Abstract
The discovery of 2dimensional (2D) materials, such as CrI_{3}, that retain magnetic ordering at monolayer thickness has resulted in a surge of both pure and applied research in 2D magnetism. Here, we report a magnetoRaman spectroscopy study on multilayered CrI_{3}, focusing on two additional features in the spectra that appear below the magnetic ordering temperature and were previously assigned to high frequency magnons. Instead, we conclude these modes are actually zonefolded phonons. We observe a striking evolution of the Raman spectra with increasing magnetic field applied perpendicular to the atomic layers in which clear, sudden changes in intensities of the modes are attributed to the interlayer ordering changing from antiferromagnetic to ferromagnetic at a critical magnetic field. Our work highlights the sensitivity of the Raman modes to weak interlayer spin ordering in CrI_{3}.
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Introduction
Magnetic van der Waalsbonded materials represent a rapidly growing research field^{1,2,3,4,5,6}, where these materials provide a solidstate platform to study a variety of exciting physics and potential applications of magnetism in two dimensions, including proximity effects, control using strain and gating, spin fluctuations, magnetic excitations, spintronics, and possible quantum spin liquids^{7}. One material of particular interest is chromium triiodide (CrI_{3}), a ferromagnet (FM) at bulk thicknesses below the Curie temperature (T_{c}) but with the remarkable property of layered antiferromagnetism (AFM) in thin multilayers^{2}. Although each individual layer is FM, the layers themselves are AFM coupled, and this effect persists for samples tens of layers thick. Furthermore, the interlayer spin arrangement in CrI_{3} can be switched between AFM and FM by an electric field^{8,9,10}, applied pressure^{11}, and a magnetic field^{2,12,13,14,15}, providing tunability in potential devices.
Raman spectroscopy is a powerful technique to study a variety of phenomena in 2D quantum materials, including effects of strain^{16}, electron–phonon coupling^{17}, phase transitions^{18}, spinphonon coupling^{19}, and magnetic excitations^{20,21,22}. In addition, the diffractionlimited spot size allows for the investigation of atomically thin samples and heterostructures using a noncontact probe. In this work, we collect temperature and magnetic field (B)dependent Raman spectra on a thin (~10 layers) CrI_{3} single crystal encapsulated in hexagonal boron nitride (hBN). Interestingly, at low temperature, increasing the magnetic field results in dramatic changes in the Raman spectra, indicating a magnetic fieldinduced phase transition when the interlayer spin arrangement changes from AFM to FM. By calculating the phonon dispersion of CrI_{3} in both the FM and AFM state, we conclude the two modes that only appear in the AFM state are zonefolded phonons. This work validates magnetoRaman spectroscopy as a sensitive technique to probe interlayer magnetic ordering in quantum materials.
Results
Polarizationdependent Raman at zero magnetic field
A thin flake of CrI_{3} (≈7 nm from atomic force microscopy, or ≈10 layers) was encapsulated between two 20 nm and 30 nm flakes of hBN using the dry transfer technique^{22,23}. In the ab plane, the Cr^{3+} atoms are arranged in a honeycomb lattice, where each chromium atom is bonded with six iodine atoms to form a distorted octahedron (see Fig. 1a). At room temperature, bulk CrI_{3} has a monoclinic structure (C2/m) but exhibits a crystallographic phase transition below ≈220 K to rhombohedral (R\(\bar 3\))^{24}, where the main difference between the two structures is the stacking of the layers (see Supplementary Fig. 1). The bulk T_{c} is ≈61 K^{24}, with the spins aligned perpendicular to the ab plane. Surprisingly, the magnetic behavior of thinner samples is very different; whereas the spins still align perpendicular to the ab plane, the interlayer magnetic stacking is AFM, as demonstrated through a variety of experimental techniques^{2,8,9,12,13,14,15,25,26}. It has been theoretically^{27,28,29,30} and experimentally^{26,30} suggested that atomically thin CrI_{3} does not go through the crystallographic phase transition that the bulk does, but instead remains in the monoclinic structure at low temperatures, resulting in AFM interlayer stacking.
