Introduction

The discovery of ferromagnetism in two-dimensional van der Waals (vdW) ferromagnets has opened exciting frontiers in quantum matter research1,2,3. In this context, the ternary Fe-Ge-TevdW materials, such as Fe3GeTe2and Fe5GeTe2, hosting high-temperature long-range ferromagnetic order down to the two-dimensional (2D) structural limit, is a unique platform where miniaturized spintronics devices have already been proposed4,5,6,7,8,9,10,11,12,13,14. In addition, strong electronic correlations are reported to drive these systems towards exotic ground states, that is, the heavy Fermions/Kondo physics15,16, charge order (CO)17, flat bands18, optical anomalous hall effect (AHE)19, and orbital selective Mott transition (OSMT)20.

Fe3GeTe2(150 < TC < 230 K) is the most thoroughly investigated member of the ternary Fe-Ge-TevdW magnets. One of the intriguing findings is the coexistence of low energy coherent magnetic excitations (magnons) and a dispersionless non-Stoner-type continuum at higher energies16,20,21. This dual character of magnetic excitations is beyond the framework of the linear spin wave theory, invoking the OSMT scenario—atypical to 3d transition metals—to explain the experimental observations20. Are these dual magnetic excitations, a generic feature of the ternary Fe-Ge-TevdW materials? If so, how do these excitations evolve with TC?

Fe4.75GeTe2 with the highest TC ≈ 315 K among Fe-Ge-Te2D-vdW ferromagnetic materials is an ideal member to investigate these questions. Moreover, it hosts the long-range ferromagnetic order remarkably close to room temperature ≈ 270 K in the 2D structural limit4,5,6,8. Deciphering the mechanism behind these high-temperature 2D vdW ferromagnets is essential to engineer novel heterostructures from 2D layers. However, despite enormous progress in understanding transport, magnetic, and structural properties of Fe5−xGeTe24,5,6, to date, the character of the magnetic excitations, their energy scale, and dimensionality remain unexplored in this material. The inelastic neutron scattering (INS) is a standard technique to address these issues22,23, but the small size of the Fe4.75GeTe2single crystals poses a challenge. Furthermore, a recent angular resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) study reports a CO 17, that is shown to compete with the magnetic ordering. However, a bulk-sensitive signature of the CO, its electronic character and propagation vector are unexplored so far.

Here we present an investigation of the magnetic excitations and CO in Fe4.75GeTe2. To elucidate the character, energy scale, and dimensionality of the magnetic excitations, we employed high-resolution Fe L3-edge resonant inelastic X-ray scattering (RIXS) on a mm-sized single crystal Fe4.75GeTe2. RIXS complements INS to probe collective spin excitations and, in addition, can measure small sample volumes24 easily accessing the high-energy spectral range where the thermal neutron flux is heavily reduced. Our findings suggest that Fe4.75GeTe2hosts dual character of magnetic excitations, similarly to Fe2.72GeTe2, and despite being a 2D system structurally, it displays a significant three-dimensional (3D) interaction between Fe-Ge-Te slabs that are ~10 Å apart. To investigate the bulk and electronic character of the proposed CO, we used synchrotron X-ray diffraction (XRD) and Fe K-edge resonant elastic X-ray scattering (REXS)25,26,27. Our results demonstrate that the observed ±(1/3, 1/3, L) peaks are of structural origin, suggesting a doubling of structural unit cell along the c-axis. Overall, our work advances the current understanding of the magnetic properties of Fe4.75GeTe2 and shed light onto the whole family of Fe-Ge-Te vdW magnets.

The high-quality quenched single crystal of Fe4.75GeTe2 used for this study originated from the same batch as in refs. 4,28, which suggested similar magnetic properties for nominal composition ranging from Fe4.7GeTe2 to Fe6.0GeTe2. Figure 1a shows the rhombohedral unit cell of Fe4.75GeTe2(\(R\bar{3}m\) No. 166, a = b ≈ 4.04 Å, c ≈ 29.19 Å), characterized by three distinct Fe-Ge-Teslabs separated by ≈ 10 Å. Within each slab, the Fe and Ge atoms occupy interior positions, while the Te atoms occupy the external positions. It develops ferromagnetic order below TC ≈ 315 K with magnetic moment pointing along the c-axis4.

