Origin of Large Effective Phonon Magnetic Moments in Monolayer MoS$_2$

Recent helicity−resolved magneto−Raman spectroscopy measurement demonstrates large effective phonon magnetic moments of ~2.5 $\mu_B$ in monolayer MoS$_2$, highlighting resonant excitation of bright excitons as a feasible route to activate $\Gamma$−point circularly polarized phonons in transition metal dichalcogenides. However, a microscopic picture of this intriguing phenomenon remains lacking. In this work, we show that an orbital transition between the split conduction bands ($\Delta_0$ = 4 meV) of MoS$_2$ couples to the doubly degenerate $E^{′′}$ phonon mode ($\Omega_0$ = 33 meV), forming two hybridized states. Our phononic and electronic Raman scattering measurements capture these two states: (i) one with predominantly phonon contribution in the helicity−switched channels, and (ii) one with primarily orbital contribution in the helicity−conserved channels. An orbital−phonon coupling model successfully reproduces the large effective magnetic moments of the circularly polarized phonons and explains their thermodynamic properties. Strikingly, the Raman mode from the orbital transition is superimposed on a strong quasi−elastic scattering background, indicating the presence of spin fluctuations. As a result, the electrons excited to the conduction bands through the exciton exhibit paramagnetic behavior although MoS$_2$ is generally considered as a non-magnetic material. By depositing nanometer−thickness nickel thin films on monolayer MoS$_2$, we tune the electronic structure so that the A exciton perfectly overlaps with the 633 nm laser. The optimization of resonance excitation leads to pronounced tunability of the orbital−phonon hybridized states. Our results generalize the orbital−phonon coupling model of effective phonon magnetic moments to material systems beyond the paramagnets and magnets.