Raman spectra were collected with a triple grating spectrometer using an excitation laser wavelength of 632.8 nm and keeping the power below 150 μW (≈1 µm spot size) at the sample to avoid heating. The laser polarization of the incoming ε_{i} light makes an angle φ with respect to the b axis (Fig. 1a), and the scattered ε_{s} light angle θ is changed from θ = 0° (parallel, xx) to θ = 90° (perpendicular, xy). As the crystallographic a and b axes are not known in our sample, the angle φ is an arbitrary, yet constant angle in our experiments. Figure 1b shows the Raman spectra at T = 5 K, in both the xx and xy polarization configurations. We confirm the monoclinic symmetry in our ≈10 layer flake by resolving two peaks at 108 cm^{−1} and 109 cm^{−1} between xx (black, scaled by 0.5) and xy (red), unlike the doubly degenerate peak seen in the rhombohedral structure^{31}. Thus, we label the phonons using the irreducible representations of the 2/m point group, where only the A_{g} and B_{g} modes are Raman active^{32,33}. The density functional theory (DFT) calculated atomic displacements associated with these modes are shown in Supplementary Table 1.
Two modes appear below T_{c} in the xy configuration at 77 cm^{−1} (9.5 meV) and 126 cm^{−1} (15.6 meV), labeled P_{1} and P_{2} in Fig. 1b, respectively. These modes were previously attributed to onemagnon excitations since they appear in the magnetically ordered state and have their largest intensity in xy (inset of Fig. 1b, Supplementary Fig. 2), indicating B_{g} symmetry^{34}. Instead, the bulk magnon dispersion^{35} at 5 K shows a lowenergy magnon at Γ below 1 meV (8 cm^{−1}), similar to what was measured by recent FM resonance experiments^{36}, and magnons at the M point of the Brillouin zone at ≈9 meV and 15 meV. Furthermore, a recent Raman study of magnon excitations in FePS_{3} showed it is possible for magnons to be present in both xx and xy in quasi2D van der Waals magnets^{20}. Thus, the B_{g} nature of P_{1} and P_{2} is not conclusive evidence that they are magnons.
MagnetoRaman measurements of 10 L CrI_{3} in Faraday geometry
We studied the effects of an applied magnetic field perpendicular to the ab plane (B ⊥ ab, Faraday geometry) on P_{1} and P_{2}, as detailed in Fig. 2. Two spectral ranges from 65 cm^{−1} to 90 cm^{−1} (P_{1}, \({\mathrm{A}}_{\mathrm{g}}^1\)) and 120 cm^{−1} to 136 cm^{−1} (P_{2}, \({\mathrm{A}}_{\mathrm{g}}^6\)) are shown on different intensity scales (≈a factor of 3:1, respectively) for clarity. At B = 0 T and in xy, P_{1} and P_{2} have strong intensities, whereas the two A_{g} modes at slightly higher frequencies have minimum intensities as they are forbidden in the xy configuration. Increasing the magnetic field results in drastic changes in the Raman spectra, where P_{1} and P_{2} behave in the same fashion. Above ≈1.6 T, the intensities of P_{1} and P_{2} abruptly start to vanish and \({\mathrm{A}}_{\mathrm{g}}^1\) and \({\mathrm{A}}_{\mathrm{g}}^6\) begin to appear in xy. By B = 2 T, P_{1} and P_{2} are absent in all polarization configurations, whereas \({\mathrm{A}}_{\mathrm{g}}^1\) and \({\mathrm{A}}_{\mathrm{g}}^6\) are no longer forbidden in xy. No further changes occur above 2 T, and no hysteresis was observed when the field was lowered back to 0 T. It should be noted that P_{1} and P_{2} do not show frequency shifting with magnetic field, suggesting they are not onemagnon processes with spins perpendicular to the ab plane.