Fig. 1: Magnetic excitations in the Fe L3 − edge RIXS spectra of Fe4.75GeTe2.
figure 1

a Fe4.75GeTe2crystal structure drawn using VESTA54. A single unit cell contains three Fe-Ge-Te slabs. b Schematic of RIXS experimental geometry. In the hexagonal structure representation, two orthogonal wave vectors—(100) and (001)—form the scattering plane highlighted in pink. θ is an angle between the incident X-ray and the (100) axis while Ω is the scattering angle between incoming and outgoing X-ray. The double-headed arrow represents the π polarization of the incident light. c Fe L3,2- edge XAS measured at θ = 15∘ in total electron yield (TEY) mode at 70 K. A solid vertical line represents the Fe L3-edge maximum, that corresponds to the incident photon energy (707.9 eV) used for the RIXS spectra. d RIXS intensity map measured as a function of incident photon around the Fe L3—edge, and zoomed in to cover excitations below 300 meV. For this dataset, θ = 20∘ and Ω = 95∘ corresponding to Q = (−0.16 0 2.17). e, f Two representative RIXS scans (black dotted line) at (−0.35 0 1.4) and (−0.3 0 1.74). The low-energy excitations are fitted with an elastic peak (gray), a phonon (blue), a magnon (red), a broad continuum, and a background (gray line) stretching to higher energies. The red solid line represents the fit sum. The inset in (e) shows the measured Fe5GeTe single crystal. All RIXS spectra displayed in this work were measured at T = 70 K, using π polarization. The error bars of the RIXS spectra are defined assuming a Poisson distribution of the single-photon counted events.

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For the X-ray absorption spectroscopy (XAS) and RIXS studies, the Fe4.75GeTe2single crystal was oriented with (1 0 0) and (0 0 1) in the scattering plane, see Fig. 1b. The sample was cleaved in air with scotch tape just before loading it into the vacuum chamber. Figure 1c shows the XAS measured in the total electron yield (TEY) mode at 70 K. The observed L3 and L2 absorption peaks are in agreement with literature29, supporting the high quality of the sample. The XAS data was used to identify the resonant energy for the RIXS study. To reduce the elastic scattering signal in the RIXS measurements, we used π-polarized incoming X-rays. The same sample was used for both REXS and XRD experiments, and it was aligned using an out-of-plane and two in-plane nuclear reflections.

The momentum transfer Q(HKL) associated with the RIXS spectra and the diffraction data are expressed in reciprocal lattice units (\(4\pi /\sqrt{3}a4\pi /\sqrt{3}a2\pi /c\)). The in-plane and out-of-plane momentum coverage was achieved by rotating both the scattering angle Ω and the X-rays incident angle θ. Extensive momentum coverage was achieved for the XRD experiment (2 keV of photon energy) and for the Fe K-edge REXS (≈ 7 keV of photon energy). For Fe L3-edge RIXS (≈ 710 eV of photon energy), we could span a large portion of the Q-space in the L direction across several brillouin zone (BZ) and up to L = 3.23 (2π/c), thanks to the large c-axis (≈29.19 Å) of the Fe4.75GeTe2, while in-plane we could cover up to \({H}_{max}=-0.35(4\pi /\sqrt{3}a)\) within the first BZ.

Results and discussion

Magnetic excitations in Fe4.75GeTe2

In the following two sections, we describe the investigation of the magnetic excitations and their momentum dependence in Fe4.75GeTe2using Fe L3-edge RIXS, and we discuss the results in comparison Fe2.72GeTe216,20,30. Figure 1d presents a RIXS intensity map measured as a function of incident photon energy across the Fe L3-edge. Although most of the spectral weight goes into high-energy fluorescence as expected for a metal (see Supplementary Fig. 2)24, a weak component stretches from 0 up to ~150 meV resonating at the Fe L3 peak. By fixing the incident photon energy to the maximum of the Fe L3 resonance, we measured high-resolution RIXS spectra as a function of momentum transfer Q.

