our work. We have revised the manuscript accordingly based\non your suggestions/comments. Below are the detailed point-by-point responses. The\nreply to reviewers is highlighted in blue, and the changes to our manuscript are\nhighlighted in red. The corresponding changes are also highlighted in yellow in the\nmain text and Supplementary Information.\nReferee #1 (Remarks to the Author):\nGeneral comment R1:\nThe authors have addressed all the points raised in this final stage. I can now\nrecommend this work for publication as is.\nResponse: We sincerely thank the reviewer for carefully assessing our revisions at this\nfinal stage and for the positive evaluation. We are pleased that we have addressed all\npoints satisfactorily and that the reviewer now recommends publication of the\nmanuscript as is. We also appreciate the reviewer’s constructive comments throughout\nthe review process, which have significantly improved the clarity and overall quality of\nthe work."}]

Decision letter