We first identify magnetically driven charge orders from STM measurements performed across the AF transition at TN ≈ 1.5 K under zero magnetic field (see Methods for sample characterization). At 4 K, the topographic image (Fig. 2a) exhibits a unidirectional modulation with a Fourier wavevector qCDW1 = (0, 0.28) (Fig. 2b), consistent with the well-established CDW1 phase of CeTe3 (Fig. 1b). Upon cooling to 300 mK, qualitatively distinct stripe-like modulations emerge. One is oriented perpendicular to CDW1 and is characterized by charge-propagation vectors (0.33, 0), and another is parallel to CDW1, characterized by (0, 0.08) (Fig. 2c, d). The same periodicities are clearly resolved in energy-dependent dI/dV maps in real space (Fig. 2e). They are consistently captured in Fourier space (Fig. 2f–i), visualizing their non-dispersive nature with energy. Because the wavevector (0.33, 0) resembles the conventional CDW2 reported in other RTe3 compounds, establishing whether this modulation is intrinsically linked to antiferromagnetism requires a detailed temperature-dependent study.
Fig. 2: Temperature dependence of CDW2mag and CDW3mag.
The topographic image at 4 K (a) and its corresponding Fourier transform (FT) image (b). The topographic image at 300 mK (c), and its FT image (d). The setpoint conditions for (a) and (c) are similar (50 mV/4 nA and 50 mV/5 nA, respectively). All peaks corresponding in (b) and (d) are identified as a linear combination of relevant peaks of charge orders and crystal structures. See Supplementary Note 1 for the full assignment of the FFT components. e The dI/dV maps acquired over a 5 × 23 nm² area at various energies from −50 mV to 0 mV (setpoint conditions: 50 mV/5 nA with a lock-in modulation of 2 mV). The blue and purple arrows indicate the periodicity appeared only below TN corresponding to qCDW2mag and qCDW3mag, respectively. f, h The energy evolution of the line-cut profiles along qy and qx directions obtained from the dI/dV maps (Fig. 2e) (see the arrow indicated in (d)). g, i Line-cut profiles of the Fourier signal along the qy and qx direction at 300 mK. The signal is obtained from the topographic image (Fig. 2d). j Temperature dependence of the Fourier components at (0.33, 0), (0, 0.28), (0, 0.08) and (0, 0.2) extracted from the topographic images. The setpoint is −10 mV/500 pA.
For efficient tracking of the relevant charge orders, we note that while the modulation at (0.33, 0) can be visualized over a relatively wide bias window of ±50 mV, topographic images acquired within a narrower bias window of ±10 mV are optimal for resolving the modulation with wavevector (0, 0.08) (see Methods and Supplementary Note 2). Accordingly, to track the simultaneous evolution of both charge orders, we focus on topographic images acquired, for example, at −10 mV. Notably, by following this strategy, while CDW1 shows little change across TN, the additional charge modulations characterized by wavevectors (0.33, 0) and (0, 0.08) collectively exhibit a clear onset below TN (Fig. 2j). Combined with their suppression above the spin-flop field Bflop (discussed later), the modulation (0.33, 0) is established as a charge order intrinsically intertwined with antiferromagnetism, which we denote CDW2mag. Similarly, the modulation at (0, 0.08), which also develops exclusively below TN, is denoted CDW3mag (Fig. 2d, j). Throughout this work, the subscript “mag” is used to indicate charge orders that emerge only within magnetically ordered states.
Applying an in-plane magnetic field induces a pronounced reorganization of charge order within the AF phase. Similar to the previous study17, in-plane field is applied along horizontal c-axis, which is parallel to the CDW1 direction (Fig. 1f). At B = 2.0 T, exceeding the spin-flop field Bflop ≈ 1.5 T, the topographic image and its Fourier transform (Fig. 3a, b) reveal the emergence of two orthogonal charge modulations with wavevectors (0.19, ±0.19) (red and yellow circles in Fig. 3b). These modulations are directly visualized in real-space dI/dV maps (Fig. 3c) and corroborated by Fourier line profiles (Fig. 3d–g). The absence of measurable energy dispersion indicates that these modulations originate from static ordering (Fig. 3d, e). Because this charge order appears only within the magnetically ordered phase and is stabilized by an applied magnetic field, we refer to this state as CBCmag.
