Review of Raman spectroscopy of two-dimensional magnetic van der Waals materials*

Yu-Jia Sun(孫宇伽) Si-Min Pang(龐思敏) and Jun Zhang(張俊)

1State Key Laboratory of Superlattices and Microstructures,Institute of Semiconductors,Chinese Academy of Sciences,Beijing 100083,China

2Center of Materials Science and Optoelectronics Engineering,University of Chinese Academy of Sciences,Beijing 100049,China

3CAS Center of Excellence in Topological Quantum Computation,University of Chinese Academy of Sciences,Beijing 100049,China

4Beijing Academy of Quantum Information Science,Beijing 100193,China

Keywords: two-dimensional(2D)magnets,Raman spectroscopy,magnon,spin-lattice interaction

1. Introduction

Since the successful preparation of monolayer (1L)graphene, new families of two-dimensional (2D) van der Waals(vdW)materials,including hexagonal boron nitride(h-BN), black phosphorus (BP), and transition metal dichalcogenides (TMDCs) have been discovered.[1]In recent years,the 2D vdW materials have attracted great interest due to their unique properties that are difficult to be accessed in their bulk crystal form.[1-6]Remarkably,among all the 2D vdW materials,2D vdW magnets have gained extensive attention because they are ideal systems for studying the 2D magnetism.[7-10]Additionally, the 2D vdW magnets exhibit many fascinating electrical and optical properties, such as ultrafast optical response,magnetoresistance effect,high-frequency spin waves,and linear dichroism.[11-16]The long-range magnetic ordering in some 2D vdW magnets, such as CrI3, Cr2Ge2Te6, and FePS3, depends on the number of layers and can be retained down to the 1L limit.[17-19]In the 2D limit,the magnetic properties are substantially different from those in their bulk counterparts, such as the existing skyrmions, spin-phonon coupling, spin fluctuations, and magnetic excitations in 2D vdW magnets.[18,20,21]Furthermore,the magnetism of 2D vdW materials can be effectively modulated by electrostatic gating,chemical doping,and epitaxial strain.[13,22,23]

The magnetism of 2D vdW materials can be characterized by some optical methods,including Raman spectroscopy,second harmonic generation (SHG), magnetic force microscope(MFM), magnetic circular dichroism (MCD), and magnetooptic Kerr effect(MOKE).[9,13,24,25]Among the various methods mentioned above, Raman spectroscopy is indispensable for the characterization of elementary excitations in 2D vdW magnets. Utilizing the Raman spectroscopy, rich information about the spin-related elementary excitations can be obtained, including magnons, spin-phonon coupling, and Brillouin zone folding.[17,21,26,27]Additionally,the different stacking orders in vdW magnets can also be distinguished by Raman spectroscopy, which is significant for the study of the layer-dependent magnetism.[12,28]Due to the atomic thickness, 2D magnets are susceptible to the external perturbations. Therefore, the response of Raman spectra to the external perturbation allows the deeper insight into the magnetic ordering.[13,29]

In this paper, some important advances of Raman spectroscopy applied in investigating the properties of 2D vdW magnets are reviewed. Firstly, we briefly summarize the atomic structures and magnetic properties of some vdW magnets. Subsequently,we introduce the ways to detect the magnetic phase transition by Raman spectroscopy. The Curie temperature (TC) and N′eel temperature (TN) of 2D magnets can be obtained from the evolution of the Raman spectral features (including frequency, intensity, and the number of Raman peaks) with temperature. We also illustrate the Raman spectral features of spin-wave (magnon) under various conditions, including external magnetic field, low-temperature,and different polarization configurations. Next, we present the strategies regarding how to use the Raman spectroscopy to monitor the magnetism which is modulated by the magnetic(electric)field,pressure,and chemical methods. Furthermore,we elucidate two mechanisms about the rotation of the polarization axis of Agmode with the magnetic field in CrI3. At the end of the review, we give a conclusion and brief perspective for the development directions of the Raman spectroscopy in investigating the 2D magnets in the future.

2. The 2D vdW magnets in atomically thin limit

The atomic structures and magnetic properties of several typical vdW antiferromagnetic (AFM) and ferromagnetic (FM) materials are introduced here, including ternary tetradymite compounds, ternary iron-based tellurides, transition metal halides, and transition metal phosphorous trisulfides.

