Direct measurement of interfacial Dzyaloshinskii-Moriya interaction at the MoS$_{\rm 2}$/Ni$_{80}$Fe$_{20}$ interface.

We report on a direct measurement of sizable interfacial Dzyaloshinskii-Moriya interaction (iDMI) at the interface of two-dimensional transition metal dichalcogenide (2D-TMD), MoS$_{\rm 2}$ and Ni$_{80}$Fe$_{20}$ (Py) using Brillouin light scattering spectroscopy. A clear asymmetry in spin-wave dispersion is measured in MoS$_{\rm 2}$/Py/Ta, while no such asymmetry is detected in the reference Py/Ta system. A linear scaling of the DMI constant with the inverse of Py thickness indicates the interfacial origin of the observed DMI. We further observe an enhancement of DMI constant in three to four layer MoS$_{\rm 2}$/Py system (by 56$\%$) as compared to 2 layer MoS$_{\rm 2}$/Py which is caused by a higher density of MoO$_{\rm 3}$ defect species in the case of three to four layer MoS$_{\rm 2}$. The results open possibilities of spin-orbitronic applications utilizing the 2D-TMD based heterostructures.