Raman spectra were collected as the magnetic field was increased in finer steps up to 2 T. This is shown as a falsecolor map (Fig. 3a) and spectra (Fig. 3b) for the frequencies near P_{2} and \({\mathrm{A}}_{\mathrm{g}}^6\), where six distinct magnetic field ranges are revealed. Upon close inspection, there is additional Raman scattering intensity, i.e., spectral weight, present between P_{2} and \({\mathrm{A}}_{\mathrm{g}}^6\) ≈128 cm^{−1}, although it cannot be discerned if the spectral weight is attributed to a single or multiple mode(s). No changes to P_{2}, \({\mathrm{A}}_{\mathrm{g}}^6\), or the spectral weight were observed in Range 1 from 0 T and 0.6 T. In Range 2 between 0.7 T and 0.8 T, the spectral weight between P_{2} and \({\mathrm{A}}_{\mathrm{g}}^6\) appears to shift in frequency and intensity. The spectra are again stable through Region 3 from 0.8 T to 1.4 T, after which striking changes are seen in Regions 4 and 5. In Region 4, P_{2} starts to decrease in intensity, the intensity of \({\mathrm{A}}_{\mathrm{g}}^6\) stays relatively constant, and the spectral weight shifts in frequency and increases in intensity. In Region 5, P_{2} and the spectral weight both decrease in intensity until they disappear, whereas \({\mathrm{A}}_{\mathrm{g}}^6\) grows in intensity until B > 1.95 T (Region 6), when the phase transition is finally complete. It should be noted that experimental uncertainty, including instrumental drift and corrections for Faraday rotation in magnetocryostat objective lenses, can lead to small changes in peak intensities (generally less than 5%) when comparing consecutively taken Raman spectra. The intensity changes being tracked in the field ranges in Fig. 3b, however, are more significant than any changes seen in the Γ point phonons (see Supplementary Fig. 3) and are thus outside of experimental uncertainty. Moreover, frequency shifts, such as those observed in the spectral weight between P_{2} and \({\mathrm{A}}_{\mathrm{g}}^6\) in Regions 2 and 4, are significantly more reliable than intensity changes, generally reproducible to within one CCD detector pixel (≈0.4 cm^{−1} with He–Ne excitation herein). For fitted peaks (e.g., welldefined phonons), changes in the Raman shift frequency are even more precise (better than 0.1 cm^{−1}).
Recent magnetotunneling measurements of fewlayered CrI_{3} observed large changes in the tunneling current at nearly the same magnetic field values where we observe marked changes in the Raman spectra, such as at 0.8 T and 2 T^{12,13,14,15,25}. These changes were attributed to the spinfiltering effect when the magnetic field is strong enough to change the interlayer spin arrangement from AFM to FM, and the effect was observed even for 20 nm thick samples (our sample is ≈7 nm). The striking resemblance in the evolution with magnetic field observed with magnetotunneling, including sharp changes between regions of stability, to those reported herein implies Raman spectroscopy is detecting the phase transition caused by layers flipping spins from AFM to FM stacking. The observation of the first jump at 0.8 T in a variety of thicknesses of CrI_{3} in magnetotunneling^{12,13,14,15,25} suggests it is most likely a result of the surface layers (adjacent to the hBN) flipping while the second, final jump is the flipping of the internal layers at ≈2 T. This spinflip phase transition is supported by the observation of the lower energy FM magnon for B > 6.5 T (Supplementary Fig. 4), which matches previous results on bulk, FM CrI_{3}^{35,36}, and the lack of change in the Raman spectra between 2 T and 9 T (Supplementary Fig. 5). The 10 L sample remains monoclinic at high magnetic fields (Supplementary Fig. 6), demonstrating that a change in crystal structure is not the source of the evolution in the Raman spectra. In particular, the spectral weight present between P_{2} and \({\mathrm{A}}_{\mathrm{g}}^6\) is extremely sensitive to the spinflipping, displaying strong frequency shifts and intensity variations where the spin flips occur. The fact that the spectral weight does not shift in magnetic field in Regions 1 and 3, which are regions of stability, suggests its presence does not involve a onemagnon process. It is possible that the spectral weight results from the excitation laser wavelength (λ = 632.8 nm) being nearly resonant with the ligandtometal charge transfer transition^{37,38,39,40}, but the weak Raman signal at offresonance excitation laser wavelengths makes this difficult to verify.