Mn-Bi-Te family is a layered ternary tetradymite compound containing long-range magnetic ordering introduced by Mn2+ions and the band inversion caused by the strong coupling between spin and orbit,so it is one of the ideal candidates for magnetic topological materials.[32,33]The basic building blocks of the Mn-Bi-Te family are magnetic compound MnBi2Te4(A layer) and non-magnetic compound Bi2Te3(B layer). So far, many structures can be obtained by stacking A layer and B layer experimentally, such as MnBi2Te4,MnBi4Te7, MnBi6Te10, and MnBi8Te13.[34]Recently, the intrinsic vdW AFM MnBi2Te4has aroused widespread attention for its implementation of Chern insulator state.[33]In the layered MnBi2Te4with the space groupRˉ3m, septuple layers (SLs) Te-Bi-Te-Mn-Te-Bi-Te are bundled via vdW interaction, as shown in Fig. 1(a).[12]The N′eel temperature (TN)of MnBi2Te4is 25 K. In the AFM phase (T

The Fe3GeTe2(FGT),as a representative of ternary ironbased tellurides, exhibits robust long-range ferromagnetic ordering with strong out-of-plane anisotropy in monolayer and epitaxial grown thin films.[30,37,38]As shown in Fig.1(b),with the space groupP63/mmc, each layer of FGT is composed of five sublayers with sandwich-like stacking order and the adjacent layers interact through vdW force. The Curie temperature(TC)of monolayer FGT is around 130 K,[30]while it reaches up to about 220-230 K for bulk FGT. More importantly, the bulk vdW magnet Fe5GeTe2, with a similar structure to Fe3GeTe2, possesses a higherTCof about 310 K.[39]By changing the ratio of elements, number of layers, and external gating, the magnetic properties of FGT can be modulated,which renders it a potential material for the application in spintronic devices.[25,40,41]

Transition metal halides mainly containMX2andMX3(M= Mn, V, Cr, Co, Fe, Ru, Ni;X= I, Cl, Br). Their magnetic properties strongly depend on the number of layers, by varying of which, the magnetic ground state can be correspondingly modified. In CrI3, one of the typical transition metal halides, its bulk crystal displays Ising ferromagnetism below theTC(61 K) with the spins orienting along the out-of-plane direction, as shown in Figs. 1(c) and 1(d).The exfoliated monolayer retains long-range ferromagnetic order when CrI3is cooled below itsTCof 45 K.[9,42]In CrI3flakes(≥2 L),the magnetism in a single-layer component is FM, while the coupling between adjacent layers is AFM.[43]Moreover,the transformation of the magnetic orders between FM and AFM states has been realized by controlling the stacking, magnetic field, pressure, and electric gating, which provides the possibility to design highly tunable spintronics devices and even create new quantum states in 2D magnets.

Fig. 1. Atomic structure diagrams of some typical 2D magnetic materials. (a) Crystal lattice and spin structure of MnBi2Te4. The red arrow indicates the magnetic moment of each Mn ion (adapted from Ref. [12]). (b) Side view of Fe3GeTe2 bilayer atomic structure. The dashed box represents the crystal unit cell(adapted from Ref.[30]). (c)-(d)The top and side views of atomic lattice and Ising spin structure of 1L CrI3. Each Cr3+ ion (gray ball) is surrounded by six I?ions (purple balls) (adapted from Ref. [9]). (e) The atomic structure of transition metal phosphorus trisulfides(adapted from Ref.[31]). The crystal structures of(f)MPS3 (M=Mn,Fe,Ni,Cd,and Zn)and(g)MPSe3 (M=Mn and Fe).

Transition metal phosphorus trisulfidesMPX3(M=Mn,Fe, Ni, etc.;X= S and Se) are another class of vdW antiferromagnets studied in the 2D limit.[31,44,45]As shown in Figs. 1(e)-1(g), each [P2X6]4?unit within a layer is surrounded by six metal ions,forming a honeycomb structure.[31]The space group ofMPS3isC2/m, whileMPSe3belongs toRˉ3 space group.[31]By selecting different elements, the band gaps ofMPX3can be tuned in the range of 1.3-3.5 eV with their spin structures varying dramatically. In the bulk form, the spin model of FePS3(TN≈120 K) belongs to the Ising model,[46]while the one for MnPS3(TN≈78 K)is the Heisenberg model,[26]for NiPS3(TN≈155 K) is theXYmodel.[27,47]In addition, the one-magnon scattering in FePS3[21]and MnPS3,[48]together with the two-magnon scattering in NiPS3[27]have been revealed, which suggests that they have potential in magnon-based spintronic devices.

