Tunable layered-–assisted -Raman effect in a two-dimensional CrI3 Wencan Jina,1, Zhipeng Yeb, Xiangpeng Luoa, Bowen Yangc,d, Gaihua Yeb, Fangzhou Yinc,d, Hyun Ho Kimc,d,2, Laura Rojasb, Shangjie Tiane,f, Yang Fue,f, Shaohua Yane,f, Hechang Leie,f, Kai Suna, Adam W. Tsenc,d, Rui Heb,3, and Liuyan Zhaoa,3

aDepartment of Physics, University of Michigan, Ann Arbor, MI 48109; bDepartment of Electrical and Computer Engineering, Texas Tech University, Lubbock, TX 79409; cInstitute for Quantum Computing, Department of Physics and Astronomy, University of Waterloo, ON N2L 3G1, Canada; dDepartment of Chemistry, University of Waterloo, ON N2L 3G1, Canada; eDepartment of Physics, Renmin University of China, 100872 Beijing, China; and fBeijing Key Laboratory of Opto-electronic Functional Materials & Micro-Nano Devices, Renmin University of China, 100872 Beijing, China

Edited by S. Lance Cooper, University of Illinois, Urbana, IL, and accepted by Editorial Board Member Zachary Fisk August 14, 2020 (received for review June 22, 2020) We used a combination of polarized Raman spectroscopy experi- the linear crossed polarization channel across the layered-AFM to ment and model magnetism–phonon coupling calculations to study FM transition (7, 16–18). However, the physical origin of the the rich magneto-Raman effect in the two-dimensional (2D) magnet magneto-optical Raman effect remains elusive with diverse pro- CrI . We reveal a layered-magnetism–assisted phonon scattering 3 posals ranging from Davydov split for bilayer CrI3 (16, 18), to mechanism below the magnetic onset temperature, whose Raman zone-folded phonon for few-layer CrI3 (17), to coupled magnetism– excitation breaks time-reversal symmetry, has an antisymmetric phonon scattering for bulk CrI3 (7), none of which can be trivially Raman tensor, and follows the magnetic phase transitions across generalized to explain CrI3 of arbitrary thickness. critical magnetic fields, on top of the presence of the conventional In this work, we systematically examine the magneto-optical phonon scattering with symmetric Raman tensors in N-layer CrI . 3 Raman effect for N-layer CrI (N = 1to4)byperformingpo- We resolve in data and by calculations that the first-order A pho- 3 g larization, temperature, and -dependent micro- non of the monolayer splits into an N-fold multiplet in N-layer CrI3 due to the interlayer coupling (N≥2) and that the phonons within Raman spectroscopy measurements and unambiguously identify – the multiplet show distinct magnetic field dependence because of the layered-magnetism assisted phonon scattering as the origin APPLIED PHYSICAL SCIENCES their different layered-magnetism–phonon coupling. We further applicable for CrI3 of any thickness. N-layer CrI3 crystalline flakes find that such a layered-magnetism–phonon coupled Raman scatter- were exfoliated from high-quality CrI3 single crystals, sandwiched ing mechanism extends beyond first-order to higher-order multi- between hexagonal boron nitride (hBN) thin flakes, and then phonon scattering processes. Our results on the magneto-Raman effect of the first-order phonons in the multiplet and the higher- Significance order multiphonons in N-layer CrI3 demonstrate the rich and strong behavior of emergent magneto-optical effects in 2D and The two-dimensional (2D) magnetic semiconductor CrI hosts a – 3 underline the unique opportunities of spin phonon physics in van variety of strong and tunable magneto-optical effects and al- der Waals layered magnets. lows for the development of novel magneto-optical devices.