Figure 1e, f show RIXS spectra at two representative Q points with largest in-plane momentum components, Q = (−0.35 0 1.4) and (−0.3 0 1.74). We make use of both RIXS spectra to establish a minimum fitting model that describes the observed inelastic spectral weight below 200 meV. Details regarding the fitting and its procedure are reported in Supplementary Note 3. Taking Fe2.72GeTe2as a reference case16,20, we include in the fitting model a resolution limited phonon (blue peak), a magnon mode (red peak) due to spin-spin correlations between localized spins, and a broad magnetic continuum (green peak) coming from spin-spin interactions among itinerant electrons. We fix the phonon energy to 20 meV based on the room temperature Raman measurements presented in Supplementary Fig. 1 and consistently with20. From the remaining spectral weight, we extract a magnon peak centered at 36 ± 1 meV and a continuum centered at 75 ± 2 meV, extending up to ≈150 meV. At higher energies, a background from the fluorescence tail dominates the spectral weight (gray solid line). While the magnetic continuum is peaked at twice the energy of the magnon, we exclude a dominant double magnon character, since this type of excitation is ~10 times weaker than the magnon31,32. In our dataset, the continuum amplitude is comparable to the magnon, and its area is significantly larger than the latter, ruling out the double magnon character. While we cannot exclude the presence of double magnons in our data, their faint spectral weight would not impact the interpretation nor the extraction of the magnetic continuum.

For the spectra presented in Fig. 1e, f, we were not able to resolve any significant magnon dispersion given the proximity of the in-plane Q components. However, a comparable magnon energy for similar momentum transfer has been reported for Fe2.72GeTe216,20,30, further supporting the nature of the ≈36 meV peak. Similarly, the broad continuum peak (stretching up to 150 meV) resembles the one identified in Fe2.72GeTe216, although in the latter system it extends only up to 100 meV. Based on these findings, we identify the low energy magnetic excitations in Fe4.75GeTe2 and assess the coexistence of the dual electron spin character in this system.

Our conclusion is underpinned by the INS studies of Fe2.72GeTe216,20. To explain this uncommon behavior in a 3d transition metal33,34,35, an OSMT mechanism has been proposed for Fe2.72GeTe220, typically invoked in the context of strong multi-orbital correlations as realized by 4d/5d and f electron compounds36,37,38,39. Within this scenario, it is possible to explain both the itinerant and the local magnetism manifesting in a multi-orbital system20. Considering the emergence of giant Fe(3d)–Te(5p) and Fe(3d)–Ge(4s/4d) hybridization40 and the flat bands18,41, and the dual character of magnetic excitations evidenced by our study, the magnetic ground state of Fe4.75GeTe2 is likely governed by OSMT physics as well as in Fe2.72GeTe2. Theoretical validation would be valuable to confirm this aspect, requiring a comprehensive treatment of the strong multi-orbital correlations manifesting within such a complex crystal structure.

Origin of the magnetic continuum

Figure 2 shows the L dependent RIXS spectra along (0 0 L) from L = 1.74 r.l.u. to L = 3.23 r.l.u. In these measurements, we maximized the out-of-plane coverage by scanning mostly along (0 0 L), while minimizing the in-plane momentum transfer, e.g., H < ∣0.04∣ r.l.u. and K = 0 r.l.u. A clear continuum peak emerges from all spectra, see Fig. 2a–g, and its position remains mostly invariant versus L as marked by a vertical dashed line. The dispersionless nature of the continuum agrees with the Fe2.72GeTe2findings16. To directly compare the absolute RIXS intensities as a function of L (or scattering geometries), all spectra reported here are normalized to integrated fluorescence peak and self-absorption corrected as described in Supplementary Note 2. Already from the raw data, the continuum intensity appears to decrease for decreasing L. Note that while in Fe2.72GeTe2 the continuum is maximized around the in-plane BZ boundary16, here we find a significant spectral weight close to the in-plane BZ center.

Fig. 2: L – dependent study of the magnetic continuum in Fe4.75GeTe2.
figure 2

a–g RIXS spectra measured at different L values from 1.74 to 3.23 r.l.u., at 70 K. For all spectra, H < ∣0.04∣ and K = 0. Each spectrum is fitted with an elastic peak (gray), a phonon (blue), a magnon (red), and a continuum (green), as introduced in Fig. 1e, f. The vertical dashed line marks the continuum centers around ~75 meV. h L-dependence of the continuum integrated spectral weight (green dotted line). The error bars are half of one standard deviation. The thick green line is a sinusoidal fit of the data using Eq. (1) for d = 10 Å, while the dotted lines represent the upper and lower boundaries considering the extracted fit error for d of ±1 Å. i Calculated intensity modulation for intra-slab (red) and inter-slab (black) distances, as defined within the crystal structure displayed in (j) using with the same color convention. A gold curved line in (j) highlights the Te–Te distance across two neighboring slabs.

