Memory devices operating due to the fast proton transfer (PT) process are proposed by the means of first-principles calculations. Writing information is performed using the electrostatic potential of scanning tunneling microscopy (STM). Reading information is based on the effect of the local magnetization induced at the zigzag graphene nanoribbon (Z-GNR) edge—saturated with oxygen or the hydroxy group—and can be realized with the use of giant magnetoresistance (GMR), a magnetic tunnel junction or spin-transfer torque devices. The energetic barriers for the hop forward and backward processes can be tuned by the distance and potential of the STM tip; this thus enables us to tailor the non-volatile logic states. The proposed system enables very dense packing of the logic cells and could be used in random access and flash memory devices.