The polar plots for \({\mathrm{A}}_{\mathrm{g}}^6\), which track the intensity of \({\mathrm{A}}_{\mathrm{g}}^6\) as a function of angle θ, at various magnetic fields provide further evidence of the magnetic phase transition. As seen in Fig. 4a, the polar plot is rotated by ≈35° at B = 2 T when compared with B = 0 T. This can be understood if we write the Raman tensor for the A_{g} phonon with an induced magnetization m under applied magnetic field (B ⊥ ab) as
which separates the spinindependent and spindependent terms. The point group of CrI_{3} requires that the total Raman tensor \(R_{A_g}\) is symmetric under twofold rotation around the b axis (C_{2x}). Thus, \(R_{A_g,m = 0}\) and \(m_z \cdot R_{A_g,m_z}\) must be symmetric under twofold rotation individually. As m_{z} itself is antisymmetric under C_{2x}, then the form of \(R_{A_g,m_z}\) is required to also be antisymmetric under C_{2x} such that their product is symmetric:
Thus, for the B = 0 T case (AFM state) where there is no induced magnetization, the Raman tensor would be purely symmetric, and we would not expect to detect the A_{g} phonon in xy polarization configurations. A magnetic field applied perpendicular to the ab plane that spinpolarizes the CrI_{3} to the FM state, however, introduces offdiagonal tensor elements and breaks this expectation, causing the polar plot to rotate as seen in Fig. 4a. Assuming there are minimal changes between the monoclinic (C_{2h}), 10 L CrI_{3} and the hexagonal point group of the monolayer (D_{3d}), then β ≈ α + Δ and δ ≈ −(γ + Δ′), where Δ and Δ′ are small corrections.
Writing the matrices as in Eq. (3) makes it clear that when the magnetic field direction is flipped from B_{z} to −B_{z}, thus flipping the direction of the induced magnetization, the signs of the offdiagonal elements switch, resulting in the opposite rotation of the polar plot, exactly as we observed in Fig. 4b and Supplementary Fig. 7.
Figure 4c shows the angle of maximum intensity of the polar plot in 4a as the magnetic field is swept through the phase transition, where Regions 1–6 from Fig. 3 are marked with vertical dashed lines. Although Fig. 3 and magnetotunneling results indicate that parts of the phase transition occur between Regions 2 and 4, there is no observable change in the maximum intensity of the polar plot in those field ranges. In Region 5, however, it increases to ≈10° for B = 1.7 T and 1.8 T, and then finally to ≈35° for 1.8 T and above. The lack of rotation of the polar plot between 0.7 T and 0.8 T reveals that not enough magnetization is induced in this field range to introduce the offdiagonal Raman tensors in Eq. (2).