3. Raman spectroscopy of 2D magnets

3.1. Principle of Raman spectroscopy

As a convenient and non-destructive tool with high spatial and spectral resolution,Raman spectroscopy has been widely used to characterize 2D materials.[49-56]The prominent features of Raman peaks, including frequency, full width at half maximum (FWHM), intensity, and line shape, contain useful information to investigate the fundamental physical properties of 2D materials,such as phonon frequency,the number of layers,stacking orders,electron-phonon coupling,charge density wave(CDW),phase transition,et al.[57-60]

The quantum picture of the inelastic Raman scattering process can be understood as shown in Fig. 2(a).[61]Raman scattering describes the interaction between photons and phonons. Electrons are excited by the incident photons from the initial state to the intermediate state through electronradiation interaction, and then scattered by phonons accompanied by the emission of scattered photons. According to the creation or annihilation of phonons,Raman process can be divided into Stokes and anti-Stokes processes. In the Stokes(anti-Stokes) process, the energy of the scattered light satisfies ?ωS(AS)=?ωi??ωph, where ?ωi(?ωph) is the energy of the incident light (phonon) and ?ωS(AS)is the energy of the Stokes (anti-Stokes) light. Especially, if the intermediate state is a real electronic state, the energy of the incident or scattered light will resonant with the energy of the intermediate real electronic level, and thus the resonant Raman scattering occurs. Since the real electronic transition is involved,many novel phenomena can be investigated by resonant Raman scattering, including the breakdown of Raman selection rules,[62]forbidden Raman modes,[63]high order or combined Raman modes.[63]Experimentally,the resonance Raman scattering can be achieved by either selecting the excitation energy or changing the electronic levels.

Inelastic light scattering provides access to explore the energy, symmetry and statistics of lattice, electronic excitations, and magnetic excitations in nanomaterials. Through spin-orbit and spin-lattice couplings, Raman scattering can measure various magnetic excitations, including fluctuations of the magnetic energy density, spin-orders, spin-related symmetry and topology, magnons, and spinons (fractional magnons expected in frustrated systems). For example, the transition from paramagnetic phase to antiferromagnetic phase could result in the unit cell associated with the antiparallel spin arrangement becoming twice as large as that with paramagnetic order.[17]Correspondingly, the Brillouin region of the antiferromagnetic phase would fold to half as large as that of the paramagnetic phase. Therefore, the frequencies of the relevant Raman modes would exhibit an abrupt shift or the new Raman modes would be activated. Concerning some ferromagnetic materials,the symmetry of Raman tensor changes when the time-reversal symmetry is broken near the Curie temperature, which suggests that temperature-dependent polarized Raman spectroscopy can be used to detect the magnetic phase transition temperature.[29]As an elementary excitation,magnon originates from the collective excitation of the spins with long-range magnetic order in magnets. The energies of the one-magnon and two-magnon excitations increase when the temperature decreases, leading to the blueshift of the Raman modes.[21]Additionally, the antiferromagnetic onemagnon mode will split into two Raman peaks that vary linearly with the magnetic field due to the Zeeman effect.[21]For uncovering novel topology, Raman spectroscopy can also be used to measure the non-trivial statistics associated with the fractional spin excitations.[64]

Fig. 2. Principle and application of Raman spectroscopy. (a) Schematic diagrams of energy level transitions in Stokes and anti-Stokes Raman processes. (b) Experimental setup of circularly polarized Raman spectra. (c) The intensity maps of the polarized-dependent Raman spectra in rhombohedral(left)and monoclinic(right)phases of bulk CrI3 (adapted from Ref.[28]).

Raman spectroscopy is widely used in both laboratory and mass-scale production. The polarization-dependent and ultralow-frequency Raman spectroscopy systems combining the polarizer,wave plate,and volume-Bragg-gratings(VBG)-based notch filter with confocal microscopes provide a powerful technique to investigate the low-energy elementary excitations, interlayer stacking, lattice symmetry, together with the anisotropy in 2D materials and heterostructures.[65,66]The polarization Raman spectroscopy, which includes linear polarization and circular polarization configurations,is available to investigate the symmetry of lattice and elementary excitations by controlling the polarization configurations of the incident and scattered light.[67-69]Figure 2(b) shows one of the experimental setups of circularly polarized Raman spectra.Since the polarized intensity can be calculated by the Raman tensor, which directly depends on the symmetry of the crystal and corresponding phonon mode, the polarization Raman spectroscopy can be used to characterize the crystal symmetry.For instance,the crystal lattice of bulk CrI3undergoes a structural phase transition near 210 K from a rhombohedral phase to a monoclinic phase. As shown in Fig.2(c),the monoclinic(right)and rhombohedral(left)phases can be distinguished according to their polarization behaviors of the corresponding Raman modes.[28]

