arXiv:1001.1263v1 [cond-mat.mes-hall] 8 Jan 2010 Hydrogenated Graphene Nanoribbons for Spintronics D. Soriano, 1 F. Mu˜ noz-Rojas, 1, 2 J. Fern´ andez-Rossier, 1 and J. J. Palacios 1, 3 $^{1}$Departamento de F´ısica Aplicada, Universidad de Alicante, San Vicente del Raspeig, Alicante 03690, Spain $^{2}$Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea $^{3}$Departamento de F´ısica de la Materia Condensada, Universidad Aut´ onoma de Madrid, Cantoblanco, Madrid 28049, Spain (Dated: October 24, 2018) We show how hydrogenation of graphene nanoribbons at small concentrations can open new venues towards carbon-based spintronics applications regardless of any especific edge termination or passivation of the nanoribbons. Density functional theory calculations show that an adsorbed H atom induces a spin density on the surrounding π orbitals whose symmetry and degree of localization depends on the distance to the edges of the nanoribbon. As expected for graphene-based systems, these induced magnetic moments interact ferromagnetically or antiferromagnetically depending on the relative adsorption graphene sublattice, but the magnitude of the interactions are found to strongly vary with the position of the H atoms relative to the edges. We also calculate, with the help of the Hubbard model, the transport properties of hydrogenated armchair semiconducting graphene nanoribbons in the diluted regime and show how the exchange coupling between H atoms can be exploited in the design of novel magnetoresistive devices. transmission electron microscopy $^{18}$. There is a widespread consensus on the large pote- tial of graphene for electronic applications $^{1,2}$. Theoret- ically, graphene also holds promise for a vast range of applications in spintronics, although clear evidence of magnetic graphene is, however, elusive to date. In a broad sense, two factors may account for this elusive- ness. First, the fact that hydrocarbons of high spin are known to be highly reactive and, unless fabricated or syn- thesized under very clean and controled conditions, they will likely bind surrounding species with the concomit- tant disappearance of magnetism $^{3}$. A second reason re- lates to the fact that the ground state of graphene is near an interaction-driven phase transition into an insulating antiferromagnetic state $^{4}$. This underlying antiferromag- netic correlations prevent the magnetic moments, even if they develop, from ordering ferromagnetically and pre- clude the possibility of observing hysteresis in standard magnetic measurements. Notwithstanding, a few reports of magnetic graphite 5 and graphene 6 can be found in re- cent literature. Most of recent theoretical ideas for graphene based spintronics applications are rooted on the magnetic prop- erties of nanoribbons 7–11 or nanographenes 12–15 with zigzag edges. All these proposals assume a very par- ticular edge hydrogenation where H atoms passivate the σ dangling bonds, leaving all the π orbitals un- saturated and carrying the magnetic moments. How- ever, this is just one out of many possible edge realiza- tions which range from H-free self-passivation 16 to full H passivation $^{17}$. According to the work of Wassmann et al. $^{17}$, relatively low H concentations at room tempera- ture suffice to completely passivate the edges, including the edge π orbitals responsible for the magnetic order. The self-passivated or reconstructed zigzag edges 16 are, in fact, among the least energetically favorable of all, although, interestingly, have been recently observed by As shown in Sec. III, after a brief introduction to the theoretical basics presented in Sec. II, the magnetic- field driven ferromagnetic (F) state, where the H-induced magnetic moments are aligned by the field [as shown in Fig. 2(b)], can present a different resistance from that of the natural antiferromagnetic (AF) zero-field state [as that in Fig. 2(a)]. Two different cases are discussed: Infi- nite semiconducting AGNR’s and finite ones connected to conductive graphene [see schematic piture in Fig. 1(d)]. The differences in conductance between the F and the AF In the light of the present controversy on the actual possibilities of ever encounter zigzag magnetic edges, we propose in this work an alternative to edge-related spin- tronics in which to exploit the recently shown controled hydrogenation of graphene $^{19}$. The key factor here is that adsorption of atomic H in the bulk of graphene is ac- companied by the appearance of a magnetic moment of 1 µ$_{B}$ localized on the π orbitals surrounding each H atom $^{20}$. These magnetic moments interact with one an- other ferromagnetically or antiferromagnetically, depend- ing on whether their respective adsorption sublattices (usually labeled A and B) are the same or not $^{20–22}$. Sta- tistically speaking, a sublattice compensated H coverage is expected unless adsorption on one sublattice is privi- leged, e.g., by the substrate. To date, however, there is no evidence that such an uncompensated coverage can be achieved. In the more likely compensated case an overall antiferromagnetic alignment with a total spin S = 0 is thus energetically favored over a ferromagnetic one with S > 0. As a proof of principle and since we are inter- ested in the diluted regime, we consider in this work the fundamental problem of two H atoms. These are cova- lently bonded to the surface of a semiconducting arm- chair graphene nanoribbon (AGNR) on different sublat- tices [see Fig. 1(a)]. Here the σ bonds of the edges are fully passivated with H so that they are irrelevant at low energies. I. INTRODUCTION