Electronic spin transport in graphene field-effect transistors Popinciuc, M.; Jozsa, C.; Zomer, P. J.; Tombros, N.; Veligura, A.; Jonkman, H. T.; van Wees, B. J. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Spin transport experiments in graphene, a single layer of carbon atoms ordered in a honeycomb lattice, indicate spin-relaxation times that are significantly shorter than the theoretical predictions. We investigate experimentally whether these short spin-relaxation times are due to extrinsic factors, such as spin relaxation caused by low impedance contacts, enhanced spin-flip processes at the device edges, or the presence of an aluminum oxide layer on top of graphene in some samples. Lateral spin valve devices using a field-effect transistor geometry allowed for the investigation of the spin relaxation as a function of the charge density, going continuously from metallic hole to electron conduction ͑charge densities of n ϳ 10 12 cm −2 ͒ via the Dirac charge neutrality point ͑n ϳ 0͒. The results are quantitatively described by a one-dimensional spin-diffusion model where the spin relaxation via the contacts is taken into account. Spin valve experiments for various injector-detector separations and spin precession experiments reveal that the longitudinal ͑T 1 ͒ and the transversal ͑T 2 ͒ relaxation times are similar. The anisotropy of the spin-relaxation times ʈ and Ќ , when the spins are injected parallel or perpendicular to the graphene plane, indicates that the effective spin-orbit fields do not lie exclusively in the two-dimensional graphene plane. Furthermore, the proportionality between the spinrelaxation time and the momentum-relaxation time indicates that the spin-relaxation mechanism is of the Elliott-Yafet type. For carrier mobilities of 2 ϫ 10 3 -5ϫ 10 3 cm 2 / V s and for graphene flakes of 0.1-2 m in width, we found spin-relaxation times on the order of 50-200 ps, times which appear not to be determined by the extrinsic factors mentioned above.

Linear scaling between momentum and spin scattering in graphene Jozsa, C.; Maassen, T.; Popinciuc, M.; Zomer, P. J.; Veligura, A.; Jonkman, H. T.; van Wees, B. J.

at integer multiples of 2e 2 /h at zero magnetic field in a high mobility suspended graphene ballistic nanoconstriction. This quantization evolves into the typical quantum Hall effect for graphene at magnetic fields above 60 mT. Voltage bias spectroscopy reveals an energy spacing of 8 meV between the first two subbands. A pronounced feature at 0.6 × 2e 2 /h present at a magnetic field as low as ∼0.2 T resembles the '0.7 anomaly' observed in quantum point contacts in a GaAs-AlGaAs two-dimensional electron gas, possibly caused by electron-electron interactions 11 . Conductance quantization in zero magnetic field in graphene ribbons is expected to strongly depend on the type of edge termination 6,7,[12][13][14] . In the case of ideal non-disordered armchair edges the valley degeneracy is lifted, leading to a quantization sequence 0 (for a semiconducting ribbon), 1,2,3,... × G 0 , when the Fermi energy is raised or lowered from the charge neutrality point. Here G 0 = 2e 2 /h, with e the electron charge, h the Planck constant and the factor two is due to the spin degeneracy. For zigzag edges on the other hand, theory predicts a quantization in odd multiples 1,3,5,... × G 0 , reflecting the presence of both spin, as well as valley degeneracy. However, realistic devices have a finite (edge) disorder which will dominate the electronic transport in long and narrow ribbons, making the experimental observation of conductance quantization very challenging. Signatures of the formation of one-dimensional subbands because of quantum confinement have been reported for nanoribbons fabricated on a silicon oxide (SiO 2 ) substrate 15,16 . However, those devices are not in the ballistic regime because they have the characteristics of a diffusive, disordered system and lack uniform doping owing to strong interaction with the substrate. In such a narrow and long ribbon an edge disorder of typically only a few per cent of missing carbon atoms will prevent the observation of quantum ballistic transport and conductance quantization [17][18][19] . A way to circumvent this problem is to prepare a constriction with a length comparable or shorter than the width, for which conductance quantization is theoretically possible for an edge disorder of 10% or even higher [18][19][20] . To investigate quantum ballistic 1 Molecular Electronics, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, NL-9747AG Groningen, The Netherlands, 2 Physics of Nanodevices, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh, NL-9747AG Groningen, The Netherlands. *e-mail: n.tombros@rug.nl. No current annealing was applied to region C. b, A schematic cross-section of the device. The graphene layer is suspended about 1 µm above the 500 nm thick SiO 2 and the electrodes are kept in place by pillars of LOR polymer. The n+ doped silicon substrate is used as a back gate electrode to control the charge-carrier density.transport and conductance quantization in graphene it is therefore crucial to prepare a narrow, short...

Spin relaxation in graphene is investigated in electrical graphene spin valve devices in the nonlocal geometry. Ferromagnetic electrodes with in-plane magnetizations inject spins parallel to the graphene layer. They are subject to Hanle spin precession under a magnetic field B applied perpendicular to the graphene layer. Fields above 1.5 T force the magnetization direction of the ferromagnetic contacts to align to the field, allowing injection of spins perpendicular to the graphene plane. A comparison of the spin signals at B=0 and B=2 T shows a 20% decrease in spin relaxation time for spins perpendicular to the graphene layer compared to spins parallel to the layer. We analyze the results in terms of the different strengths of the spin-orbit effective fields in the in-plane and out-of-plane directions and discuss the role of the Elliott-Yafet and Dyakonov-Perel mechanisms for spin relaxation.

No abstract