## 3 Results and Discussion
One can see that both 2 LA(M) and \(E^{\prime}\) modes vary significantly with increasing magnetic field in VV configuration. At 6 T, 2 LA(M) mode is still clearly identified, and \(A^{\prime}_{1}\) mode is still greatly residual under VV configuration. The VV spectra at 6 T resembles the line shape of the VH spectra at 0 T.  
The magnetic field-dependent Raman spectra for WS\({}_{2}\)/SiO\({}_{2}\) and WS\({}_{2}\)/Au were deconvoluted using the Lorentz function, in order to get a clear view of the magnetic field dependence of peak intensity of WS\({}_{2}\) on different substrates. As presented in Figure 4a-c, the intensities of 2 LA(M), \(A^{\prime}_{1}\) and \(E^{\prime}\) modes for WS\({}_{2}\)/SiO\({}_{2}\) exhibit similar magnetic field dependences. The peak intensities vary oppositely in VV and VH polarization configurations. The maximum intensity in VH configuration and the minimum intensity in VV configuration take place at around 5 T. For simplicity, the magnetic field for the extreme point of intensity is defined as the resonance magnetic field. The similar magnetic field-induced intensity modulations are also observed on WS\({}_{2}\)/Au, as displayed in Figure 4d-f.  
Figure 3: Polarized–Raman spectra of (**a**,**b**) WS\({}_{2}\)/SiO\({}_{2}\) and (**c**,**d**) WS\({}_{2}\)/Au collected at different magnetic fields. The resonance magnetic field for WS\({}_{2}\)/Au is 5.5 T, which is a little higher than that for WS\({}_{2}\)/SiO\({}_{2}\). Noticeable, the intensity amplitudes of 2 LA(M), \(E^{\prime}\) and \(A^{\prime}_{1}\) modes for WS\({}_{2}\)/Au are very close in VH configuration, which are different from those for WS\({}_{2}\)/SiO\({}_{2}\). The reason for the striking difference between these two WS\({}_{2}\) samples is discussed below. To quantify the effects of magnetic fields on Raman intensity, the magneto-Raman intensity of monolayer WS\({}_{2}\) on two different substrates was calculated according to previous literature [24; 25], as follows:  
\[\text{Magneto-Raman intensity}=\frac{I(B)-I(0)}{I(0)}\times 100\% \tag{1}\]  
where \(I(B)\) is the Raman intensity obtained under different magnetic fields. As presented in Figure 5a, the magneto-Raman intensity of the 2 LA(M), \(E^{\prime}\) and \(A^{\prime}_{1}\) modes for WS\({}_{2}\)/SiO\({}_{2}\) exhibit a similar variation with increasing magnetic field, which are negative under VV configuration and reach the lowest value at around 5 T. In contrast, the VH polarization configuration witnesses the largest magneto-Raman intensity at 5 T. The VH magneto-Raman intensity of \(A^{\prime}_{1}\) is higher than that of 2 LA(M) and \(E^{\prime}\). Moreover, the lowest VV magneto-Raman intensity is nearly \(-100\%\), whereas the magneto-Raman intensity for the 2 LA(M) and \(A^{\prime}_{1}\) modes boosts to \(1300\%\) under VH polarization configuration. On the other hand, the magneto-Raman intensity for WS\({}_{2}\)/Au exhibits similar variations as that of WS\({}_{2}\)/SiO\({}_{2}\), as shown in Figure 5c,d. In the VV configuration, the VV magneto-Raman intensity for WS\({}_{2}\)/Au varies in the range from \(20\%\) to \(-90\%\), while the highest magneto-Raman intensity is just \(800\%\) in the VH configuration. It is worthy to note that the magneto-Raman intensity of \(A^{\prime}_{1}\) mode for WS\({}_{2}\)/Au is much lower than that for WS\({}_{2}\)/SiO\({}_{2}\). The magneto-Raman intensities of \(A^{\prime}_{1}\) and 2 LA(M) modes for WS\({}_{2}\)/Au were reduced to \(\sim\)60\(\%\) of that for WS\({}_{2}\)/SiO\({}_{2}\). This difference in the amplitude of the magneto-Raman intensity between WS\({}_{2}\)/SiO\({}_{2}\) and WS\({}_{2}\)/Au can be attributed to the Au NPs underneath WS\({}_{2}\) flake, which breaks the polarization rules for WS\({}_{2}\). Due to the light-matter interaction, LSPR takes place at the surface of Au NPs. When plasmonic losses couple to WS\({}_{2}\), momentums with different wave vectors are provided by the near-field components in the nanogap between metal NPs [34].