The temperature dependence of the spin flips was investigated by tracking the intensity of P_{2} as a function of magnetic field for different temperatures between T = 9 K and 26 K, as detailed in Fig. 4d. The intensity of P_{2} is shown relative to the intensity of the combination peak \({\mathrm{A}}_{\mathrm{g}}^5{\mathrm{/B}}_{\mathrm{g}}^3\) at ≈115 cm^{−1} at B = 0 T for each temperature, as this peak appears to remain constant with temperature and magnetic field (in the probed range). The spinflip transition field, or the amount of magnetic field necessary to cause P_{2} to disappear, decreases with increasing temperature. In addition, the distinct jumps from spin flips and flat plateaus observed in the intensity of P_{2} smooth out for higher T. Further temperature dependence is analyzed in Supplementary Fig. 8. This behavior is consistent with a phase transition where there is a strong correlation between the temperature and magnetic field, which suggests that the magnetic field takes the transition temperature to zero. Although this behavior is akin to a quantum phase transition, there is no evidence yet of any quantum critical behavior in this material, but it is a very interesting avenue for future investigation.
MagnetoRaman measurements of 10 L CrI_{3} in Voigt geometry
Finally, we investigated the directional dependence of the spinflip phase transition by rotating the sample such that the applied magnetic field is parallel to the ab plane (B ∥ ab, Voigt geometry). Figure 4e shows \(I\left( {{\mathrm{P}}_2} \right){\mathrm{/}}I\left( {{\mathrm{A}}_{\mathrm{g}}^5{\mathrm{/B}}_{\mathrm{g}}^3} \right)\) for B ∥ ab and at T = 2 K. Unlike in the case for B ⊥ ab, no jumps or plateaus are observed in the intensity of P_{2}. Instead, the intensity of P_{2} continuously decreases with increasing applied magnetic field up to B = 6 T, after which the layers are stacked FM with the spins pointing in the ab plane. This observation matches nicely with measurements of the magnetotunneling current when the field is in the ab plane^{12,13,14,15}. Furthermore, no frequency shift of P_{2} is observed as a function of magnetic field (Supplementary Fig. 9). We perform the same tensor analysis that was done for Eqs. (1) and (2) above, but this time for the magnetic field applied in the ab plane.
where x (y) corresponds to b axis (a axis). Requiring that the total Raman tensor be symmetric under C_{2x}, then \(R_{A_g,{\mathbf{B}}\parallel {\mathrm{ab}}}\) is written as:
From Eq. (5), when the magnetic field is directed along the b axis and strong enough to align the spins and create a net magnetization m_{x}, we expect the Raman tensor to be symmetric and the polar plot of the intensity of \({\mathrm{A}}_{\mathrm{g}}^6\) as a function of θ not to rotate. However, when the magnetic field has a component pointed along the a axis that results in a net magnetization m_{y}, offdiagonal tensor elements are introduced, and some rotation of the polar plot would be expected. To test these predictions, we rotated the sample while the magnetic field was applied in the ab plane such that the magnetic field was pointed along two different crystal orientations φ_{1} and φ_{2} = φ_{1} + 90°. The polar plot of the intensity of \({\mathrm{A}}_{\mathrm{g}}^6\) at B = 0 T and 7 T (in the spinpolarized state) are shown in Fig. 4f. Interestingly, for both orientations, in which either φ_{1} or φ_{2} must contain magnetic field components along the a axis, the polar plot of the intensity of \({\mathrm{A}}_{\mathrm{g}}^6\) does not show the same rotation that was observed for spins pointing perpendicular to the ab plane in the spinpolarized state. This indicates that the offdiagonal elements γ′ and δ′ are negligible for magnetic fields pointing in the ab plane.
Discussion
Our data shows that P_{1} and P_{2}, which appear (disappear) in the AFM (FM) state and are absent in bulk samples (Supplementary Fig. 10), are not onemagnon excitations, as their frequencies do not shift with applied magnetic field. After considering other theoretical models (see Supplementary Notes 1 and 2, Supplementary Tables 2–5, Supplementary Fig. 11), we conclude that P_{1} and P_{2} are actually zonefolded phonons owing to a doubling of the AFM unit cell in the c direction. This is illustrated in Fig. 5a, where the opposite spins of consecutive layers in the AFM configuration lead to a unit cell that is twice as large in the c direction compared to the FM configuration.