3.2. Magnetic phase transitions

The critical temperature of magnetic phase transition is an important parameter for 2D magnets, which reflects the competition between long-range magnetic order and thermal fluctuation. Most of the 2D magnets possess a low magnetic phase transition temperature, such as bulk CrI3(TC≈61 K), VI3(TC≈50 K), CrSiTe3(TC≈32 K), and CrOCl(TN≈13 K).[9,70-72]Obviously,the vdW magnets with the magnetic phase transition temperature above the room temperature are urgently demanded to achieve antiferromagnetic/ferromagnetic devices.[14]Therefore, a fast and convenient method to measure the magnetic phase transition temperature is necessary for the application of 2D magnets in spintronic devices.

The magnetic phase transition temperature of intrinsic magnets can be characterized by magnetic susceptibility measurement. However, this technique is difficult to be applied to investigate the magnetic properties of 2D ultrathin materials.[46]In contrast,due to the high spatial resolution and high sensitivity to the symmetry of the lattice, spin?phonon coupling, and electronic states, Raman spectroscopy can reveal the magnetic order and phase transitions of 2D magnets down to the monolayer limit. The comparison of the magnetic phase transition temperatures measured by Raman spectroscopy and other methods is shown in Table 1. In the vicinity of the magnetic phase transition temperature, some spectral features of Raman spectra, such as frequency, intensity,linewidth, and polarization of phonon peak, will exhibit noticeable variations, which makes the temperature-dependent Raman spectroscopy a powerful tool to determine the magnetic transition temperature of vdW magnets.[26]The related experimental results are presented in Fig.3.

Fig. 3. The transition temperature (TC and TN) of 2D magnets detected by temperature-dependent Raman spectra. (a) Temperature-dependent magnetic susceptibility (upper panel) of bulk FePS3 along in-plane and out-of-plane axes, depicted by gray and black spheres, respectively. The temperature-dependent intensities (lower panel) of corresponding Raman peaks in bulk FePS3 (adapted from Ref. [46]). (b) Raman frequencies and intensities of P2 in MnPS3 flakes with different thickness as a function of temperature(adapted from Ref.[26]). (c)The circular polarization Raman spectra of the Ag mode(128 cm?1)for bulk VI3 under the σ±/σ± polarization configurations at 60 K,and the corresponding calculated circular polarization(ρ)with the temperature ranging from 1.7 K to 60 K(adapted from Ref.[29]). (d)The temperature-dependent ? (blue)and the remanence RMCD signal(red)of monolayer CrI3 at 0 T.? is defined as the angle of the polarization axis away from the excitation polarization axis(adapted from Ref.[13]).

Table 1. Comparison of the magnetic phase transition temperatures measured by Raman spectroscopy and other methods.

As shown in Fig. 3(a), the slope of the magnetic susceptibility-temperature curve for FePS3exhibits a mutation when the sample undergoes the antiferromagneticparamagnetic phase transition, which can be exploited to determine the magnetic phase transition temperature. Meanwhile, the intensities of P1aand P2Raman peaks vary dramatically near theTN(118 K) obtained from the magnetic susceptibility measurement,[46]which is thus also the indicator for the magnetic phase transition. Compared with the changes of the intensity in FePS3, the steep Raman shift of the P2peak in MnPS3(originates from the Mn-S vibration),as shown in Fig. 3(b), suggests that the transition between paramagnetic and antiferromagnetic phases occurs.[26]The temperature-dependent Raman spectra of MnPS3with different thickness indicate that the transition temperature is independent of the number of layers.[26]The Raman intensities of the P2mode in MnPS3with different thickness reach a maximum at around 120 K, while a minimum at around 55 K,which are related to the single-ion andXYanisotropies, respectively.

