Abstract
In addition to the well-known anti-ferromagnetic and ferromagnetic edge states in zigzag graphene nanoribbons (GNR), we find that there also exist some excited spin density wave (ESDW) states, the energies of which are close to the anti-ferromagnetic state (ground state). We thus argue that these ESDW states may coexist in experiment. Our numerical results from the self-consistent mean-field method as well as the first-principles calculations indicate that the allowed ESDWs are commensurate; and their dispersion curves are linear in the long wave limit. The coupling of the two edge portions in an ESDW becomes very weak in a wide GNR, in which case these ESDW portions may have different phases. Finally our calculations in the non-equilibrium Green’s function theory combined with the Hubbard model show that these ESDW states can also exist in some localized (middle or terminal) region of GNR.
Highlights
Graphene, an important two-dimensional material, has attracted a lot of research interests in the past decade [1,2,3]
We find that in some short supercells, the AF-typed or FM-typed excited spin density wave (ESDW) states does not exist in our SC calculations
Hybrid SDW excitations With these self-consistent calculations, we discover a lot of hybrid ESDW states in the graphene nanoribbons (GNR) supercells
Summary
An important two-dimensional material, has attracted a lot of research interests in the past decade [1,2,3]. The energy bands of these materials often exhibit half-metallic property with potential applications in the spintronic devices Besides these periodic graphene systems, some people found that there exist magnetic orders in finite graphene nanoislands [14]. These modes, corresponding to some excited spin-density-wave (ESDW), have very similar band gaps as insulators. Their energies are close to the AF or FM state. Combined with the non-equilibrium Green’s function (NEGF) theory, we find that in the local region of zigzag GNR, there exist similar SDW excitations All these novel states can be viewed as some spin excitations in the configuration space of magnetic orders. Is the eigenvector of ith site for the pth eigenvalue with the Bloch wavevector K
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