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Register a new userImprinting Tunable ${pi}$-Magnetism in Graphene Nanoribbons via Edge Extensions
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Magnetic carbon nanostructures are currently under scrutiny for a wide spectrum of applications. Here, we theoretically investigate armchair graphene nanoribbons patterned with asymmetric edge extensions consisting of laterally fused naphtho groups, as recently fabricated via on-surface synthesis. We show that an individual edge extension acts as a spin-$frac{1}{2}$ center and develops a sizable spin-polarization of the conductance around the band edges. The Heisenberg exchange coupling between a pair of edge extensions is dictated by the position of the second naphtho group in the carbon backbone, thus enabling ferromagnetic, antiferromagnetic, or non-magnetic states. The periodic arrangement of edge extensions yields full spin-polarization at the band extrema, and the accompanying ferromagnetic ground state can be driven into non-magnetic or antiferromagnetic phases through external stimuli. Overall, our work reveals precise tunability of the ${pi}$-magnetism in graphene nanoribbons induced by naphtho groups, thereby establishing these one-dimensional architectures as suitable platforms for logic spintronics.
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Carbon-based magnetic structures promise significantly longer coherence times than traditional magnetic materials, which is of fundamental importance for spintronic applications. An elegant way of achieving carbon-based magnetic moments is the design of graphene nanostructures with an imbalanced occupation of the two sublattices forming the carbon honeycomb lattice. According to Liebs theorem, this induces local magnetic moments that are proportional to the sublattice imbalance. Exact positioning of sublattice imbalanced nanostructures in graphene nanomaterials hence offers a route to control interactions between induced local magnetic moments and to obtain graphene nanomaterials with magnetically non-trivial ground states. Here, we show that such sublattice imbalanced nanostructures can be incorporated along a large band gap armchair graphene nanoribbon on the basis of asymmetric zigzag edge extensions, which is achieved by incorporating specifically designed precursor monomers during the bottom-up fabrication of the graphene nanoribbons. Scanning tunneling spectroscopy of an isolated and electronically decoupled zigzag edge extension reveals Hubbard-split states in accordance with theoretical predictions. Investigation of pairs of such zigzag edge extensions reveals ferromagnetic, antiferromagnetic or quenching of the magnetic interactions depending on the relative alignment of the asymmetric edge extensions. Moreover, a ferromagnetic spin chain is demonstrated for a periodic pattern of zigzag edge extensions along the nanoribbon axis. This work opens a route towards the design and fabrication of graphene nanoribbon-based spin chains with complex magnetic ground states.
Graphene nanoribbons (GNRs) possess distinct symmetry-protected topological phases. We show, through first-principles calculations, that by applying an experimentally accessible transverse electric field (TEF), certain boron and nitrogen periodically co-doped GNRs have tunable topological phases. The tunability arises from a field-induced band inversion due to an opposite response of the conduction- and valance-band states to the electric field. With a spatially-varying applied field, segments of GNRs of distinct topological phases are created, resulting in a field-programmable array of topological junction states, each may be occupied with charge or spin. Our findings not only show that electric field may be used as an easy tuning knob for topological phases in quasi-one-dimensional systems, but also provide new design principles for future GNR-based quantum electronic devices through their topological characters.
We study the magnetic properties of graphene edges and graphene/graphane interfaces under the influence of electrostatic gates. For this, an effective low-energy theory for the edge states, which is derived from the Hubbard model of the honeycomb lattice, is used. We first study the edge state model in a mean-field approximation for the Hubbard Hamiltonian and show that it reproduces the results of the extended 2D lattice theory. Quantum fluctuations around the mean-field theory of the effective one-dimensional model are treated by means of the bosonization technique in order to check the stability of the mean-field solution. We find that edge magnetism at graphene/graphane interfaces can be switched on and off by means of electrostatic gates. We describe a quantum phase transition between an ordinary and a ferromagnetic Luttinger liquid - a realization of itinerant one-dimensional ferromagnetism. This mechanism may provide means to experimentally discriminate between edge magnetism or disorder as the reason for a transport gap in very clean graphene nanoribbons.
A bosonic field theory is derived for the tunable edge magnetism at graphene zigzag edges. The derivation starts from an effective fermionic theory for the interacting graphene edge states, derived previously from a two-dimensional interacting tight-binding model for graphene. The essential feature of this effective model, which gives rise to the weak edge magnetism, is the momentum-dependent non-local electron-electron interaction. It is shown that this momentum-dependence may be treated by an extension of the bosonization technique, and leads to interactions of the bosonic fields. These interactions are reminiscent of a phi^4 field theory. Focussing onto the regime close to the quantum phase transition between the ferromagnetic and the paramagnetic Luttinger liquid, a semiclassical interpretation of the interacting bosonic theory is given. Furthermore, it is argued that the universal critical behavior at the quantum phase transition between the paramagnetic and the ferromagnetic Luttinger liquid is governed by a small number of terms in this theory, which are accessible by quantum Monte-Carlo methods.
It is shown that apart from well-known factors, like temperature, substrate, and edge reconstruction effects, also the presence of external contacts is destructive for the formation of magnetic moments at the edges of graphene nanoribbons. The edge magnetism gradually decreases when graphene/electrode interfaces become more and more transparent for electrons. In addition to the graphene/electrode coupling strength, also the aspect ratio parameter, i.e. a width/length ratio of the graphene nanoribbon, is crucial for the suppression of edge magnetism. The present theory uses a tight-binding method, based on the mean-field Hubbard Hamiltonian for $pi$ electrons, and the Greens function technique within the Landauer-Buttiker approach.
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