Fig. 3: Competing CDW2mag and CBCmag at 300 mK across the spin-flop transition at Bflop under an in-plane magnetic field applied along the c-axis.
a STM topograph acquired at B = 2 T applied along the c-axis at 300 mK. b FT image corresponding to (a). The measurement conditions for (a) are 50 mV/2.5 nA. See Supplementary Note 1 for the full assignment of the FFT components. c The dI/dV mapping at various energies as indicated inside. The set point is 50 mV/2.5 nA with the lock-in modulation of 2 mV. d, e The energy evolution of the line-cut profiles along (1,-1) and (1,1) directions, respectively (see the red and yellow arrows indicated in b). f, g Line-cut profiles of the Fourier signal of the STM topograph (b) along (1,-1) and (1,1) directions, respectively. h Magnetic field evolution of the FT peak intensities at qCDW1, qCDW2mag, qCDW1-qCDW3mag, and qCBCmag, which are normalized by the Bragg peaks at (qy,qx) = (0,1), (1,0), (0,1), (±1,1), respectively, extracted from topographic images taken with the set-point of +50 mV/2.5 nA.This choice of normalization factors for each charge modulation is not to compare the amplitude between them, but to reduce the effect of a small tip anisotropy. The background colors represent the magnetic phases across Bflop.
It should be noted that the charge-propagation vectors associated with CDW2mag, CDW3mag, and CBCmag connect nearly nested regions of the Fermi surface (Fig. 1k). As a result, competition among these orders is naturally expected: stabilization of one charge order partially gaps the Fermi surface, thereby reducing the fermionic energy gain available to competing instabilities. Here, we use the term “nesting” in a broad sense, referring not only to ideal parallel Fermi-surface segments but also more generally to wavevectors connecting regions with a relatively large joint DOS. Within the scope of this study, deviations from ideal nesting conditions are not emphasized, provided that partial gap opening still yields a substantial net fermionic energy gain.
The relevant competition is directly visualized through the magnetic-field dependence of the Fourier intensities associated with CDW2mag, CDW3mag, and CBCmag (Fig. 3h). While CDW3mag is optimally visualized using bias voltages of approximately ±10 meV (Fig. 2c, d), we find that the competition between CDW2mag and CBCmag is more efficiently captured in topographic images acquired at larger bias voltages on the order of ±50 meV (see Methods and Supplementary Note 2). As shown in Fig. 3h, the CDW3mag-related signal is nearly buried within the background noise at a bias voltage of +50 meV at B = 0 (see dashed line). With increasing magnetic field, however, the enhancement of the CDW3mag signal enables the simultaneous visualization of CDW2mag, CDW3mag, and CBCmag within a single topographic dataset, allowing a consistent comparison across the entire field range. Here, to minimize extrinsic anisotropic contrast arising from the STM tip, the Fourier intensities are normalized by the corresponding Bragg peaks: (0,1) for CDW1 and CDW3mag, (1,0) for CDW2mag, and (1, ±1) for CBCmag. Although CDW3mag evolves relatively smoothly with the magnetic field, a weak discontinuity is nevertheless observed across the spin-flop field Bflop. More strikingly, as the magnetic field increases from zero, the intensity of CDW2mag is sharply suppressed. At the same time, CBCmag is enhanced across Bflop, leading to a pronounced anti-correlation between the two orders.
