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.