While the elastic magneto-optical effects in CrI3 are well un- two-dimensional layered magnetism | magneto-Raman effect | Raman derstood, its recently discovered inelastic magneto-Raman ef- spectroscopy fect remains to have case-specific interpretations varying upon

the thickness of CrI3. We perform comprehensive Raman wo-dimensional (2D) CrI3 of few-layer form features a measurements on 2D CrI3 with polarization, temperature, layer Tlayered-antiferromagnetic (AFM) order where the spins align number, and magnetic field dependence. We resolve a Davydov- along the out-of-plane direction ferromagnetically within each split–induced N-fold multiplet in N-layer CrI3 and reveal the dis- layer and antiferromagnetically between adjacent layers (1–5). It tinct magneto-Raman behaviors of individual phonons within undergoes a layered-AFM to ferromagnetic (FM) phase transition the multiplet. Our results discover a layered-magnetism–coupled upon applying a moderate magnetic field (1–7), or electric field phonon scattering mechanism that explains the rich magneto- (8–10), or electrostatic doping (11), or hydrostatic pressure (12, Raman effect in CrI3 of arbitrary thickness and elucidates the 13). The strong coupling between spin and charge degrees of spin–phonon coupling physics in layered magnets. freedom in 2D CrI3 allows magneto-optical effects manifested in a variety of ways including large magneto-optical Kerr effect (5) and Author contributions: W.J., R.H., and L.Z. designed research; W.J., Z.Y., X.L., B.Y., G.Y., F.Y., H.H.K., L.R., S.T., Y.F., S.Y., H.L., K.S., A.W.T., R.H., and L.Z. performed research; W.J., magnetic circular dichroism (8–13), spontaneous helical photo- X.L., K.S., R.H., and L.Z. analyzed data; W.J., X.L., R.H., and L.Z. wrote the paper; B.Y., F.Y., luminescence (14), giant nonreciprocal second harmonic genera- H.H.K., and A.W.T. fabricated the sample; and S.T., Y.F., S.Y., and H.L. grew the tion (15), and anomalous magneto-optical Raman effect (7, single crystal. 16–19). All of these magneto-optical effects can be tuned across The authors declare no competing interest. This article is a PNAS Direct Submission. S.L.C. is a guest editor invited by the the layered-AFM to FM phase transition, making 2D CrI3 a promising candidate for applications in magnetic sensors, optical Editorial Board. modulation, and data storage. This open access article is distributed under Creative Commons Attribution-NonCommercial- NoDerivatives License 4.0 (CC BY-NC-ND). Among all magneto-optical effects in CrI3, the magneto-optical 1Present address: Department of Physics, Auburn University, Auburn, AL 36849. Raman effect is of particular interest for two reasons. First, among 2Present address: School of Materials Science and Engineering, Kumoh National Institute all known magnets, the largest magnetism-induced optical rotation of Technology, Gumi, Gyeongbuk 39177, Korea. is observed for the linearly polarized, inelastically scattered light 3 −1 To whom correspondence may be addressed. Email: [email protected] or lyzhao@ off the Ag phonon mode (∼129 cm ) in the FM phase of CrI3 umich.edu. (16). Second, different phonon modes exhibit distinct magneto- This article contains supporting information online at https://www.pnas.org/lookup/suppl/ optical behavior that the Ag mode emerges whereas its neigh- doi:10.1073/pnas.2012980117/-/DCSupplemental. − boring strongest antisymmetric mode (∼127 cm 1)disappearsin

