Dilute Magnetic Impurity-Induced Effective Phonon Magnetic Moment in Fe-doped Monolayer MoS$_2$

Realization of large effective phonon magnetic moment in monolayer MoS$_2$ has established an important route for exploring intriguing magnetic phenomena in a nonmagnetic material. The sizable coupling between the orbital transition and the circularly polarized phonon results in the large effective phonon magnetic moment. In this work, using magneto-Raman spectroscopy, we investigate substitutional doping of magnetic atoms as a tuning knob of the electronic and phononic properties of MoS$_2$. We show that Fe-doping polarizes the spin of the conduction bands and introduces a localized Fe band underneath the conduction band. As a result, an additional orbital transition between the Mo 4$d$ and Fe 3$d$ states emerges, producing an orbital-phonon hybridized mode at 283 cm$^{-1}$. Our magnetic field dependent measurements demonstrate that this new mode carries 2.8 $\mu_B$ effective phonon magnetic moment, which is comparable to that of the undoped MoS$_2$. Moreover, even though a long-range magnetic order is absent in Fe-doped MoS$_2$, the local magnetic moment of Fe modifies the nature of the spin fluctuation, producing monotonically increasing quasielastic scattering spectral weight as temperature decreases. Our results highlight two-dimensional dilute magnetic semiconductors synthesized by substitutional doping as a promising material platform to manipulate the phonon magnetic moment through orbital-phonon coupling.