Using DFT, we calculated the phonon dispersions for monoclinic, bulk CrI_{3} in both the FM and AFM stacking configurations. The full phonon dispersions, Brillouin zone, and table of frequencies are given in Supplementary Figs. 12 and 13 and Supplementary Table 6. Figure 5b shows only the Ramanactive phonons in the FM state (red, solid) and AFM state (blue, dotted) for frequencies near P_{1} and P_{2}. In general, Raman spectroscopy is only sensitive to modes at the Γ point in the phonon dispersion due to conservation of momentum. Thus, phonons at the A point (in direction of k_{z}) in the FM state are not observed. However, the doubling of the unit cell in the AFM state leads to zonefolding, where the phonons at the A point in the Brillouin zone in the FM state fold back onto Γ in the AFM state and can be observed in Raman spectroscopy. Two pairs of modes with similar frequencies to P_{1}/\({\mathrm{A}}_{\mathrm{g}}^1\) and P_{2}/\({\mathrm{A}}_{\mathrm{g}}^6\) have an easily resolvable frequency splitting at Γ (highlighted Fig. 5b), with the zonefolded phonon (P_{1} or P_{2}) between 2 cm ^{−1} and 4 cm^{−1} lower in frequency than the original phonon (\({\mathrm{A}}_{\mathrm{g}}^1\) or \({\mathrm{A}}_{\mathrm{g}}^6\)). Illustrations of these vibrations are shown in Fig. 5c, d, where the two layers vibrate inphase for \({\mathrm{A}}_{\mathrm{g}}^1\) and \({\mathrm{A}}_{\mathrm{g}}^6\) and outofphase for P_{1} and P_{2}. In the bulk, P_{1} and P_{2} would have B_{u} symmetry and would thus be Raman silent but infrared active. However, the breaking of inversion symmetry for an even number of layers in the AFM configuration would allow P_{1} and P_{2} to be Raman active with B symmetry (only seen in xy configurations). These zonefolded phonons would not shift in magnetic field and would be Ramanactive (forbidden) in the AFM (FM) state, aligning with the observed behaviors of P_{1} and P_{2}.
Even though the doubling of the unit cell is purely magnetic in nature, the observation of very strong zonefolded phonons that have similar intensity as the observed Γ point phonons reveals the strong coupling between magnetism and the lattice in atomically thin CrI_{3}. Of note, the origins of P_{1} and P_{2} as zonefolded phonons predict they would disappear for a monolayer sample (no zonefolding) or a sample with an odd number of layers because the AFM state preserves inversion symmetry with an odd number of layers. Recent work^{41,42} has shown P_{1} and P_{2} are not present in monolayers of CrI_{3}, yet data by Jin et al.^{34} suggests the presence of P_{1} and P_{2} for odd layer thicknesses. One possibility is that the encapsulation of thin layers of CrI_{3} in hBN breaks inversion symmetry naturally, leading to the presence of P_{1} and P_{2} in all thicknesses. Further studies as a function of layer thickness and encapsulation parameters are needed to elucidate the symmetry response of P_{1} and P_{2} for even vs. odd numbers of layers.
In conclusion, we utilized temperaturedependent, magnetoRaman spectroscopy to elucidate a magnetic phase transition in CrI_{3} where the interlayer stacking changes from AFM to FM. Substantial changes in the Raman spectra are detected at specific magnetic field values due to spin flips of layers to a FM stacking state, indicating that Raman modes are extremely sensitive to this phase transition. Moreover, Raman scattering proves to be crucial to understanding the symmetry and frequency shifts of the modes. We deduce that the modes P_{1} and P_{2} are not high frequency magnons as previously concluded, but instead attribute the modes to zonefolded phonons using symmetry arguments, polarizationdependent Raman responses, and calculated phonon dispersions in the FM and AFM stacking configurations. This study paves the way for further use of magnetoRaman spectroscopy to investigate spinflip phase transitions in 2D van der Waals magnets.
