**3.2 Light scattering of 2D magnets**

Raman scattering measures light in elastically scattered from collective quasiparticle excitations. In particular, Raman scattering from spin-phonon coupling, electron-phonon coupling, phase transitions, and magnetic excitations has yielded incisive information on recently developed 2D magnets. **CrI3** has been demonstrated that hosts various interesting light scattering properties: (i) the tuning of in elastically scattered light through symmetry control in atomically thin CrI3, as shown in **Figure 6a** [83, 87]. Raman spectra taken at 5 K in the cross-linear polarization channel (xy) shows a forbidden Raman activity of Ag series mode, as shown in **Figure 6a** (left) [83]. In contrast, there are two modes appearing in the cross-linearly polarized Raman scattering at 77 and 126 cm−1, labeled as P1 and P2 in **Figure 6a** (right) [83]. These modes have been previously attributed to one-magnon excitations since they appear in the magnetically ordered state and have their largest intensity in xy configuration, as shown in the inset of **Figure 6a** (right). Besides, in bilayer CrI3, the A1g phonon mode becomes Davydov-split into two modes of opposite parity, which exhibit divergent selection rules that depend on inversion symmetry and the underlying magnetic order. At zero magnetic field (AFM state), there are two peaks distinct in energy appeared at 126.7 and 128.8 cm−1 in the cross- and co-linearly

#### **Figure 6.**

*a, The left: Raman spectra of few-layer CrI3 at 5 K (0 T) for xx (black) and xy (red) polarization configurations. Spectra in xx were divided by two for clarity. Peaks that appear below Tc are highlighted with blue asterisks. Inset shows intensity as a function of collection polarization angle for P2 and* <sup>6</sup> Ag *in a polar plot [83] Copyright 2020, Springer Nature. The right: co- and cross-linearly polarized Raman spectra taken in an AFM state at 0 T (top) and the fully spin-up polarized state at −1.0 T of Ag Raman mode from bilayer CrI3 [84] Copyright 2020, American Chemical Society. b, Temperature-dependent Raman spectra of FePS3 single crystal (left). A single broad peak at 120 K splits into four sharp peaks at 4.2 K. Raman spectra of FePS3 in magnetic field 0–30 T (middle). Raman spectra have been vertically shifted for clarity, in steps of 2.5 T. Zeeman splitting of the M branch identifies it as magnon mode. The two branches are denoted as M↑ (red) and M↓ (blue). Magnetic-fielddependent peak position of P1, P2, P3, M↑ and M↓, which are denoted as black squares, black circles, green diamonds, red up-triangles, and blue down-triangles (right). The solid lines are fitted to the data [85] Copyright 2021, American Physical Society. c, Optical spectra of NiPS3 plotted in terms of Raman shift, i.e., energy difference from excitation energy, excited by different lasers with energies from 2.73 to 2.34 eV (left). Integrated intensity of two electronic Raman (ER) peaks as a function of excitation energy (middle). The dashed lines are the fitting curves. Schematic illustration of ER scattering in between the ground state and first excited triplet state for Ni2+ ion in a trigonally distorted octahedral environment (D3h) (right). Oh represents the crystal field splitting in an octahedral field; hν0 and hν1 (hν2) are the energy of incident and scattered photons of R1 (R2) mode [35] Copyright 2022, AAAS. d, Helicity-resolved Raman spectra of bulk CrBr3 at 10 K (left). Inset: polar plot of the Raman intensities of these four modes versus the rotation of the quarter-wave plate. The 0° and 90°correspond to the (σ<sup>+</sup> σ+ ) and (σ<sup>+</sup> σ− ) configuration, respectively. Right: superposition of two orthogonal linear vibrations of Eg* 1 *(143.0 cm−1) results in right-handed or left-handed circular motions at the Γ-point, i.e., chiral phonons with PAM of l = ±1 [86] Copyright 2021, Wiley-VCH GmbH.*