www.pnas.org/cgi/doi/10.1073/pnas.2012980117 PNAS Latest Articles | 1of6 Downloaded by guest on September 28, 2021 placed onto SiO2/Si substrates inside a high-purity (>99.999%) between√̅̅̅̅̅̅̅̅̅ adjacent layers, equivalent to a coupling frequency nitrogen-filled glovebox. Micro-Raman spectroscopy measure- ω = k=m. Diagonalizing H leads to N nondegenerate eigenfre- ~ ments in the backscattering geometry were carried out with a quencies Ωi(ω0, ω) and their corresponding eigenmodes Ui (i = 1, 633-nm excitation laser resonant with the charge-transfer transi- 2, ..., N) (i.e., Davydov splitting), with i = 1 being the highest- frequency mode and i = N being the lowest-frequency mode. By tion (14), inside a vacuum cryostat at a base pressure lower than − − −7 ω = ± 1 ω = ± 1 7 × 10 mbar, and under an out-of-plane magnetic field (B⊥) up choosing 0 129.10 0.10 cm and 15.98 0.55 cm , Ω to 2.2 T. the calculated frequencies i (solid lines with open diamonds) We start with resolving in N-layer CrI3 the interlayer coupling- match well with all of the experimental values (red solid squares induced split of the A mode of monolayer CrI (20, 21). Fig. 1A and blue solid circles), as highlighted by the fan diagram in g 3 Ω ~ shows Raman spectra in both parallel and crossed linear polar- Fig. 1B. See detailed calculations of i and Ui in SI Appendix, ization channels taken at T = 10 K and B⊥ = 0 T on 1L to 4L section II and Tables S1 and S2. Because N-layer CrI3 is structurally centrosymmetric, its CrI3 (see full-range spectra in both channels and comparison to off-resonance 532-nm excitations in SI Appendix, section I and N-calculated eigenmodes have alternating parities, with the highest-frequency mode always parity even as a result of Figs. S1 and S2, respectively). It has been established for CrI3 ~ = that the modes in the crossed channel in Fig. 1A correspond to equal, in-phase√̅̅̅̅ atomic displacement between layers (i.e., U1 (1,1, ...,1)= N). In the parallel channel where only modes with antisymmetric Raman tensor (RAS) whereas those in the parallel even parity and symmetric Raman tensor RS can be detected, we channel are for symmetric Raman tensor of Ag symmetry (RS) (19). We highlight three key observations that have not been expect to see every other mode starting with the highest- frequency one (i = 1, 3, 5, ...). This expectation is indeed con- reported in previous work (7, 16–19, 22, 23) and summarize them sistent with our data that U for N = 1 and 2 and U for N = 3 in Fig. 1B with fitted mode frequencies vs. N. First, the number 1 1,3 and 4 are observed in the linear parallel channel in Fig. 1 A and of modes increases proportional to the number of layers (with an B. In contrast to the structure of N-layer CrI , the layered-AFM exception for N = 3 that is explained in SI Appendix, section II). 3 order is centrosymmetric for odd N and noncentrosymmetric for Second, the highest frequency remains constant while the lowest even N. Therefore, it should couple to parity-even phonon frequency decreases with increasing N, leading to a greater fre- modes for odd N and parity-odd phonons for even N to make the quency separation between them. Third, the parallel and crossed coupled layered-AFM–phonon entity parity even and thus channels show modes of the same frequencies for odd N whereas Raman active. Due to the broken time-reversal symmetry from they select modes with distinct frequencies for even N. To in- the magnetism, this layered-AFM–assisted phonon scattering terpret the Ag mode splitting, we take a simple linear chain corresponds to antisymmetric Raman tensor RAS and can appear model of N-layer CrI3, as introduced in few-layer transition – only in the linear crossed channel. We anticipate observing in the metal dichalcogenides (24 27), linear crossed channel every other mode from the lowest- = − − ... ~ N N frequency one (i N, N 2, N 4, ), because UN always 1 2 1 2 1 2 H = H + ∑ k(u − − u ) , with H = ∑( mu_ + k u ), has the same parity as the layered AFM for any N. The result in 0 i 1 i 0 i 0 i = 2 i=2 i=1 2 2 Fig. 1 A and B corroborates with this prediction that U1 for N 1, U2 for N = 2, U3,1 for N = 3, and U4,2 for N = 4 are present in where√̅̅̅̅̅̅̅̅̅̅̅H0 represents the original Ag mode at frequency the linear crossed channel. The coupling efficiency between a ω = k =m within individual layers, u represents the displace- phonon mode and the layered-AFM order can be evaluated by 0 0 i ~ ~ ~ ment field in the ith layer, and k stands for the coupling constant the projection Ui · M of the eigenmode vector Ui onto the