The energy scale associated with the competition among multiple magnetic charge-ordered states is directly reflected in the magnetic-field dependence of the tunneling spectra dI/dV(E) (Fig. 4a). Using the bimodal color scheme (blue and red) shown in Fig. 4b, the spectra can be clearly classified into two distinct groups below and above the spin-flop field Bflop. To quantify the characteristic energy scale, we directly compare representative spectra measured at B = 0 T (<Bflop) and B = 2 T (> Bflop). Taking the derivatives of the dI/dV spectra and overlaying them (Fig. 4c) highlights the energy range over which the DOS is most strongly modified. The gray curve in Fig. 4c represents a reference spectrum, denoted d2I/dV2B-ave, obtained by averaging representative spectra shown in Fig. 4a and b. This comparison demonstrates that the dominant spectral changes are confined to an energy window of approximately ±20 meV around EF. Consistently, the field evolution, plotted as d2I/dV2(B)−d2I/dV2B-ave, further reveals a pronounced DOS reconstruction across Bflop within the same energy range (Fig. 4d).
Fig. 4: dI/dV deformation at 300 mK under an in-plane magnetic field applied along the c-axis.
a Evolution of the spatially averaged dI/dV spectra under in-plane magnetic fields at 300 mK. Spectra are vertically offset for clarity. The measurement condition is 50 mV/2.5 nA with the lock-in modulation of 0.8 mV. b Representative spectra above and below the spin-flop field (B > Bflop and B < Bflop), highlighted in two distinct colors. c Derivative of the dI/dV spectra (d2I/dV2) at B = 0 and 2 T. The yellow-highlighted region indicates the energy window where substantial spectral renormalization is observed. The gray line indicates the magnetic field averaged spectrum (d2I/dV2B-ave, obtained by averaging six curves (0, 0.5,1, 1.5, 2, 2.5 T), where three are representative for B < Bflop (0, 0.5, 1 T) and the other three are representative for B > Bflop (1.5, 2.0, 2.5 T). d The Magnetic field dependence of d2I/dV2(B)-d2I/dV2B-ave, revealing the pronounced spectral evolution within −20 meV to +10 meV. e Schematic spectral evolution with changing temperature and magnetic field.
Rather than emphasizing fine spectral structures visible in Fig. 4d, the most robust outcome of the magnetic-field-dependent analysis is the identification of this characteristic energy window. In two-dimensional multiband systems, superlattice formation driven by Fermi-surface nesting typically produces complicated fine spectral features within the reconstructed energy range. Moreover, in LaTe3—where only CDW1 order exists (Fig. 1b)—electron–boson coupling generates dip-like structures near EF that are not directly related to the CDW condensation energy41. Similar spectral complexity is therefore expected in CeTe3. In this context, the energy scale of the DOS modulation across Bflop provides a more reliable indicator than the detailed fine structure within the soft gap.
Combining the field-dependent evolution of the raw spectra (Fig. 4b) with the derivative analysis yields a consistent picture: the electronic structure changes across Bflop on an energy scale of approximately ±20 meV. Notably, the dominant spectral modifications extend across EF, indicating that the DOS reconstruction reflects a fermionic energy gain or loss associated with the competing phases. As schematically illustrated in Fig. 4e, the strongest manifestation of this energy competition appears near −10 meV, highlighted by the shaded regions in Fig. 4b and c.
To deepen our understanding of the electronic competition in momentum space, we investigate quasiparticle interference (QPI). Motivated by the DOS reconstruction observed at 300 mK around −10 meV across Bflop (Fig. 4e), we concentrate on comparing high-resolution QPI data taken at 0 and 2 T at the same temperature and energy (Fig. 5a, b). To isolate the field-induced evolution across Bflop, the QPI pattern at 0 T is subtracted from that at 2 T, yielding a differential QPI map (Fig. 5c) that reveals characteristic suppression (blue) and enhancement (red) of QPI intensity with increasing magnetic field. To interpret this red/blue contrast, we consider nesting vectors associated with CDW2mag, CDW3mag, and CBCmag on approximate constant-energy contours constructed from ARPES measurements of the parent band structure above TN (Fig. 1k). At B = 0 T, nesting associated with CDW2mag (blue arrows in Fig. 5d) leads to partial gap opening predominantly on the inner pocket (Fig. 5e). In contrast, at B = 2 T, nesting associated with CBCmag and CDW3mag collectively produces pronounced gap opening on the outer pocket (Fig. 5f, g).