#### *Novel Light-Matter Interactions in 2D Magnets DOI: http://dx.doi.org/10.5772/intechopen.112163*

polarized channels, respectively (top right corner of **Figure 6a**) [84]. When the field was above the spin-flip transition (−1 T) to fully align the spins into FM states, the 126.7 cm−1 peak presented in the AFM states is abruptly suppressed and only 128.8 cm−1 peak is observed in both polarized channels (bottom right corner of **Figure 6a**) [84]. These findings shed light on exploring the emergent magnetooptical effects in 2D magnets. (ii) the 2D magnons has been directly observed in atomically thin CrI3 [88]. The ultra-low frequency magneto-Raman spectroscopy probed the effects of symmetry on magnetic excitations in monolayer CrI3, a lowfrequency feature emerges on both Stokes and anti-Stokes sides when a magnetic field is applied at −4 T. Interestingly, these Stokes and anti-Stokes modes obey opposite optical selection rules: for a given magnetization orientation, Stokes mode only appears when excited by on helicity of light, while anti-Stokes mode emerges with excitation of the opposite helicity. Further magnetic-field and temperature dependence measurements demonstrate that these Stokes and anti-Stokes modes are the signature of an acoustic magnon. Besides, strong coupling between magnons and phonons are directly observed in a 2D AFM semiconductor FePS3, vis magneto-Raman spectroscopy at magnetic fields up to 30 T [85]. The temperature-dependent Raman spectra on FePS3 shows a Raman active magnon peak at 121 cm−1. And the broad Raman band evolves into three sharp Lorentz peaks, P1, P2 and P3 as temperature decreased to below TN, as shown in **Figure 6b** (left). The evolution of the Raman spectrum of FePS3 in an out-of-plane magnetic field shows that P1, P2 and P3 peaks have no energy shift with low magnetic field, therefore verified as phonons, as shown in **Figure 6b** (middle). In contrast, the peak *M* exhibits a Zeeman splitting, confirming its magnonic character. These two split peak sections are labeled as *M*↓ and *M*↑, which have opposite spins. The *M*↓ and *M*↑ peak positions of show linear dependence on a magnetic field with similar slopes (0.99 and −0.94 cm−1/T), which is the effective *g* factor of the magnon, as shown in **Figure 6b** (right). Until 22.5 T, the shift of P1 and P2 is negligible, while the field-driven anticrossing of *M*↑ and P3 with a 6.1 cm−1 energy gap signals a repulsive interaction between magnon *M*↑ and P3 modes when their energies are in resonances, which is evidence that two modes are strongly coupled [85]. Due to the correlated-electron system of NiPS3, the scattering of incident photons with *d* electrons in Ni2+ ions has been observed at ~1.0 eV [35]. As shown in **Figure 6c** (left), the measured distinct optical spectra as the excitation wavelength varying from 454 nm (2.73 eV) to 531 nm (2.34 eV), show a peak at the same position ~1.39 eV assigned to the phonon sideband of the coherent ZR exciton. In contrast, there are two other peaks, R1 and R2 exhibiting an obvious redshift with decreasing of the excitation energy, and, finally, disappear when the excitation energy is below ~2.35 eV. These two peaks present a fixed energy difference between the collected signal and the laser excitation, suggesting that their origin is Raman scattering rather than luminescence. The intensity of electronic Raman peaks of R1 and R2 exhibit a clear dependence on the excitation energy, indicating a resonant effect, which is related to an external electronic state as an intermediate state, as shown in **Figure 6c** (right). Fitting results demonstrate that the intensities of R1 and R2 reach the maximum at ~2.61 and ~2.73 eV, respectively. The different resonant energies of these two modes indicate a scattered light resonance. After calculation, they obtained the intermediate state energy of ~1.70 eV, which matches the energy of the second excited states (3 T1g) from the ground states. The electronic Raman scattering process is proposed in between the ground state and first excited triplet state for Ni2+ ion in a trigonally distorted octahedral environment, as shown in **Figure 6c** (right). Phonon chirality and spin-phonon coupling have been observed in 2D **CrBr3**

[86]. The helicity-resolved Raman scattering measurement at 10 K can be used to resolve the chirality of phonon modes in CrBr3 (FM phase), since chiral phonon modes originate from the circular vibration of sublattices. As shown in **Figure 6d** (left), the Raman peaks corresponding to Eg modes appear only in the cross-circularly polarized configuration (σ<sup>+</sup> σ− ), which means that Raman scattering involved Eg modes reverses the helicity of the incident photons. In contrast, Raman scattering involving the two Ag modes does not change the helicity of the incident photons. The corresponding polar plot of Eg and Ag modes clearly presents their distinct polarization properties, where Eg modes have maximum Raman intensity in the cross-circularly polarized configuration (σ<sup>+</sup> σ− ) rather than the almost extinct Ag modes (inset in the left side of **Figure 6d**). Since Raman scattering involving Eg modes switches the polarization of circularly polarized light, the Eg modes in CrBr3 must have a non-zero pseudo-angular momentum (PAM), based on the conservation of PAM in the Raman scattering process. Besides, single-phonon Raman scattering process can only induce zone-center phonons due to the conservation of crystal momentum. However, the zone-center phonons have real eigenvectors which have zero phonon circular polarization by definition. Thus, the only zone-center Raman active phonon modes that can reverse the helicity of incoming light are complex superposition of the degenerate Eg modes, as demonstrated by the top right corner of **Figure 6d**. Furthermore, it is nature to explore the magnetic effect on the phonon properties of CrBr3 upon cooling, given the existence of a 2D long-range FM order below Curie temperature in CrBr3. As shown in **Figure 6d** (the bottom right corner), the Raman peak shift and linewidth change of Ag mode with decreasing temperature exhibit an anomalous behavior when the temperature is near to the Curie temperature. For example, in the temperature range between 290 and 50 K, a conventional hardening of phonon with decreasing temperature is observed due to the suppression of the anharmonic phonon-phonon interactions. While such temperature dependence becomes much stronger with the onset of magnetic ordering below ~50 K, as demonstrated by the additional anomalous phonon hardening due to the short-range local ordering of magnetic moments.