3000 130 ABCT = 10 K Number of layers U mode Magnetic order 2000 N 1000 1L N = 1 0 129 U1 3 15x10 10 N = 2 )

5 -1 128 2L 0 U2 U1 3 30x10 N = 3 20 127 Frequency (cm 10

Intensity (counts/2mins) 3L 0 U3 U1 3 N = 4 40x10 126

20 Parallel channel 4L Crossed channel 0 Linear chain model U4 U3 U2 U1 125 120 125 130 135 140 1 2 3 4 -1 Raman shift (cm ) N

Fig. 1. (A) Raman spectra of 1L to 4L CrI3 acquired in linear parallel (red) and crossed (blue) channels at 10 K. The solid curves are fits to the raw data (dots). The vertical bars underneath individual spectra denote the fitted frequencies and Ui (i = 1, ..., N) labels the corresponding modes in N-layer CrI3.(B) Plot of the fitted frequencies of the modes in A as a function of layer number N. Red solid circles and blue solid squares correspond to modes extracted from the linear parallel and crossed channels, respectively. Solid curves with open diamonds are fits to the Davydov-split frequencies calculated from the linear chain ~ ~ model. (C) Atomic displacement of the lowest-frequency mode UN along with the layered-AFM order to illustrate that Ui and M share the same parity and ~ ~ that Ui · M is maximized at i = N. The rectangular bar represents the atomic displacement amplitude and phase for individual layers, by its length and color (red and blue for opposite phase), respectively.

2of6 | www.pnas.org/cgi/doi/10.1073/pnas.2012980117 Jin et al. Downloaded by guest on September 28, 2021 pseudovector (i.e., axial vector) for the layered-AFM layered-AFM order results in the magnetic counterparts (blue) ~ N−1 M =(1, − 1, .., (−1) ) with +1 for spin up and −1 for spin in the linear crossed channel. down in a single layer. In particular, for any N > 1, the lowest- We then proceed to explore the magnetic field dependence of ~ frequency mode UN features out-of-phase atomic displacement the layered-magnetism–assisted phonon modes in N-layer CrI3. between adjacent layers and matches best the pattern of alter- From here on, we chose circularly polarized light to perform nating spin orientations in the layered-AFM state (Fig. 1C), Raman measurements to prevent any artifacts from the Faraday ~ · ~ yielding the strongest coupling strength of Ui M and thus the rotation of light from passing through optical components in a most intense signal among the modes in the linear crossed stray magnetic field. In this work, we focus on two representative ~ · ~ channel (Fig. 1A). See the computed Ui M in the layered-AFM thicknesses, 2L and 4L CrI3, having one and two critical mag- state of 1L to 4L CrI in SI Appendix, Table S3. 3 netic transitions, respectively (Raman spectra of 3L CrI3 at 0 T in So far we have established the physical origin of the N-fold SI Appendix, section II and Fig. S3). We note that the mechanism multiplet for N-layer CrI3 as a combined effect of Davydov described below is applicable for arbitrary N-layer CrI3. splitting and layered-AFM–phonon coupling, leading to the The 2L CrI3 undergoes a layered-AFM to FM transition at a conventional phonons of RS in the linear parallel channel critical magnetic field Bc =±0.6 T (5). Fig. 3A presents Raman (24–27) and the layered-AFM–coupled phonons of R in the AS spectra of first-order modes taken at B⊥ = 0 T and ±1.4 T, linear crossed channel (7, 19). We note that a magnetism- below and above Bc, respectively, at 10 K in both LL and RR induced symmetric Eg phonon mode splitting was previously channels, where LL(RR) stands for the polarization channel with reported in 2D Cr2Ge2Te6 (28). Here, the structural and mag- the incident and scattered light being left(right)-hand circularly netic nature of modes in the linear parallel and crossed channel, polarized. At 0 T, both modes (U and U ) of 2L CrI are present respectively, is further supported by their distinct temperature 1 2 3 in Raman spectra that are identical in LL and RR channels. At dependence in these two channels. Taking 2L CrI as an exam- 3 ±1.4 T, only the high-frequency mode (U ) survives, and it shows ple, the crossed-channel signal emerges below the magnetic 1 − = I. I. LL I. I. RR transition temperature TC 45 K whereas the parallel channel giant Raman circular dichroism of ±78% ( ). See the I. I. LL +I. I. RR signal is present above TC and increases only slowly below TC,as illustrated by representative spectra taken at 70, 40, and 10 K in comparison of selection rules between linear and circular po- Fig. 2A. Such a behavior extends beyond the first-order phonons larization bases for 2L CrI3 in SI Appendix, Table S5. The (Fig. 2 A, Left) to the second- and third-order ones (Fig. 2 A, magnetic field dependence of the U2 integrated intensity clearly Center and Right, respectively). For all three orders, the tem- shows its disappearance at Bc, whereas that of U1 increases perature dependence of integrated intensity (I.I.) in the linear (decreases) abruptly in the LL (RR) channel at Bc, as shown in APPLIED PHYSICAL SCIENCES crossed√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ channel fits well with an order parameter-like function Fig. 3B. Fig. 3 E and F shows the magnetic field dependence of I0 + I TC − T (blue curves in Fig. 2B), in contrast to those in the the second- and third-order modes of 2L CrI3. Both of them linear parallel channel following a smooth anharmonic decay mimic the magnetic field dependence of U1 with a reduction of behavior (29) (red curves in Fig. 2B). As pictorially summarized circular dichroism above Bc, ±71% for the second order and in Fig. 2C, we propose that a multiphonon process (30, 31) leads ±50% for the third order. This observation suggests the partic- to conventional first-, second-, and third-order phonon modes ipation of U1 in the second- and third-order multiphonon (red) in the linear parallel channel, and their coupling with the process.