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The origin of the L-dependent intensity modulation of the continuum in Fe2.72GeTe2was associated with the two Fe sites, yielding a characteristic length scale along the c-axis within Fe-Ge-Te slab16. The goal of this section is to extract this information for Fe4.75GeTe2. We fit the RIXS spectra in Fig. 2 using the model introduced in Fig. 1e, f. To effectively implement the fitting model, we made some key assumptions. Given the strong elastic line intensity and the unknown magnon dispersion for this material, we fixed the fitting parameters (peak position and width) of the lowest energy modes—phonon and magnon—to match the values extracted for Q = (−0.35 0 1.4) r.l.u. These assumptions are valid because the low-energy spectral weight (below 40 meV) only influences the elastic line shape and leaves the high-energy dispersionless continuum unaffected. This approach enabled us to utilize a consistent fitting model across all RIXS spectra. Regarding the fitting of the continuum itself, we fixed its position and width to reproduce the broad and dispersionless character of this excitation16,20, while its amplitude was allowed to change. More details on the fitting procedure can be found in Supplementary Note 3. As a result of this analysis, we obtain the L-dependent evolution of the continuum intensity which follows a sinusoidal behavior, as highlighted in Fig. 2h. A comparison of the L-dependent magnetic continuum intensity with and without self-absorption correction is shown in Supplementary Fig. 3. The magnitude of intensity modulation is robust and independent of self-absorption correction.

When dealing with a continuum or a dispersionless excitation, the Q-dependent modulation of its intensity or structure factor encodes the distance between the interacting atoms along the selected Q-direction. Hard X-ray RIXS and INS—enabling a wide coverage of reciprocal space—have been extensively used to show the formation of new magnetic superstructures by monitoring the Q-modulation of the spectral weight16,42,43. Following these works, the frequency of the continuum structure factor modulation can be captured by a simple qualitative function:

$$I(L)\propto \cos {(L\cdot d/2)}^{2},$$
(1)

where L is the momentum transfer vector and d is the real space inter-atomic distance along the c-axis within the unit cell. By fitting the data points displayed in Fig. 2h, we extract a distance of d = 10 ± 1 Å.

In the case of Fe2.72GeTe2, the L-dependent INS structure factor of the continuum yielded an intra-slab distance d ~2.7 Å16. Such a length-scale corresponds to the Fe-Fe dumbbell (a dimer-like structure corresponding to the largest exchange interaction) superstructure oriented along the c-axis within an individual Fe-Ge-Te slab. This finding suggests that the magnetic continuum in Fe2.72GeTe2 originates from the quasi-molecular character of the magnetic states formed by the Fe-Fe dumbbell, and furthermore, it identifies the atoms and exchange path that contribute to the strongest magnetic exchange interaction in the system20.

To identify the interacting atoms and exchange path behind the continuum intensity modulation in Fe4.75GeTe2, we display in Fig. 2i a simulation of I(L) based on a representative intra-slab distance (red) and inter-slab distance (black). Such distances are highlighted in the unit cell of Fig. 2l, using the same color code. The intra-slab distance d ~2.53 Å connecting two Fe atoms within the same Fe-Ge-Te slab fails in reproducing the observed modulation, despite it well described the L-dependent continuum modulation for Fe2.72GeTe216. Rather, we find that an inter-slab distance d ~11 Å connecting the center of two consecutive slabs well reproduces the continuum modulation for Fe4.75GeTe2. Our finding supports the presence of an inter-slab exchange path along the c-axis, suggesting a three-dimensional character for the magnetic interaction in Fe4.75GeTe2. Additionally, we identify the Fe-Ge-Te slabs as the interacting magnetic units in Fe4.75GeTe2. This is consistent with recent X-ray magnetic circular dichroism and ARPES studies underlining the key role of Te and Ge in determining the itinerant long-range ferromagnetism in Fe4.75GeTe229,40, owing to the strong hybridization and covalent nature of the Fe-Te and the Fe-Ge bonds. Based on atomic position considerations, we suggest that the shorter Fe-Te nearest neighbor distance (2.63 Å) in Fe4.75GeTe2with respect to Fe2.72GeTe2 (2.643 Å) possibly favors the inter-slab exchange mediated by the Te sites (highlighted by the curved line in Fig. 2j). Overall, we speculate that the inter-slab exchange interaction revealed by our study could be crucial for determining the high TC in Fe4.75GeTe2, endorsed by recent studies on epitaxially grown thin films where TC is found to be inversely proportional to the inter-slab distance44.

