Vibronic response of a spin-1/2 state from a carbon impurity in two-dimensional WS$_2$

We demonstrate the creation of a spin-1/2 state via the atomically controlled generation of magnetic carbon radical ions (CRIs) in synthetic two-dimensional transition metal dichalcogenides (TMDs). Hydrogenated carbon impurities located at chalcogen sites introduced by chemical doping can be activated with atomic precision by hydrogen depassivation using a scanning probe tip. In its anionic state, the carbon impurity exhibits a magnetic moment of 1 $\mu_\text{B}$ resulting from an unpaired electron populating a spin-polarized in-gap orbital of C$^{\bullet -}_\text{S}$. Fermi level control by the underlying graphene substrate can charge and decharge the defect, thereby activating or quenching the defect magnetic moment. By inelastic tunneling spectroscopy and density functional theory calculations we show that the CRI defect states couple to a small number of vibrational modes, including a local, breathing-type mode. Interestingly, the electron-phonon coupling strength critically depends on the spin state and differs for monolayer and bilayer WS$_2$. These carbon radical ions in TMDs comprise a new class of surface-bound, single-atom spin-qubits that can be selectively introduced, are spatially precise, feature a well-understood vibronic spectrum, and are charge state controlled.