st nd rd 1 order 2 order 3 order A 3 C 40x10 1500 400 1st 2nd 3rd 2L 70 K 70 K 70 K 30 300 1000

20 200 40 K 40 K 40 K 500 10 100

Intensity (counts/2mins) 10 K 10 K 10 K 0 0 0 124 128 132 136 140 250 260 270 280 320 360 400 440 -1 -1 -1 Ramans shift (cm ) Ramans shift (cm ) Ramans shift (cm ) CrC 3d

B 3 20x10 3000 3000 TC = 45 K TC = 45 K TC = 45 K 2500 15 2500 2000 10 2000 1500 I 5p 5 1000 1500 I.I. (counts/2mins) 500 0 1000 20 40 60 20 40 60 20 40 60 T (K) T (K) T (K)

Fig. 2. (A) First-, second-, and third-order Raman spectra of 2L CrI3 in the linear parallel (red) and crossed (blue) channels at selected temperatures of 70, 40, and 10 K. Spectra are vertically offset for clarity. First-order spectra show raw data points and fitting curves, and second- and third-order spectra are raw spectra. (B) Temperature dependence of integrated intensity (I.I.) of first-, second-, and third-order Raman modes in the parallel (red circles) and crossed√ffiffiffiffiffiffiffiffiffiffiffiffiffiffi (blue squares) channels. Solid curves are fits to the anharmonic decay model in the parallel channel (red curves) and the order parameter-like function I0 + I TC − T in the crossed channel (blue curves). Critical temperature TC = 45 K is marked by a dashed vertical line in each panel. (C) Schematic illustration of the single- to multiphonon scattering (red) and its layered-AFM–assisted counterpart (blue). The springs with one to three windings represent first- to third-order process.