Methods
Sample preparation and encapsulation
Bulk CrI_{3} crystals were grown by a chemical vapor transport technique using stoichiometric mixtures of Cr and I in a sealed evacuated quartz tube, as mentioned in other references^{5,24}. The phase of the obtained crystals were checked by Xray diffraction. These crystals were then exfoliated onto Si/SiO_{2} substrates in an Arfilled glovebox having O_{2} and H_{2}O concentrations of <0.1 ppm. hBN/CrI_{3}/hBN heterostructures were fabricated using a dry transfer technique detailed elsewhere^{23,43}. Specifically, PDMS (polydimethylsiloxane) was used as the polymer stamp.
Raman spectroscopy
A triple grating Raman spectrometer (Horiba JY T64000^{†}, 1800 mm^{−1} grating) coupled to a liquid nitrogen cooled CCD detector was used to collect Raman spectra. The excitation wavelength was 632.8601 nm from a He–Ne laser and spectra were measured in the 180° backscattering configuration. Raman spectra as a function of temperature and magnetic field were collected using an attoDRY cryostat (Attocube Inc.^{†}), where the sample was zerofield cooled and studied with a magnetic field compatible objective (×50, N.A. 0.82). Ultrabroadband polarizers and achromatic half wave plates were used to select and control polarization, including correcting for Faraday rotation in the objective under applied magnetic field. The laser power was ≈150 µW to avoid local heating and integration times were ≈12 min.
DFT phonon calculations
We performed DFT calculations^{44,45} with the Quantum Espresso^{46} code, using the GBRV ultrasoft pseudopotential set^{47,48}. We used the vdwdfob86 exchange correlation functional^{49,50}, which includes long range van der Waals interactions, for our main results. We also tested the PBEsol^{51} functional, finding similar results. Phonon calculations were performed using a finite differences (frozen phonon) approach, using PHONONPY^{52} to perform symmetry analysis and the cluster_spring^{53} code to calculate phonon dispersions. A 6 × 6 × 4 kpoint sampling was used for the ferromagnetic unit cell.
(Certain commercial equipment, instruments, or materials are identified in this manuscript in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the materials or equipment are necessarily the best available for the purpose).
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
A.M., T.T.M., and A.R.H.W. would like to acknowledge the National Institute of Standards and Technology (NIST)/National Research Council Postdoctoral Research Associateship Program and NISTSTRS (Scientific and Technical Research and Services) for funding. Work at The Ohio State University was supported by the Center for Emergent Materials, an NSF MRSEC under grant DMR1420451. D.S. is supported by NSF/DMR 1807928. The single crystal growth efforts at Penn State are supported by the US Department of Energy under grant DESC0019068. D.W. gratefully acknowledges the financial support by the German Science Foundation DFG Research Fellowship (WE6480/1). Growth of hexagonal boron nitride crystals was supported by the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST(JPMJCR15F3), JST.
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A.M., T.T.M, J.R.S., R.V.A, and A.R.H.W conceived the project. Bulk CrI_{3} crystals were grown by Y.Z, J.H., D.W, J.E.G, and Z.M. Hexagonal boron nitride crystals were supplied by K.W. and T.T. Heterostructures were fabricated by D.S. and C.N.L. Raman measurements and analysis were carried out by A.M., T.T.M., J.R.S., R.V.A., and A.R.H.W. Theoretical analysis, including modeling, and numerical calculations, were carried out by F.G.U. and X.F., N.T., and Y.M.L. Phonon DFT calculations were carried out by K.F.G. All authors contributed to the writing of the manuscript.
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McCreary, A., Mai, T.T., Utermohlen, F.G. et al. Distinct magnetoRaman signatures of spinflip phase transitions in CrI_{3}. Nat Commun 11, 3879 (2020). https://doi.org/10.1038/s41467020173203
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DOI: https://doi.org/10.1038/s41467020173203
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