When some ferromagnetic materials undergo the paramagnetic to ferromagnetic phase transition, the time-reversal symmetry is broken due to the spin inversion, which results in an extra antisymmetric component in the original symmetric Raman tensor. The variation of the Raman tensor further induces the rotation of the polarization plane,[13]which illustrates that the transition temperature (TC) of some ferromagnetic materials can be obtained by the polarization Raman spectroscopy. Furthermore, the circular polarizationρcan be obtained from the intensity difference of Raman mode underσ+/σ+(I+) andσ?/σ?(I?) polarization configurations. Specifically, circular polarizationρcan be calculated by

Figure 3(c) shows the temperature-dependent circular polarizationρof Agmode (～128 cm?1) in bulk VI3.[29]AboveTC(50 K),the intensity of the Agmode underσ+/σ+circular configuration is the same as that underσ?/σ?configuration. When the temperature goes below theTC, the spins are oriented to form ferromagnetic phase along the out-of-plane.The ordered alignment of the spins is responsible for the broken time-reversal symmetry in bulk VI3,which manifests the appearance of asymmetric matrix elements in the Raman tensor. The circular polarizationρof materials with FM phase is a nonzero value. In particular,ρis positive for bulk VI3, as shown in Fig.3(c). Thus,in-situcharacterization of the magnetic phase transition via circular polarization Raman spectra is available. Figure 3(d) displays the extracted polarization rotation (?) of the A1gpeak in 1L CrI3when the temperature drops down from 60 K to 15 K.?is defined as the angle of polarization axis away from the excitation polarization axis. WhenT

3.3. Magnons in 2D magnets

Spin wave,whose quasiparticle is called magnon,is a collective excitation of the spins with long-range magnetic order in magnetic materials.[50]The discovery of the vdW magnets makes it possible to explore the spin dynamics when the dimension is down to the 2D limit.[50]Magnons have now been observed in several 2D magnets, including CrI3,α-RuCl3, and theMPX3family (FePS3, MnPS3, NiPS3, and MnPSe3),[21,27,82]which can efficiently transport the spin angular momentum and sensitively respond to the magnetic field.

With the linear fitting, the gyromagnetic ratioγ=0.9348 cm?1/T andg ≈2.0023 of FePS3can be calculated.[21]Apart from the antiferromagnetic magnon, the Raman peak of ferromagnetic magnon also shifts linearly with the applied magnetic field. As depicted in Fig. 4(d), the magnon frequency of monolayer CrI3shifts linearly with a slope of 0.94 cm?1/T under the out-of-plane magnetic field, revealing that the magnon in 1L CrI3is a quasiparticle with spinS=1.[50]From the magnon energy at 0 T obtained by linear fitting, the spin-wave gap around～2.4 cm?1is determined,which would increase with the magnetic anisotropy.

Fig.4. Raman spectroscopy detects the one-magnon(two-magnon)in 2D magnetic materials. (a)The Zeeman splitting of ψ4 peak in FePS3 at 5 K(adapted from Ref.[21]). (b)The Raman spectra of MnPSe3 under crossed(VH)polarization configuration collected through the N′eel transition at 74 K(adapted from Ref.[82]). (c)Temperature-dependent Raman spectra of two-magnon signals and Fano resonance in monolayer NiPS3(adapted from Ref.[27]). (d)The magnon frequency of monolayer CrI3 when an out-of-plane magnetic field sweeps from ?7 T to+7 T.The working range of the filter determines that the Raman signal in the gray area is inaccessible(adapted from Ref.[50]).(e)The polarization-dependent Raman spectra of CrI3 flake(13 L).Magnon modes M1 and M2 completely disappear under the parallel polarization configuration(adapted from Ref.[83]).(f)The Raman spectra of FePS3 under the magnetic field along out-of-plane ranging from 0 T to 30 T(adapted from Ref.[91]). The green,red,and blue spectra correspond to phonon(P3),spin-up magnon(M↑),and spin-down magnon(M↓),respectively. (g)The frequencies of P1,P2,P3,M↑,and M↓under the magnetic field sweeping from 0 T to 30 T(adapted from Ref.[91]). P1,P2,and P3 denote three different phonon modes in FePS3.