Fig. 5: Quasiparticle interference revealing competing Fermi-surface instabilities under an in-plane magnetic field applied along the c axis.
Quasi-particle interference (QPI) patterns measured at (T, B) = (0.3 K, 0 T) (a), and (0.3 K, 2 T) (b). The set point is −10 mV/1 nA, and lock-in modulation is 3 mV with 961 Hz. Both were symmetrized with respect to qx = 0 line, assuming the quasi-tetragonal crystalline symmetry in the non-magnetic phase. Note that the color scale is identical in (a) and (b). c Difference map of the QPI intensity between (0.3 K, 0 T) and (0.3 K, 2 T), showing alternating contrasts. Note that the area around q = (0,0) is masked since the major contribution of the irrelevant long wavelength signal is expected to contribute. For transparency, the non-masked data is shown in Supplementary Note 6. Additional QPI features in other momentum regions and their consistency with this model are discussed in Supplementary Note 6. Schematic constant-energy contour evolution owing to the gap opening by the charge orders at B = 0 T (d, e) and B = 2 T (f, g), respectively. The colored arrows indicate the ordering vectors at each phase. h, i Constrained scattering channels due to the gap opening at B = 0 T (h) and 2 T (i). The solid arrows indicate the possible channels, while the broken arrows indicate the suppressed channels. j Expected QPI contrast by subtracting the data at B = 2 T by B = 0 T, which shows good agreement with the experiments.
The essential physics underlying the experimental QPI difference between 0 and 2 T is most clearly manifested near q = (0,0). In this region, the QPI is governed by scattering between quasi-one-dimensional, predominantly 5p-orbital-derived Fermi surfaces (Fig. 1c, d), whose parallel constant-energy contours generate features that cross the q = (0,0) point. Within this framework, the dominant scattering shifts from the outer pocket at B = 0 T to a shorter vector within the inner pocket at B = 2 T, as indicated by the solid and dashed arrows in Fig. 5h, i. This shift naturally results in a characteristic change in the momentum-space extent of the QPI across q = (0,0) (Fig. 5j), which is directly captured in the experimental differential QPI map (Fig. 5c).
The validity of this picture is further supported by its ability to account for the QPI modulation associated with the development of CDW3mag at higher magnetic fields (Fig. 3h). In our model, the corresponding QPI signal is expected to deform and become suppressed as CDW3mag is stabilized, consistent with the k-space reconstruction shown in the magnified regions of Fig. 5h, i. The propagation vector q = (0, 0.08) associated with CDW3mag is indicated by the arrow in Fig. 5c, around which extended QPI features are observed. While a prominently extended QPI signal is present at B = 0 T, this signal is strongly suppressed at B = 2 T, concomitant with the enhanced CDW3mag intensity localized at q = (0, 0.08) (highlighted regions in Fig. 5a, b). Accordingly, the theoretically expected disappearance (blue-coded) of an arc-like extended QPI feature around q = (0, 0.08) at 2 T (Fig. 5j) is faithfully reproduced in the experimental differential QPI map (Fig. 5c). Taken together, the QPI deformations observed between B = 0 and 2 T—particularly near q = (0,0)—are consistently explained within a minimal modeling framework incorporating CDW2mag, CDW3mag, and CBCmag, providing direct momentum-space evidence for the competition and coexistence of these charge-ordered states.