Jin et al. PNAS Latest Articles | 3of6 Downloaded by guest on September 28, 2021 nd rd st 2 order 3 order ACE3 1 order 90x10 3000 900 2L T = 10 K T = 10 K 2500 1.4 T 1.4 T 60 0.6 T 2000 600

U1 1500 U2 0 T 0 T 30 -0.6 T 1000 300 Intensity (counts/2mins) Intensity (counts/2mins) 500 -1.4 T -1.4 T 0 0 0 120 125 130 135 140 250 260 270 280 320 340 360 380 400 420 -1 -1 -1 Raman shift (cm ) Raman shift (cm ) Raman shift (cm ) B DF 3 40x10 6000 6000 20 U1 U1

0 4000 4000 LL 3 12x10 LL RR RR 2000

Intensity (a. u.) 2000 6 U2 U2 I. (counts/2mins) I. (counts/2mins)

0 0 0 -2.0 -1.0 0.0 1.0 2.0 -2.0 -1.0 0.0 1.0 2.0 -2.0 -1.0 0.0 1.0 2.0 -2.0 -1.0 0.0 1.0 2.0 B (T) B (T) B (T) B (T)

Fig. 3. (A) Raman spectra of 2L CrI3 in cocircularly polarized channels, LL (red) and RR (blue), in selected out-of-plane magnetic field (B⊥) of 1.4, 0, and −1.4 T. Dots are raw data points and solid curves are fitting curves. (B) Magnetic field dependence of integrated intensities (I.I.) of the two modes of 2L CrI3, U1 and ~ ~ U2, in both LL (red circles) and RR (blue squares) channels. (C) List of phonon modes in 2L CrI3 that have finite coupling strength Ui · M for individual magnetic orders at B⊥ above and between Bc = ±0.6 T, the critical magnetic field for the layered-AFM to FM transition. (D) Calculated B⊥ dependence of U1 and U2 of 2L CrI3.(E) Second- and third-order Raman modes (raw spectra) acquired in the same condition as A.(F) B⊥ dependence of I.I. of second- and third-order modes of 2L CrI3.

We refer to the layered-magnetism–phonon coupling that we field dependence of both first-order modes of 2L CrI3 in LL and have developed above to understand the magnetic field depen- RR channels by tuning only λi and ai (Fig. 3D). > dence of the two first-order modes (U1 and U2) of 2L CrI3. For Different from 2L CrI3, N-layer CrI3 (N 2) undergoes two i – ⊥ =± each mode Ui, its Raman tensor R is composed of the con- spin flip transitions with increasing B , one at Bc1 0.7 T for ( i ) – spins in surface layers and the other at Bc2 =±1.6 T for spins in ventional structural RS and the layered-magnetism assisted ( i ) i = i + λ i i interior layers (1, 2). For simplicity but without losing any gen- magnetic RAS contributions; i.e., R RS iRAS, where RS is magnetic field independent and is present only for parity-even erality, we pick 4L CrI3 and focus on measurements with the i ~ ~ upward magnetic field and in the RR polarization channel. modes, R ∝ Ui · M reflects the magnetic origin and selects the AS Fig. 4A shows Raman spectra of first-order modes taken at zero-momentum component, and λi is the ratio of the magnetic B⊥ = 0 , 1, and 2 T, below B , between B and B , and above to structural contribution for the ith mode that depends on mi- c1 c1 c2 B , respectively, at 10 K and in the RR channel. At 0 T, we can croscopic parameters such as spin–orbit coupling. Here, M~ c2 reliably resolve only three of the fourfold multiplet of 4L CrI , changes from (1, − 1) to (±1, ± 1) across the layered-AFM to 3 =± namely, U1, U3, and U4 as fitted by the red, orange, and blue FM transition at Bc 0.6 T with the fully polarized FM spin Lorentzian profiles, respectively. This is because U is spectrally moments pointing upward/downward. Specifically, for the parity- 2 so close to U1 but has a much weaker intensity (Fig. 1A), thus ~ √1̅̅ 1 a1 0 getting overwhelmed by the strong U in the RR channel. We even high-frequency mode of U1 = (1,1),R = ( ) at 1 2 S 0 a1 observe both U1 and U4 decrease subsequently at 1 and 2 T to 0 −a I finite and zero intensity, respectively, whereas U increases at 1 T all magnetic fields and R1 = U~ · M~( 1 ) = 0 below 3 AS 1 +a I 0 and then decreases at 2 T. The detailed magnetic field depen- √̅̅̅ 1 dence of the U , U , and U integrated intensity is shown in 0 ∓ 2a I 1 3 4 B and ( √̅̅̅ 1 ) above B =±0.6 T (Fig. 3 C, Top Fig. 4B, displaying the contrasting trends of U to U and U , and c ± I c 3 1 4 2a1 0 those of the second- and third-order modes are shown in Fig. 4 E and Bottom), whereas for the parity-odd low-frequency mode of √̅̅̅ and F, closely mimicking that of U1. − I We carry out a similar analysis as we have done for 2L CrI3 ~ √1̅̅ 2 2 √0̅̅̅ 2a2 U2 = (1, − 1),R = 0 always and R = ( ) 2 S AS + 2a I 0 above, but add an additional intermediate magnetic phase 2 √̅̅̅̅̅̅ M~ =(1, − 1,1,1) between the layered AFM of (1, − 1,1, − 1) I = − below Bc and 0 otherwise (Fig. 3C, Middle), where 1 to and the fully spin-polarized FM of (1,1,1,1). While the structural account for the broken time-reversal symmetry and a stands for ( i ) i contribution RS is present only for parity-even modes, U1 and the Raman scattering strength of the ith mode (see the calcu- U3, and remains magnetic field independent, the layered- lated magnetic field dependence of U and U in SI Appendix, magnetism–coupled magnetic contribution (Ri ) varies propor- 1 2 ~ ~ ~ AS Tables S4 and S5). This model faithfully reproduces the magnetic tionally to Ui · M as M changes as a function of B⊥. Fig. 4C lists