The temperature-dependent Raman spectra of MnPSe3and NiPS3under crossed polarization configuration are shown in Figs. 4(b) and 4(c). The discrete peaks correspond to the phonon modes,while the wide continuum peaks are associated with the two-magnon excitation. Unlike one-magnon peak,the two-magnon peak possesses the energy twice as large as that of the one-magnon peak and would not split under the magnetic field. As the temperature decreases below theTN,the Raman peaks of one-magnon and two-magnon show an obvious blueshift. Meanwhile, the Raman intensity of the two-magnon peak significantly increases. Similar temperature dependence of magnon has been reported in vdW magnet FePS3[21]and some three-dimensional antiferromagnets,including FeF2,NiF2,and MnF2.[85-88]

The symmetry behaviors of magnons can also be characterized by Raman spectroscopy. For example, in Fig. 4(e),two modes (M1and M2) of thick CrI3can only be detected by the cross-polarization channel. According to the theory of Fleury and Loudon,[84]the Raman tensor of one-magnon peak in magnets with orbital angular momentum ground stateL=0 contains only the asymmetric matrix elements, which thus restricts the Raman peak to be observed only under the cross-polarization configuration, while disappears under the parallel-polarization configuration. The theory has well described the symmetry behaviors of the magnons in some 3D magnets, including antiferromagnetic materials MnF2, FeF2,YFeO3, and Cd1?xMnxTe.[84,89,90]However, the polarization behavior of one-magnon peak for magnets with the nonzero orbital angular momentum at the ground state is more complex, which is not discussed here.[21]In general, the Raman peak of two-magnon does not depend on the polarization.[27]Therefore,a suitable polarization configuration can be selected according to the polarization behaviors of the phonon modes in Raman spectra to observe the two-magnon signals. For example, two-magnon signals in MnPSe3, VI3, and NiPS3can be explored under the cross-polarization configuration because most of the phonon modes only appear under the parallelpolarization configuration.[27,29,82]Generally speaking, there is still abundant space here to explore the polarization behaviors of the magnons in the 2D limit.

The coupling between magnons and phonons in 2D antiferromagnets is an emerging field in the area of light-matter interaction,which offers a powerful means to control the quantum states and is expected to be used in quantum information technologies. Recently, Liu[91]and Vaclavkova[92]et al.directly observed the strong coupling between magnons and phonons in FePS3by Raman spectroscopy under the high magnetic field up to 30 T. In Figs. 4(f) and 4(g), the Raman-active magnon(M↑)is coupled with the nearby phonon mode(P3)to from a hybridized magnon-phonon quasiparticle,which features an evident anti-crossing in the eigen-spectrum.In addition, the circular polarized Raman spectra shows that the magnon(M↑)transfers its spin to the phonon(P3)through the strong coupling under the out-of-plane magnetic field.These works unveil the magnon polarons in FePS3and evoke further explorations in the domain of magnon-phonon coupling.

3.4. Modulation of the magnetism in 2D magnets

VdW materials are extremely flexible, and their electron density can be efficiently tuned by the electric field, leading to the fantastic transport properties. The vdW magnets provide an ideal platform to combine the magnetic properties with the unique properties of vdW materials, which makes it possible to investigate,modify the magnetic excitations,and even switch the magnetic configurations in the 2D limit. Regarding the magnetic modification,the electrical,mechanical,and chemical methods(such as elemental substitution and absorption)can be applied to modulate the magnetic properties in 2D vdW magnets.[93,94]The magnetism of vdW magnets strongly depends on the stacking order because of their ultrathin thickness. The interlayer coupling in CrI3with monoclinic stacking order exhibits AFM feature, while that in rhombohedral stacking order is FM. The monoclinic-to-rhombohedral(AFM-FM) transition in exfoliated 5L CrI3induced by pressure(1.8 GPa)has been probed by Raman spectroscopy.[51]

Fig. 5. Spin-dependent Raman scattering modulated by an external field in the 2D magnets. (a) The circularly polarized Raman spectra of 2D ferromagnet VI3 under the out-of-plane magnetic field(adapted from Ref.[29]). (b)The polarized Raman spectra of 2L CrI3 at Vg equaling to 0 V(upper panel)and 5 V(lower panel)with an applied magnetic field ranging from ?0.4 T to ?0.8 T(adapted from Ref.[13]). The white dotted-lines represent the spin-flip field when Vg is 0 V.

Compared with other vdW materials,vdW magnets have an additional degree of freedom, namely, the spin order,which can be easily tuned to control the symmetry. Below theTC, the antisymmetric elements in the Raman tensor of VI3appear due to the broken time-reversal symmetry.[29]As shown in Fig.5(a1),when the applied magnetic field is+2 T,the intensity of Agmode (128 cm?1) under theσ+/σ+circular polarization configuration is lower than that under theσ?/σ?configuration, which would remain unchanged when lowering the magnetic field to 0 T[Fig.5(a2)]. However,the intensities from both channels are reversed under the opposite field of?2 T[Fig.5(a3)],due to the spin-flip transition,which are retained when the magnetic field is back to 0 T[Fig.5(a4)].The reversed intensities reflect the presence of coercive field in VI3. These results suggest that Raman selection rules are highly sensitive to the magnetism.

