Zero-field spin resonance in graphene with proximity-induced spin-orbit coupling

We investigate collective spin excitations in graphene with proximity-induced spin-orbit coupling (SOC) of the Rashba and valley-Zeeman types, as it is the case, e.g., for graphene on transition- metal-dichalcogenide substrates. It is shown that, even in the absence of an external magnetic field, such a system supports collective modes, which correspond to coupled oscillations of the uniform and valley-staggered magnetizations. These modes can be detected via both zero-field electron spin resonance (ESR) and zero-field electric-dipole spin resonance (EDSR), with EDSR response coming solely from Rashba SOC. We analyze the effect of electron-electron interaction within the Fermi- liquid kinetic equation and show that the interaction splits both the ESR and EDSR peaks into two. The magnitude of splitting and the relative weights of the resonances can be used to extract the spin-orbit coupling constants and many-body interaction parameters that may not be accessible by other methods.