Absence of charge order in bulk Fe4.75GeTe2

Recently, selected area electron diffraction studies45 reported a superstructure modulation vector Q1 = ±1/3 (1 1 3) above 100 K, fading away at lower temperatures with a diffused line along 1/3 (1 1 L) together with a new Q2 = ±3/10 (0 0 3L) order. A short range \(\sqrt{3}a\times \sqrt{3}a\,R3{0}^{\circ }\) order was observed by single crystal XRD and the high-angle annular dark field image and associated with Fe occupancy of a crystallographic split-site4. Further STM and ARPES investigations17 confirmed the existence of a \(\sqrt{3}a\times \sqrt{3}a\,R3{0}^{\circ }\) in-plane periodic modulation and assigned it to the charge ordering. To further the understanding of the bulk signature, electronic character, and propagation vectors of Q1 and Q2 in Fe4.75GeTe2, in the following, we present synchrotron XRD (~2.1 keV) and REXS (Fe K-edge, ~7.1 keV) investigations.

We confirmed the in-plane order \(\sqrt{3}a\times \sqrt{3}a\,R3{0}^{\circ }\) in our Fe4.75GeTe2single crystal by finding several symmetry-equivalent peaks at 150 K, as represented in Fig. 3a. Figure 3b reports the H, K, and L scans of a representative peak with (1/3 1/3) in-plane components, measured using ~2.1 keV X-rays. Interestingly, we find that the out-of-plane component peaks at L = 7.5 r.l.u. No significant temperature dependence is detected for this peak while going across 100 K, as displayed in Fig. 3c. The extended L scan of (2/3 –1/3 L) and (1/3 1/3 L) peaks are presented in Fig. 3d, using ~7.1 keV X-rays (dotted lines): a clear (1/3 1/3 3n + 1.5) with n = 0, 1, 2, 3.... periodicity emerges even at 7 K. The observed (1/3 1/3 3n + 1.5) modulation differs from the previously reported ±1/3 (1 1 3) order45 and it is also distinct from the (0 0 3n) selection rule expected for a rhombohedral unit cell (space group \(R\bar{3}m\)). For reference, we reproduce in Fig. 3(d) the (0 0 L) scan (gray line) showing the (0 0 3n) periodicity of the structural Bragg peak. The satellite structure visible in the (0 0 L) scan is attributed to a second crystallite present in the sample. Also, no fingerprint of Q2 = ±3/10(0 0 3L) is observed in our data down to 7 K.

Fig. 3: Investigation of charge order in Fe4.75GeTe2by REXS and XRD.
figure 3

a A sketch highlighting the measured symmetry equivalent Q positions. b H, K, and L scans of a representative (1/3 1/3 7.5) peak using 2.1 keV X-ray energy at 150 K. c The temperature dependence of the (1/3 1/3 7.5) peak. d Fixed-energy Q-scan of (1/3 1/3 L) (green dotted line), (2/3 −1/3 L) (pink dotted line), and of (0 0 L) (gray line) along the L direction. The temperature was set to 7 K for this measurement and the X-ray energy was tuned prior to the Fe K-edge, ~7.1 keV. Double peaks in (0 0 L) scan are due to a second crystallite. (0 0 L) scan is rescaled to match y-scale. e Absolute intensity comparison between (1/3 1/3 22.5) and (0 0 9) peaks. f Fixed-Q energy scan of (1/3 1/3 22.5) (green dotted line) and (0 0 9) (gray dotted line) peaks, rescaled to match y-scale. The Fe K-edge XAS of Fe4.75GeTe2measured in total fluoresce yield (TFY) mode is displayed (rescaled) for reference (blue dotted line).

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The intensities of (0 0 L) and (2/3 −1/3 L) or (1/3 1/3 L) scans cannot be directly compared in Fig. 3d, as we used a higher intensity detuning filter for the main structural Bragg peaks along (0 0 L). An absolute intensity comparison between (1/3 1/3 22.5) and (0 0 9) is presented in 3e, showing that the intensities of both peaks are of the same order of magnitude, with the (0 0 9) peak ~50% stronger than (1/3 1/3 22.5).

Additionally, using Fe K-edge REXS, we investigated the resonance effect of the (1/3 1/3 22.5) peak. The resulting fixed-Q energy scan is presented in Fig. 3e (green dotted line) and compared to the energy scan of the (0 0 9) structural Bragg peak (gray line). Both scans present a similar behavior, with no resonance enhancement. The Fe K-edge XAS of Fe4.75GeTe2 is reproduced for reference in the same figure.