Being characterized by low energy consumption and ultra-scalability,[95]the electrical methods, such as applying current or voltage, can be used to control the magnetic properties in 2D vdW magnets,via changing the position of Fermi level, space inversion and time-reversal symmetries, together with the magnetic anisotropy.[14]For example, the direction of magnetic anisotropy in CrGeTe3is along the out-of-plane without applied field, whereas it rotates to in-plane with an ionic gating, and the correspondingTCincreases to above 200 K in this process.[96]As for 2L CrI3, the symmetry can be broken by an electric field, and thus the Raman selection rules are further modified.[13]In Fig. 5(b), the Raman peak of 1L CrI3with frequency around 127.4 cm?1splits into two peaks due to the Davydov splitting. The frequencies of these two peaks are 128.8 cm?1and 126.7 cm?1, respectively. According to the symmetry of vibration and Raman selection rules,the Raman peak with a higher frequency(128.8 cm?1) is Raman active, while the one with lower frequency (126.7 cm?1) is Raman silent in the FM phase. In the AFM state,the symmetry of bilayer CrI3varies,which induces that the 126.7 cm?1peak can only be observed in theXYpolarized channel,whereas the 128.8 cm?1peak only appears under theXXconfiguration. As the magnetic field increases beyond the spin-flip field (?0.62 T), the bilayer CrI3changes from the AFM state to FM state, which can be directly reflected in the polarized Raman spectra. Figure 5(b)shows the polarized Raman spectra of 2L CrI3atVgequaling to 0 V and 5 V, respectively, with an applied magnetic field changing from?0.4 T to?0.8 T. When the gate voltageVgis 5 V, the mode at～126.7 cm?1is Raman inactive under theXYconfiguration,while the peak at 128.8 cm?1is Raman active. These results illustrate that the gate voltage can effectively control the magnetism of CrI3from AFM to FM state by reducing the spin-flip field, as indicated by the white dottedlines in Fig.5(b).

3.5. Magneto-optic effect in 2D magnets

The magneto-optic effect is a general term for a series of phenomena that light interacts with a magnetic substance (or a non-magnetic substance in a magnetic field), causing variations in the propagation state (polarization, intensity, etc.).Magneto-optic effects include the Faraday and Kerr effects,which represent the polarization changes of the transmitted and reflected light, respectively. Recently, the magnetic field has been found to be capable of inducing the polarization plane of the anisotropic mode in 2D ferromagnet CrI3to rotate.[97,98]The polarization Raman spectroscopy has been used to detect the anisotropic inelastic phonon scattering of CrI3under the external magnetic field.

Fig.6.The magnetic field-dependent rotation of the polarization plane in CrI3.(a)Raman spectra of CrI3 flakes with different thickness at 10 K(adapted from Ref.[98]). (b)-(c),(e)-(f)The magnetic field-dependent intensity of the Ag (～128 cm?1)mode. In(b)-(c),the polarization axis rotates the same angle under ±2 T magnetic field (adapted from Ref. [97]). In (e)-(f), the polarization axis of the Ag mode rotates ?15° and 40° at ?2 T and +2 T,respectively(adapted from Ref.[98]). (d)Intensity contour plot of the Ag mode of 3L CrI3 at 0 T with the polarization of the incident light going from?90° to 270°. The red to blue colors indicate the intensity of the Ag peak varying from maximum(190)to zero(adapted from Ref.[98]).

As shown in Figs. 6(a) and 6(d), the Agmode(～128 cm?1) of multilayered CrI3exhibits pronounced anisotropy with a 180°polarization period, while the Egmode (～246 cm?1) is isotropic in-plane.[98]When the out-of-plane magnetic fieldB ≥+1.8 T,the polarization axis of the anisotropic Agmode rotates 35°relative to the external magnetic field direction[Figs.6(b)and 6(c)].[97]The rotation direction of the polarization plane changes reversely with the reverse magnetic field direction,which can be explained by introducing magnetizationminto the Raman tensor. The Raman tensor of Agphonon under an out-of-plane magnetic field can be described as

respectively, where the ?and ?'are minor corrections. This Raman tensor of magnetization modulation well explains the polar plots for the variation of the Agmode with the magnetic fields.

