First-principles study of magnetic order in graphene nanoflakes as spin logic devices

Scale effect and topological frustration can form magnetic order in the finite graphene structures (graphene nanoflakes (GNFs)). In this paper, the GNFs that can generate large net electron spin or electron spin antiferromagnetic coupling between local regions of net electron spins are classified reasonably. Representative special GNF configurations are proposed to be effectively used as fundamental logic gate devices for ultra-fast high density spintronics, and theoretically investigated by the first-principles electron structure calculations based on spin-polarized density functional theory. The first-principles calculations are performed by utilizing all-electron numerical-orbital scheme in the M11-L form of meta-GGA exchange-correlation functional. The energy spectrum of singly occupied states and the isodensity surface of total spin distribution indicate evidently that spin-single-state electrons are localized on two sides of a representative double-triangle GNF and the spin polarizations of two GNF segments are in opposite directions, resulting in antiferromagnetic coupling, which is consistent with the results derived from the graph theory and Lieb theorem. The energy of antiferromagnetic spin-coupled state is 55 meV lower than that of ferromagnetic spin-coupled state, which is obviously higher than the thermodynamic threshold of the minimum energy dissipation at room temperature. The spin coupling energy of the double triangle GNF increases with the scaling of GNF dimension increasing. The magnetic coupling strength of the double triangle GNF with and without mirror symmetry approach to the maximum stable values of 50 meV and 200 meV respectively, which are remarkably higher that of quantum dots and transition metal atom systems. Due to the fact that the spin coupling strength of the GNF logic gate spin device can reach 200 meV, it can operate normally at ambient temperature with an error rate of 0.001 which can be easily improved by an error correction technique. The calculation results demonstrate that the proposed GNF logic gate can finely operate at ambient temperature with significantly low and correctable error rate. Recent experimental studies show that graphene nanodevices on a scale of only a few nanometers can be successfully fabricated by etching technique of electron beam and scanning probe. Furthermore, the properties of GNF spin logic devices are not sensitive to intrinsic defects. The triangular GNF with n carbon rings has only (n+2)2-3 carbon atoms, while it can endure n-1 internal defects, thus persisting in non-bond states and local magnetic moments. It is suggested that the full spin logic gate devices based on GNF can be realized by using the current advanced nano-processing technology.