4of6 | www.pnas.org/cgi/doi/10.1073/pnas.2012980117 Jin et al. Downloaded by guest on September 28, 2021 st nd rd 1 order 2 order 3 order AC3 E 30x10 1500 600 4L T = 10 K T = 10 K 500 0 T 0 T 20 0.7 T 1000 400

U1 U3 300 U4 1 T 1 T 10 1.6 T 500 200 Intensity (counts/2mins) Intensity (counts/2mins) 100 2 T 2 T 0 0 0 120 125 130 135 140 250 260 270 280 320 340 360 380 400 420 -1 -1 -1 Raman shift (cm ) Raman shift (cm ) Raman shift (cm ) BD F 3 5000 5000 15x10 U1 U 2 4000 4000 U3 10 U 4 3000 3000

5 2000 2000 Intensity (a. u.) I. (counts/2mins) I. (counts/2mins) 0 1000 1000 2.01.51.00.50.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 B (T) B (T) B (T) B (T)

Fig. 4. (A) Raman spectra of 4L CrI3 in the RR channel in selected B⊥ of 0, 1, and 2 T. Gray dots are raw data points and black curves are fits to multiple Lorentzian functions. Lorentzian profiles in red, orange, and blue correspond to U1, U3,andU4 modes of 4L CrI3.(B) B⊥ dependence of I.I. of U1 (red circles), U3 (orange squares), and U4 (blue diamonds). Vertical dashed lines mark the critical magnetic fields for spin–flip transitions, Bc1 = 0.7 TandBc2 = 1.6 T. (C)Listofphonon ~ ~ APPLIED PHYSICAL SCIENCES modes in 4L CrI3 that have finite coupling strength Ui · M for magnetic orders below Bc1,betweenBc1 and Bc2, and above Bc2. The dashed green box marks U2 that is not observed in A due to its weak intensity and closeness to U1. Solid boxes of red, orange, and blue color highlight U1, U3,andU4,respectively.(D) Calculated B⊥ dependence of U1 (red), U2 (green), U3 (orange), and U4 (blue) of 4L CrI3.(E and F) B⊥ dependence of second- and third-order modes of 4L CrI3.