In Liu’s work,as shown in Figs.6(e)and 6(f),the polarization axis of the Agmode in bulk CrI3rotates?15°and 40°at?2 T and+2 T,respectively.[98]Moreover,the rotation angle of the polarization axis is greater than+60°(?20°)in the presence of a higher magnetic field 2.5 T(?2.5 T).The rotation of the polarization axis originates from the regulation of the polarizability and dielectric constant exerted by the applied magnetic field. This theory starts from the dynamics of electrons under the magnetic field and then obtains the magnetic field-dependent polarizabilityα. Exploiting the polarizabilityα,the polarized Raman tensor of the Agmode(～128 cm?1)under the out-of-plane magnetic fieldBcan be described as

The parametersα,b,g, andhcan be obtained by fitting the experimental data. This work demonstrates that the response of the polarization axis to the magnetic field results from the magnetic control of the polarizability tensor by the Lorentz force.

In summary,these two works elucidate the rotation of the polarization axis of Agmode(128 cm?1)in CrI3as a function of the magnetic field from different aspects. Similar magnetooptic effects are expected in other 2D magnets,which renders them to be potentially applied to the information coding controlled by the magnetic field.[98]

4. Conclusion and perspectives

In conclusion, Raman spectroscopy is a powerful technique to study 2D magnetic materials. Besides the capability to explore the general properties related to the lattice vibration as in other 2D materials,including interlayer stacking orders,interlayer coupling,symmetry,and strain effect,Raman spectroscopy can also sensitively detect the spin-related properties of 2D magnets,like the spin-involved elementary excitation or the spin-phonon interaction.

Recent studies have found that the 2DXY-type antiferromagnetic vdW material NiPS3is a very promising magnet in 2D opto-spintronics systems. Layer-dependent Raman spectroscopy shows that the antiferromagnetism in NiPS3can be retained in the bilayer limit, while it is almost completely inhibited in the monolayer.[27]Moreover,theTNof NiPS3flake(N ≥2L)increases gradually with the number of layers.These results suggest that theXYHamiltonian in NiPS3becomes unstable in the monolayer limit. In recent months, excitons with strong interaction between the spin and orbit are found in NiPS3.[99-101]The exciton state appearing below the N′eel temperature with ultra-sharp photoluminescence(PL)is gradually suppressed with the reduced thickness and eventually vanishes for the monolayer. Remarkably, an in-plane magnetic field can effectively control the optical anisotropic axis of photoluminescence along the zigzag direction. Furthermore, the existing spin-correlated excitons in NiPS3suggest that NiPS3provides an ideal system to explore the elementary photoexcitations,many-body excitons,and magneto-optics in the 2D semiconductors with intrinsic magnetic order. In particular,NiPS3,which is highly sensitive to the band structure,is expected to form twisted magnetic bilayer and mori′e heterostructures with different vdW materials. In addition,NiPS3shows exceptionally strong exciton-phonon coupling, which provides the possibility to study the exciton-magnon coupling by optical and magnetic manipulation. Resonant Raman and Brillouin spectroscopies are also powerful techniques to investigate the exciton-phonon interaction in NiPS3and the related heterostructures.

In addition,new 2D magnets with high transition temperature above room temperature and high air stability are imperative to achieve tunable magnetism at room temperature.Large-scale growth,manageable layer number,and insensitivity under ambient conditions of vdW magnets are essential for the application of 2D magnets from lab to industry.Lacking of ferromagnetic or antiferromagnetic semiconductors is another challenge for building semiconductor spintronic devices like spin field-effect transistor. Therefore, the more precise modulation of the magnetic properties of vdW magnets, such as the direction of magnetization,critical temperature,etc,needs to be further investigated. Additionally, the atomically sharp interface in an vdW heterostructure,which is composed of 2D magnets and other abundant vdW materials, is a new field to be explored. As one of the most convenient characterization methods of 2D magnets, Raman spectroscopy is expected to be used in more experimental work to explore the fundamental physicochemical properties of 2D magnetic vdW materials.

Considering the ultralow frequency Raman spectroscopy,which has been widely used to measure the interlayer coupling in 2D vdW materials and heterostructures, we anticipate that it will be of great use in detecting the magnetic coupling in 2D magnetic heterostructures. In much lower frequency regime below 5 cm?1,we expect that the Brillouin spectroscopy will be powerful to reveal the strength of the exchange,anisotropy,topology,symmetry,and magnons in magnetic vdW materials and devices.