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      The classical and quantum dynamics of molecular spins on graphene

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          Abstract

          Controlling the dynamics of spins on surfaces is pivotal to the design of spintronic 1 and quantum computing 2 devices. Proposed schemes involve the interaction of spins with graphene to enable surface-state spintronics 3, 4 , and electrical spin-manipulation 4- 11 . However, the influence of the graphene environment on the spin systems has yet to be unraveled 12 . Here we explore the spin-graphene interaction by studying the classical and quantum dynamics of molecular magnets 13 on graphene. While the static spin response remains unaltered, the quantum spin dynamics and associated selection rules are profoundly modulated. The couplings to graphene phonons, to other spins, and to Dirac fermions are quantified using a newly-developed model. Coupling to Dirac electrons introduces a dominant quantum-relaxation channel that, by driving the spins over Villain’s threshold, gives rise to fully-coherent, resonant spin tunneling. Our findings provide fundamental insight into the interaction between spins and graphene, establishing the basis for electrical spin-manipulation in graphene nanodevices.

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          Most cited references33

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          Electronic spin transport and spin precession in single graphene layers at room temperature

          The specific band structure of graphene, with its unique valley structure and Dirac neutrality point separating hole states from electron states has led to the observation of new electronic transport phenomena such as anomalously quantized Hall effects, absence of weak localization and the existence of a minimum conductivity. In addition to dissipative transport also supercurrent transport has already been observed. It has also been suggested that graphene might be a promising material for spintronics and related applications, such as the realization of spin qubits, due to the low intrinsic spin orbit interaction, as well as the low hyperfine interaction of the electron spins with the carbon nuclei. As a first step in the direction of graphene spintronics and spin qubits we report the observation of spin transport, as well as Larmor spin precession over micrometer long distances using single graphene layer based field effect transistors. The non-local spin valve geometry was used, employing four terminal contact geometries with ferromagnetic cobalt electrodes, which make contact to the graphene sheet through a thin oxide layer. We observe clear bipolar (changing from positive to negative sign) spin signals which reflect the magnetization direction of all 4 electrodes, indicating that spin coherence extends underneath all 4 contacts. No significant changes in the spin signals occur between 4.2K, 77K and room temperature. From Hanle type spin precession measurements we extract a spin relaxation length between 1.5 and 2 micron at room temperature, only weakly dependent on charge density, which is varied from n~0 at the Dirac neutrality point to n = 3.6 10^16/m^2. The spin polarization of the ferromagnetic contacts is calculated from the measurements to be around 10%.
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            Graphene spintronics.

            The isolation of graphene has triggered an avalanche of studies into the spin-dependent physical properties of this material and of graphene-based spintronic devices. Here, we review the experimental and theoretical state-of-art concerning spin injection and transport, defect-induced magnetic moments, spin-orbit coupling and spin relaxation in graphene. Future research in graphene spintronics will need to address the development of applications such as spin transistors and spin logic devices, as well as exotic physical properties including topological states and proximity-induced phenomena in graphene and other two-dimensional materials.
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              Electronic spin transport and spin precession in single graphene layers at room temperature.

              Electronic transport in single or a few layers of graphene is the subject of intense interest at present. The specific band structure of graphene, with its unique valley structure and Dirac neutrality point separating hole states from electron states, has led to the observation of new electronic transport phenomena such as anomalously quantized Hall effects, absence of weak localization and the existence of a minimum conductivity. In addition to dissipative transport, supercurrent transport has also been observed. Graphene might also be a promising material for spintronics and related applications, such as the realization of spin qubits, owing to the low intrinsic spin orbit interaction, as well as the low hyperfine interaction of the electron spins with the carbon nuclei. Here we report the observation of spin transport, as well as Larmor spin precession, over micrometre-scale distances in single graphene layers. The 'non-local' spin valve geometry was used in these experiments, employing four-terminal contact geometries with ferromagnetic cobalt electrodes making contact with the graphene sheet through a thin oxide layer. We observe clear bipolar (changing from positive to negative sign) spin signals that reflect the magnetization direction of all four electrodes, indicating that spin coherence extends underneath all of the contacts. No significant changes in the spin signals occur between 4.2 K, 77 K and room temperature. We extract a spin relaxation length between 1.5 and 2 mum at room temperature, only weakly dependent on charge density. The spin polarization of the ferromagnetic contacts is calculated from the measurements to be around ten per cent.
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                Author and article information

                Journal
                101155473
                30248
                Nat Mater
                Nat Mater
                Nature materials
                1476-1122
                4 November 2015
                07 December 2015
                February 2016
                07 June 2016
                : 15
                : 2
                : 164-168
                Affiliations
                [1 ]1. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart (Germany)
                [2 ]Dipartimento di Fisica, Università di Firenze, Via G. Sansone 1, I-50019 Sesto Fiorentino (Italy)
                [3 ]Istituto dei Sistemi Complessi, CNR, Unità di Firenze, Via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy)
                [4 ]Dipartimento di Scienze Chimiche e Geologiche, Università di Modena e Reggio Emilia, INSTM RU, Via G. Campi 183, I-41125 Modena (Italy)
                [5 ]Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, C/ Pedro Cerbuna 12, E-50009 Zaragoza (Spain)
                [6 ]Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart (Germany)
                [7 ]Institut de Physique de la Matière Condensée, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, (Switzerland)
                [8 ]Department of Materials, University of Oxford, 16 Parks Road, OX1 3PH Oxford, (United Kingdom)
                Author notes

                Author contributions

                C.C. performed the functionalization and most measurements. A.C. synthetized the molecules. C.C. and S.R. acquired the MALDI-TOF spectra. A.R. and F.L. performed the very-low-temperature magnetic measurements. A.R., M.G.P. and L.B. performed the theoretical analysis. L.B. and M.B. conceived the experiments. L.B. wrote the draft and all authors contributed to discussions and the final manuscript.

                Article
                EMS65454
                10.1038/nmat4490
                4800001
                26641019
                9f37f2ee-57ee-49ed-b635-2890afc2baa1

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                Article

                Materials science
                graphene,spin dynamics,nanomaterials,quantum tunneling,molecular magnetism
                Materials science
                graphene, spin dynamics, nanomaterials, quantum tunneling, molecular magnetism

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