Magnetism in Graphene Nanoislands

Abstract

We study the magnetic properties of nanometer-sized graphene structures with triangular and hexagonal shapes terminated by zigzag edges. We discuss how the shape of the island, the imbalance in the number of atoms belonging to the two graphene sublattices, the existence of zero-energy states, and the total and local magnetic moment are intimately related. We consider electronic interactions both in a mean-field approximation of the one-orbital Hubbard model and with density functional calculations. Both descriptions yield values for the ground state total spin S consistent with Lieb's theorem for bipartite lattices. Triangles have a finite S for all sizes whereas hexagons have S 0 and develop local moments above a critical size of 1:5 nm. DOI: 10.1103/PhysRevLett.99.177204 PACS numbers: 75.75.+a, 73.20.ÿr, 75.50.Xx, 75.70.Cn The study of graphene-based field effect devices has opened a new research venue in nanoelectronics [1][2][3][4][5]. Graphene is a truly two-dimensional zero-gap semiconductor with peculiar transport and magnetotransport propreties, including the room temperatrue quantum Hall effect [6], that makes it very different from conventional semiconductors and metals [7]. Progress in the fabrication of graphene-based lower dimensional structures has been reported both in the form of one-dimensional ribbons [8,9] and zero-dimensional dots [2,7,10]. Interestingly, the electronic properties of graphene change in a nontrivial manner when going to lower dimensions. Ribbons, for instance, can be either semiconducting with a size dependent gap or metallic [8,9].The electronic structure of graphene-based nanostructures is expected to be different from bulk graphene because of surface, or, more properly, edge effects [11]. This is particularly true in the case of structures with zizzag edges which present magnetic properties [12 -14]. Whereas bulk graphene is a diamagnetic semimetal, simple tight-binding models predict that one-dimensional ribbons with zigzag edges have two flat bands at the Fermi energy [11,12,[15][16][17], i.e., are paramagnetic metals. Spin polarized density functional theory (DFT) [13] and mean-field [12] calculations confirm that these bands are prone to magnetic instabilities.The fabrication of graphene nanostructures using topbottom techniques does not permit creating atomically defined edges to date [10]. In contrast, bottom-up processing of graphene nanoislands is very promising [18]. Hexagonal shape nanoislands with well-defined zigzag edges atop the 0001 surface of Ru have already been achieved [19]. This experimental progress motivates our study of the electronic structure of graphene nanostructures with various shapes. Graphene quantum dots also hold the promise of extremely long spin relaxation and decoherence time because of the very small spin-orbit and hyperfine coupling in carbon [20].We have found that, remarkably, both the DFT calculations and the mean-field approximation of the single-band Hubbard model with first-neighbors hopping yield very similar results in all c...

Half-Metallic Zigzag Carbon Nanotube Dots

“…This conclusion is in striking difference from the case of ZZ-GNRs, where the ground electronic state was found to have an AFM spin ordering regardless of the dimensions of the ribbon. [19][20][21][22][23][24][25][26]28,29,42,[45][46][47][48][49][50][51][52] Interestingly, contradicting results have been reported in the literature, 33 indicating that the ground state of unpassivated zigzag CNTs has a low-spin AFM ordering even for nanotubes that have earlier been considered to present a high-spin ferromagnetically ordered ground state. 32 In light of the considerable progress that has been made in the synthesis and fabrication of ultra-short [60][61][62][63][64] and open ended 65 CNTs and ultra-narrow GNRs, [66][67][68][69] it is desirable to obtain a full understanding of their electronic properties.…”

“…30,40,43 A unique mechanism for spin ordering in graphene based systems is related to the appearance of edge states. [18][19][20][21][22][23][24][25][26][27][28][29]42,[45][46][47][48][49][50][51][52] When cutting a graphene sheet along its zigzag axis to form a narrow and elongated graphene nanoribbon (GNR), distinct electronic states appear, which are localized around the exposed edges. [54][55][56][57][58][59] These states are predicted to carry spin polarization, resulting in a well defined magnetic ordering.…”

“…[54][55][56][57][58][59] These states are predicted to carry spin polarization, resulting in a well defined magnetic ordering. [19][20][21][22][23][24][25][26]28,29,42,[45][46][47][48][49][50][51][52] Due to the bipartite hexagonal structure of graphene, the electronic ground state of such zigzag graphene nanoribbons (ZZ-GNRs) is characterized by an antiferromagnetic (AFM) spin ordering, where the edge states located at the two zigzag edges of the ribbon have opposite spins. Under the influence of an external electric field, these systems have been predicted to become half-metallic with one spin channel being semiconducting and the other metallic, 45,47 thus acting as perfect spin filters with important implications to the field of spintronics.…”

“…Furthermore, this behavior has been shown to be preserved for finite graphene nanoribbons, where the zigzag edge may be as short as a few repeating units. [48][49][50][51][52] Similar to graphene nanoribbons, is has recently been suggested that spin ordering may occur on the zigzag edges of hydrogen terminated finite sized carbon nanotubes (CNTs). 32,37 Based on density functional theory (DFT) calculations within the local spin density approximation (LSDA), it was predicted that the ground electronic state of these systems strongly depends on their circumferencial dimension ranging from AFM to ferromagnetic (FM) ordering, where both edges of the nanotube bear spins of the same flavor.…”

Clar’s Theory, π-Electron Distribution, and Geometry of Graphene Nanoribbons

“…23,24 Magnetic ground states were also found for other graphene nanostructures. [25][26][27][28][29] In singlehydrogen-terminated armchair ribbons, however, this phenomena is absent. Despite the broad range of production techniques for graphene ribbons 10,11,17,[30][31][32][33][34][35][36][37][38][39][40][41] real control over the edge geometry and termination in them has not been achieved yet, and no atomic characterization either.…”