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...

Magnetic insulators are a key resource for next-generation spintronic and topological devices. The family of layered metal halides promises varied magnetic states, including ultrathin insulating multiferroics, spin liquids, and ferromagnets, but device-oriented characterization methods are needed to unlock their potential. Here, we report tunneling through the layered magnetic insulator CrI as a function of temperature and applied magnetic field. We electrically detect the magnetic ground state and interlayer coupling and observe a field-induced metamagnetic transition. The metamagnetic transition results in magnetoresistances of 95, 300, and 550% for bilayer, trilayer, and tetralayer CrI barriers, respectively. We further measure inelastic tunneling spectra for our junctions, unveiling a rich spectrum consistent with collective magnetic excitations (magnons) in CrI.

Abstract.The observation of ferromagnetic order in a monolayer of CrI 3 has been recently reported, with a Curie temperature of 45 Kelvin and off-plane easy axis. Here we study the origin of magnetic anisotropy, a necessary ingredient to have magnetic order in two dimensions, combining two levels of modeling, density functional calculations and spin model Hamiltonians. We find two different contributions to the magnetic anisotropy of the material, favoring off-plane magnetization and opening a gap in the spin wave spectrum. First, ferromagnetic super-exchange across the ≃ 90 degree Cr-I-Cr bonds, are anisotropic, due to the spin orbit interaction of the ligand I atoms. Second, a much smaller contribution that comes from the single ion anisotropy of the S = 3/2 Cr atom. Our results permit to establish the XXZ Hamiltonian, with a very small single ion easy axis anisotropy, as the adequate spin model for this system. Using spin wave theory we estimate the Curie temperature and we highlight the essential role played by the gap that magnetic anisotropy induces on the magnon spectrum.

We study the conduction band spin splitting that arises in transition metal dichalcogenide (TMD) semiconductor monolayers such as MoS 2 , MoSe 2 , WS 2 , and WSe 2 due to the combination of spin-orbit coupling and lack of inversion symmetry. Two types of calculation are done. First, density functional theory (DFT) calculations based on plane waves that yield large splittings, between 3 and 30 meV. Second, we derive a tight-binding model that permits to address the atomic origin of the splitting. The basis set of the model is provided by the maximally localized Wannier orbitals, obtained from the DFT calculation, and formed by 11 atomiclike orbitals corresponding to d and p orbitals of the transition metal (W, Mo) and chalcogenide (S, Se) atoms respectively. In the resulting Hamiltonian, we can independently change the atomic spin-orbit coupling constant of the two atomic species at the unit cell, which permits to analyze their contribution to the spin splitting at the high symmetry points. We find that-in contrast to the valence band-both atoms give comparable contributions to the conduction band splittings. Given that these materials are most often n-doped, our findings are important for developments in TMD spintronics.

We address the electronic structure and magnetic properties of vacancies and voids both in graphene and graphene ribbons. By using a mean-field Hubbard model, we study the appearance of magnetic textures associated with removing a single atom ͑vacancy͒ and multiple adjacent atoms ͑voids͒ as well as the magnetic interactions between them. A simple set of rules, based on the Lieb theorem, link the atomic structure and the spatial arrangement of the defects to the emerging magnetic order. The total spin S of a given defect depends on its sublattice imbalance, but some defects with S = 0 can still have local magnetic moments. The sublattice imbalance also determines whether the defects interact ferromagnetically or antiferromagnetically with one another and the range of these magnetic interactions is studied in some simple cases. We find that in semiconducting armchair ribbons and two-dimensional graphene without global sublattice imbalance, there is a maximum defect density above which local magnetization disappears. Interestingly, the electronic properties of semiconducting graphene ribbons with uncoupled local moments are very similar to those of diluted magnetic semiconductors, presenting giant Zeeman splitting.

We study the electronic structure of a heterojunction made of two monolayers of MoS 2 and WS 2 . Our first-principles density functional calculations show that, unlike in the homogeneous bilayers, the heterojunction has an optically active band gap, smaller than the ones of MoS 2 and WS 2 single layers. We find that the optically active states of the maximum valence and minimum conduction bands are localized on opposite monolayers, and thus the lowest energy electron-holes pairs are spatially separated. Our findings portray the MoS 2 -WS 2 bilayer as a prototypical example for band-gap engineering of atomically thin two-dimensional semiconducting heterostructures.

I show that recent experiments of inelastic scanning tunneling spectroscopy of single and a few magnetic atoms are modeled with a phenomenological spin-assisted tunneling Hamiltonian so that the inelastic dI/dV line shape is related to the spin spectral weight of the magnetic atom. This accounts for the spin selection rules and dI/dV spectra observed experimentally for single Fe and Mn atoms deposited on Cu2N. In the case of chains of Mn atoms it is found necessary to include both first and second-neighbor exchange interactions as well as single-ion anisotropy.

By computing spin-polarized electronic transport across a finite zigzag graphene ribbon bridging two metallic graphene electrodes, we demonstrate, as a proof of principle, that devices featuring 100% magnetoresistance can be built entirely out of carbon. In the ground state a short zigzag ribbon is an antiferromagnetic insulator which, when connecting two metallic electrodes, acts as a tunnel barrier that suppresses the conductance. The application of a magnetic field makes the ribbon ferromagnetic and conductive, increasing dramatically the current between electrodes. We predict large magnetoresistance in this system at liquid nitrogen temperature and 10 T or at liquid helium temperature and 300 G.