## 3 Results and Discussion
According to the definite lattice orientation for the single crystalline monolayer of WS\({}_{2}\), its out-of-plane \(A^{\prime}_{1}\) and in-plane \(E^{\prime}\) lattice vibrations are aligned with the vertical and horizontal EM fields [43]. The vibrations for LA mode are parallel to the direction of propagation [44; 45]. The Raman intensity of \(E^{\prime}\) mode is solely determined by the in-plane horizontal EM fields, whereas the Raman intensities of 2 LA(M) and \(A^{\prime}_{1}\) mode are contributed mainly by the vertical out-of-plane EM field. The prominent enhanced intensities of 2 LA(M) and \(A^{\prime}_{1}\) modes shown in Figure 2b demonstrate that the local EM field in the vertical direction is dominant on the Au NPs prepared in this work. To further study the LSPR effect on the polarized-Raman spectra of TMDs, nanostructures with enhanced EM field along specialized directions, such as dimer or nanogap, should be utilized in the future. The differences between the Raman spectra for WS\({}_{2}\)/SiO\({}_{2}\) and WS\({}_{2}\)/Au are closely related to the plasmon-phonon coupling effect. To study the plasmon effect on the magneto-optical property of WS\({}_{2}\), the polarized-Raman spectra of WS\({}_{2}\)/SiO\({}_{2}\) and WS\({}_{2}\)/Au were collected at different magnetic fields. In Figure 3, the spectra were normalized using the intensity of the Raman peak of Si substrate in order to see the intensity evolution of Raman modes of WS\({}_{2}\). As displayed in Figure 3a, in VV configuration, the intensity of the Raman spectra decreases with increasing field, reaches the lowest value at approximately 6 T, then recovers with continuously increasing field. Remarkably, the intensity of 2 LA(M) and \(A^{\prime}_{1}\) modes decrease much faster than that of \(E^{\prime}\) mode. The VV spectrum at 6T resembles the features of the VH spectra at 0 T, in which the \(E^{\prime}\) mode becomes an isolated peak. In sharp contrast, the Raman intensity displays an anticorrelated evolution in VH configuration. As shown in Figure 3b, the spectral intensity grows with increasing field up to 6 T, and then recedes with continuously increased field. In particular, the intensity of 2 LA(M) and \(A^{\prime}_{1}\) modes enhances more quickly than that of \(E^{\prime}\) mode. Of note, the VH spectra at 6 T resemble  
Figure 2: Polarized–Raman spectra of (**a**) WS\({}_{2}\)/SiO\({}_{2}\) and (**b**) WS\({}_{2}\)/Au collected without magnetic field. Black circles represent the experimental results, the dashed lines are fitting results for each Raman mode, and the red line is the sum of the fitting results. the features of the VV spectra at 0 T. Overall, one can see that the magnetic field-induced variations for the polarized-Raman spectra of WS\({}_{2}\)/SiO\({}_{2}\) exhibit strong similarities with previous reporting [24]. Similar magnetic field modulation behaviors of the polarized-Raman intensity were also reported in MoS\({}_{2}\)[22, 25]. The magnetic field-induced electron motion plays a key role in the Raman scattering process. [PERSON] and coauthors proposed a semi-classic scenario to illustrate the magneto-Raman effect in MoS\({}_{2}\)[22]. Under the magnetic field in normal direction to the sample plane, the in-plane electron motion generates a transverse component due to the Lorentz force, leading to a transfer of Raman intensity between the crossed polarization configurations. The elements of Raman tensor, which are normally the electronic susceptibilities with respect to lattice normal coordinates, can be expressed as a function of external field. Therefore, the expression of the measured Raman intensity can be associated with the magnitude of magnetic field and direction of light polarization. Magnetic field-induced modulations were also observed on the Raman spectra of WS\({}_{2}\)/Au, as shown in Figure 3c,d, which also exhibited obvious intensity fluctuation with increasing field. However, the field-induced variations for WS\({}_{2}\)/Au significantly differ from that for WS\({}_{2}\)/SiO\({}_{2}\).