Overall, our REXS and XRD studies report the presence of a commensurate (1/3 1/3 L) Bragg peak with a 3n + 1.5 out-of-plane modulation, no temperature dependence down to 7 K, and no resonance effect. Based on these observations, we propose these peaks originate from the crystal structure rather than CO 25,26,27,46. This conclusion is further corroborated by the comparable peak intensity with respect to main structural Bragg peaks. Furthermore, we underline that the observed 3n + 1.5 out-of-plane periodicity is not compatible with the space group \(R\bar{3}m\) proposed for Fe4.75GeTe2, instead, it infers doubling of structural unit cell along the c-axis and reduced crystal symmetry. One direct consequence of reduced lattice symmetry would be a more complex network of magnetic interactions, which might be crucial to interpret the various kinks in the magnetization versus temperature diagram4.

To reconcile the discrepancy between our observations and the ones reported in the literature17,45, we should acknowledge intrinsic differences connected with the techniques involved. STM and ARPES mostly probe the surface, which in certain materials can significantly differ from the bulk47,48,49,50. Electron diffraction instead probes the bulk, but the required sample preparation methods—such as focused ion beam and grinding—might introduce permanent micro-structural changes affecting the material response51,52. Finally, we cannot exclude a sample-to-sample variation in determining the ultimate material properties. Fe4.75GeTe2 single crystals are known to have stacking faults and different samples (especially grown by different groups) might even have slightly different Fe concentration. To advance the understanding of this complex system, it would be helpful to perform on the same sample both surface-sensitive (STM, ARPES) and bulk-sensitive (XRD, REXS) investigations.

In summary, our work sheds light on the magnetic excitaW ferromagnet Fe4.75GeTe2. Using high-resolution RIXS at the Fe L3-edge, we reveal that Fe4.75GeTe2 hosts dual character of magnetic excitations composed of a magnon and a continuum, similarly to the more extensively characterized Fe2.72GeTe2, and prove that the dual character of magnetic excitation, known to be driven by OSMT, is common to ternary Fe-Ge-TevdW materials. The out-of-plane modulation of the continuum intensity reveals the presence of a strong out-of-plane inter-slab exchange path, where the interacting magnetic units are the neighboring Fe-Ge-Te slabs. We conclude that Fe4.75GeTe2 behaves like a 3D magnet, and we discuss this finding in connection to its TC, the highest among Fe-Ge-TevdW materials. Additionally, employing XRD and REXS, we explored the bulk character, the electronic origin, and the propagation vector of the previously reported CO with (1/3 1/3) in-plane components. The absence of temperature and resonance effects, and the commensurability with the crystal structure led us to conclude that the observed Bragg peaks do not originate from CO but rather crystal structure with reduced symmetry. The presence of the (1/3 1/3 3n + 1.5) peaks suggests a doubling of the unit cell along the c-axis, indicating a subtle change in the stacking sequence or atomic positions that is not captured by the \(R\bar{3}m\) space group.

Methods

X-ray absorption (XAS) and resonant inelastic X-ray scattering (RIXS)

High-resolution XAS and RIXS experiments were carried out at the SIX 2-ID beamline of NSLS-II 53. The experimental energy resolution at the Fe L3-edge (~708 eV) was 21 meV for the RIXS measurements, determined by the full width at half-maximum of the elastic peak measured from a reference multilayer sample. To suppress the elastic line, π polarization was used throughout the experiment.

Resonant elastic X-ray scattering (REXS) and X-ray diffraction (XRD)

Synchrotron-based XRD was used to measure the rocking curves and temperature dependence of (1/3 1/3 7.5) peak at 29-ID beamline of APS, with a photon energy of 2.1 keV. The Fe K-edge REXS was performed at the 4-ID beamline of NSLS-II.

Raman spectroscopy

We performed room-temperature Raman scattering (λ = 6328 Å) on a Fe4.75GeTe2 flake exfoliated on SiO2/Si and oriented as c-axis normal using a LabRAM HR Evolution Raman microscope from Horiba Scientific using 100 × 0.9 NA Olympus air objective. Spectra were recorded using an 1800 gr/mm holographic grating and Synapse II front-illuminated EMCCD (Supplementary Fig. 1).