We next provide a semi-quantitative discussion of the possible relationship between the charge modulation vectors qc and magnetic propagation vectors qm. A natural microscopic connection arises from the Kondo exchange coupling between itinerant Te 5p electrons and localized Ce 4f moments28,29,46,53,54,55, where theoretical studies predict that intertwined charge order can emerge from linear combinations of antiferromagnetic propagation vectors qm12,15,16. At zero magnetic field below TN, neutron-scattering experiments on CeTe3 revealed antiferromagnetic order with propagation vectors qm1 = (0.17, 0.31) and qm2 = (0.17, −0.31)49. These naturally generate two candidate intertwined charge wavevectors: qm1 + qm2 = (0.34, 0) and qm1 − qm2 = (0, 0.62). Notably, qm1 + qm2 connects more strongly nested regions of the Fermi surface, providing a more efficient route for fermionic energy gain and thereby stabilizing the magnetic charge-ordered state qCDW2mag = (0.33, 0) (see blue and purple arrows in Fig. 1k). Although no direct CDW corresponding to qm1 − qm2 is observed, combining qm1 − qm2 with qCDW1 = (0, 0.28) yields qCDW3mag = (0, 0.08) through the approximate relation qCDW3mag ≈ 1 − qCDW1 − (qm1 − qm2). Owing to weaker nesting and the resulting smaller fermionic energy gain, qCDW3mag is expected to exhibit a weaker experimental signal at B = 0 (Fig. 3h).
Under finite magnetic fields, neutron-scattering information remains limited, and direct determination of the magnetic structure is an important subject for future work. Nevertheless, the emergence of the C4-symmetric CBCmag with wavevectors (±0.19, 0.19) (Fig. 3h, right) constrains the possible underlying magnetic configurations. While the C4-symmetric magnetically intertwined CDW state has not been reported in magnetically localized systems such as TbTe3 and DyTe3, in-plane magnetic propagation vectors with |qm | ≈ 0.2 r.l.u. are frequently observed in diffraction experiments on these materials42,43. This motivates us to speculate that CeTe3 may host an analogous but C4-symmetric double-qm antiferromagnetic state, uniquely stabilized by intertwined Fermi-surface instabilities. One plausible scenario involves double-qm antiferromagnetic propagation vectors qm1 = (0.19, 0) and qm2 = (0, 0.19). Within this picture, qCBCmag = (0.19, ±0.19) can be interpreted as qm1 ± qm2, while qCDW3mag = (0, 0.08) approximately follows 2qm1 − qCDW1 ≈ (0, 0.1). We also note that, when a finite net moment corresponding to (0, 0) component develops, the magnetic and charge propagation vectors coincide (qm = qc), which may contribute to the emergence of CDW3mag and CBCmag above Bflop.
To this point, in addition to conventional qCDW1 = (0, 0.28), three antiferromagnetic charge-ordered states [with qCDW2mag = (0.33, 0), qCDW3mag = (0, 0.08), and qCBCmag = (0.19, ±0.19)] have been identified in CeTe3. Each state is characterized by a distinct nesting vector (Fig. 1k and Fig. 5d, f) and can be described by different linear combinations of the propagation vectors involving qm and qCDW1. From this viewpoint, we regard all three as distinct antiferromagnetic charge-ordered states. Although the precise spin texture of the field-induced state has not yet been directly resolved by neutron diffraction, recent theoretical studies of easy-plane magnets have predicted a wide variety of stable multi-qm phases under magnetic fields, including vortex-crystal states55.
