In normal metals, the magnetic moment of impurity spins disappears below a characteristic Kondo temperature, TK, where coupling with the conduction-band electrons produces an entangled state that screens the local moment. In contrast, moments embedded in insulators remain unscreened at all temperatures. This raises the question about the fate of magnetic moments in intermediate, pseudogap systems, such as graphene. In these systems theory predicts a quantum phase-transition at a critical coupling strength which separates a local magnetic-moment phase from a Kondo screened phase. However, attempts to experimentally confirm these predictions and their intriguing consequences such as the ability to electrostatically control magnetic moments, have thus far been elusive. Here we report the observation of Kondo screening and the quantum phase-transition between screened and unscreened phases of vacancy magnetic-moments in graphene. Using scanning tunneling microscopy (STM), spectroscopy (STS) and numerical renormalization group (NRG) calculations, we identified Kondo screening by its spectroscopic signature and mapped the phase-transition as a function of coupling strength and chemical potential. We show that this transition makes it possible to turn the magnetic-moment on and off electrostatically through a gate voltage or mechanically through variations in local curvature.
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