the modes that have finite coupling to every layered magnetic between two few-layer hBN flakes and transferred onto SiO2/Si substrates i for Raman spectroscopy measurements. order and thus nonzero RAS, according to which the magnetic contribution of U1 appears above Bc1, that of U3 emerges be- Micro-Raman Spectroscopy. Micro-Raman spectroscopy measurements were tween Bc1 and Bc2, and U2,4 is present only below Bc2 (see the calculated magnetic field dependence of U , U , U , and U in carried out using a 633-nm excitation laser. The incident beam was focused 1 2 3 4 × ∼ μ SI Appendix, Tables S6 and S7). By adjusting λ and a , the ratio by a 40 objective down to 3 m in diameter at the sample site, and the i i power was kept at 80 μW. The scattered light was collected by the objective of the magnetic to structural contribution and the overall in a backscattering geometry, then dispersed by a Horiba LabRAM HR Evo- strength of the ith mode, we successfully show the consis- lution Raman spectrometer, and finally detected by a thermoelectric cooled tency between the experimental and calculated magnetic field CCD camera. A closed-cycle helium cryostat is interfaced with the micro- dependence of U1,3,4 and predict that of U2 despite its invisibility Raman system for the temperature-dependent measurements. All thermal − in our experiment (Fig. 4D). cycles were performed at a base pressure that is lower than 7 × 10 7 mbar. In In conclusion, we have established the Davydov splitting of the addition, a cryogen-free magnet is integrated with the low-temperature Ag mode of a monolayer into an N-fold multiplet in N-layer CrI3 cryostat for the magnetic field-dependent measurements. In this experi- and discovered, distinct from nonmagnetic few-layer atomic ment, the magnetic field was applied along the out-of-plane direction and crystals (24–27), a unique layered-magnetism–assisted phonon covered a range of 0 to 2.2 T. scattering mechanism in the magnetic phases of CrI3. We find this mechanism extends beyond first-order phonons to the multi- Data Availability. All study data are included in this article and SI Appendix. phonon modes and further resolve the distinct magnetic field dependence for different first-order modes within the N-fold ACKNOWLEDGMENTS. L.Z. acknowledges support by NSF Faculty Early Career Development Program (CAREER) Grant DMR-1749774. R.H. acknowl- multiplet in N-layer CrI3. Our calculations based on the combi- – edges support by NSF CAREER Grant DMR-1760668 and NSF Major Research nation of Davydov splitting and layered-magnetism phonon cou- Instrumentation Program Grant DMR-1337207. A.W.T. acknowledges sup- pling successfully explain the selection rules for individual split port from the US Army Research Office (W911NF-19-10267), an Ontario Early modes and capture the rich behavior of their distinct magnetic Researcher Award (ER17-13-199), and the National Science and Engineering Research Council of Canada (RGPIN-2017-03815). This research was under- field dependence, effective for 2D CrI3 of arbitrary thickness. taken due in part to funding from the Canada First Research Excellence Materials and Methods Fund. K.S. acknowledges support through NSF Grant NSF-EFMA-1741618. H.L. acknowledges support from the National Key R&D Program of China Sample Fabrication. CrI3 single crystals were grown by the chemical vapor (Grants 2018YFE0202600 and 2016YFA0300504), the National Natural Sci- transport method, as detailed in ref. 19. The 1L to 4L CrI3 samples were ence Foundation of China (11574394, 11774423, and 11822412), the Funda- exfoliated in a nitrogen-filled glovebox. Using a polymer-stamping transfer mental Research Funds for the Central Universities, and the Research Funds technique inside the glovebox, 1L to 4L CrI3 flakes were then sandwiched of Renmin University of China (18XNLG14, 19XNLG17, and 20XHN062).

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