Although Kondo exchange plays an essential role in mediating the coupling between localized spins and itinerant electrons, our observations point to substantially richer physics beyond this simple picture. The reported Kondo temperature is on the order of 10 K46, whereas the magnetic ordering temperature and the spin-flop field observed in this study are only about 1.5 K and 1.5 T, respectively17. These energy scales are therefore far too small to account for the pronounced reconstruction of the DOS observed here, which extends over approximately ±30 meV from EF across TN (Fig. 1g, h) and a comparable ±20 meV across Bflop (Fig. 4d). This clear separation of energy scales indicates that Kondo exchange alone cannot be the dominant driving interaction. Instead, additional interactions must play a decisive role in shaping the low-energy electronic structure, a feature that should be considered an intriguing aspect of CeTe3. Notably, the energy scale of the band deformation identified here (Fig. 4) is comparable to the dispersion kink associated presumably with electron–phonon coupling revealed by Landau-level spectroscopy in the nonmagnetic single-CDW system LaTe341. This comparison demonstrates that similarly high-energy electronic coupling is already intrinsic to the Te-based layered electronic structure, even in the absence of 4 f moments. In this context, Coulomb interactions between the small electron and hole pockets in this semimetallic system—an electronic configuration closely analogous to that of CeTe3 (Fig. 1d and 5f)—are also a candidate driving source of large energy-scale Fermi-surface deformations reminiscent of an excitonic band instability20,56,57. Although the present system is not insulating, such effects are expected to be strongly enhanced in van der Waals materials, where reduced dimensionality and weakened electronic screening amplify interaction effects. Taken together, these considerations establish CeTe3 as an exceptional two-dimensional platform in which multiple interactions—Kondo exchange, Coulomb correlations, and electron–phonon coupling—cooperatively generate versatile antiferromagnetic charge orders. Through this interplay, tunable and strongly correlated electronic states emerge on a semimetallic Fermi surface, extending well beyond a simple Kondo-driven picture.
From a real-space perspective, this rich landscape offers fertile ground for exploring exotic multi-qm magnetic orders. Such textures are widely regarded as a key ingredient for realizing topologically nontrivial magnetic states. They can give rise to large emergent electromagnetic responses, including enhanced transport signals associated with fictitious magnetic fields10. Beyond multi-qm magnetism, the coexistence of multiple charge orders is also expected to induce unconventional symmetry breaking; for example, nontrivial relative phase shifts between charge orders may generate exotic in-plane inversion symmetry breaking58. These possibilities naturally motivate future studies combining microscopic probes with Hall and non-reciprocal transport measurements.
From a complementary momentum-space viewpoint, the realization of versatile multi-q antiferromagnetic charge order on a semimetallic Fermi surface opens the door to the exploration of unconventional electronic band structures. In this regime, competing Fermi-surface instabilities may drive the emergence of Dirac-like dispersions, band inversion, and rich momentum-space textures of electronic wave functions. Moreover, the strong spin–charge intertwining uncovered in CeTe3 provides a pathway toward unconventional quantum criticality. Whereas in related RTe3 compounds such as TbTe3 and DyTe3 superconductivity emerges near the CDW2 critical point, where magnetism and charge order are largely decoupled23,35,36, the magnetically intertwined charge orders identified here point to a qualitatively distinct critical regime and suggest routes toward unconventional superconductivity driven by coupled spin and charge degrees of freedom.
Finally, guided by the general concept of moiré modulation—where the superposition of periodic structures generates distinct wave vectors through linear combinations—our observation of multiple electronic propagation vectors can be viewed, at a conceptual level, as a manifestation of versatile charge–spin intertwined electronic moiré states, rather than a superposition tied to crystalline lattice vectors59,60.
In summary, our results establish CeTe3 as a versatile platform for realizing multi-q antiferromagnetic charge orders, accompanied by large-energy-scale electronic reconstructions characteristic of strongly correlated systems. The observed phenomenology originates from the intertwining of multiple frustration channels—antiferromagnetism, charge ordering, and competing Fermi-surface instabilities—within a semimetallic state. From a conceptual perspective, this study demonstrates that van der Waals antiferromagnetic semimetals offer promising opportunities to explore previously inaccessible, tunable quantum phases in which topology and strong electronic correlations are intrinsically intertwined in two dimensions. From a functional viewpoint, these results provide guiding principles for designing quantum materials that integrate multiple input and output channels, enabling disproportionately large electronic responses to modest external stimuli at the nanoscale in versatile electronic moiré phases.