Effect of electric field and magnetic field on spin transport in bilayer graphene armchair nanoribbons: A Monte Carlo simulation study
Introduction
Due to ultra low power dissipation, non-volatility and excellent switching speeds, spintronics devices have drawn a lot of attention in the electronic industry. There is significant research going on in utilizing the spin property of an electron in storing and processing the information [1]. Graphene has drawn considerable attention for spintronic and nano-electronics applications due to unique electronic properties such as high electron and hole mobility and low spin orbit interaction. Long spin relaxation length and gate-tunable spin transport [2] has made graphene ideal candidate for future spintronics applications. Significant amount of both experimental and theoretical investigations have been done on graphene [3], [4], [5], [6], [7], [8], [9], [10], [11]. In the work of McCann et al. [12], the possibility of opening the band gap in bilayer graphene (BLG) by applying an external electric field perpendicular to graphene plane was demonstrated. In Ref. [13], Wallace theoretically explained the existence of Dirac like Fermionic states in single layer graphene (SLG).In Refs. [14], the authors experimentally observed long spin relaxation length in suspended graphene layer. In Refs. [15], [16] authors observed long spin relaxation length in few layer and monolayer graphene on hexagonal boron nitride substrate. Due to low atomic masses most of the isotopes of carbon have very weak hyperfine interaction between the nuclear and the electronic spins. Thus as predicted by many theoretical groups the spin relaxation length is expected to be long. Yet experimentally observed spin life time in graphene is much smaller than the theoretically obtained results. This difference is caused by the local magnetic moments arising from adatoms and vacancies which are not taken into consideration in theoretical modeling [17]. These local magnetic moments results in faster spin dephasing. Again in the present work we take into consideration spin relaxation due to only Rashba effect as other mechanisms are not fully understood in nanoribbons. A lot of recent studies have focused on 2D graphene sheet and very little work has been done on spin transport in Graphene nanoribbons (GNRs).
Single layer graphene has linear dispersion around the Dirac point and zero bandgap. Spin transport in semiconductors is of interest since we can exploit both charge and spin properties of an electron to transfer, store and process the information. It can combine the capabilities of semiconductors with the capabilities of the magnetic materials. Constraining one dimension of graphene sheet results in 1D nanoribbons of armchair or zigzag type which are semiconducting [18], [19]. The bandgap of these graphene nanoribbons (GNR) depends on the edge property, width and chirality. The bandgap of nanoribbons can also be tuned by external electric fields. As demonstrated by the IBM group [20], noise in bi-layer graphene nanoribbon is greatly suppressed as compared to that in single layer graphene nanoribbon and this gives a significant improvement in the signal to noise ratio of bi-layer graphene devices. In this work we take up study on the effect of external fields on spin transport in bilayer acGNR. The band structure has a parabolic nature around the band edge [21], [22], [23].
We use an ensemble self consistent semiclassical Monte Carlo approach to model the spin transport in bilayer acGNR. Monte Carlo simulations have been extensively used to model the charge transport and spin transport [24], [25], [26], [27], [28] in SLG and BLG devices. Spin evolution occurs continuously along with the evolution of momentum. Hence Monte Carlo approach is best suited for studies on the spin dephasing. The paper is organized as follows. In Section 2 we present the bilayer graphene model used in our simulations and discuss different scattering mechanisms considered. Section 3 deals with the result and discussion. Section 4 concludes this paper.
Section snippets
Simulation model
In monolayer graphene, sheet electrons and holes coexist symmetrically across the Fermi level (Dirac Point).So when graphene is used as channel material in field effect transistor, the channel current cannot be turned off. Hence formation of bandgap in Graphene is necessary for electronic device applications. Converting infinite monolayer sheet into 1D nanoribbons result in the spatial confinement of electrons and can open up the bandgap. These nanoribbons are classified into armchair and
Results and discussion
The length of the device considered in simulation is 5 um. The distance between the two graphene planes is considered to be 0.36 nm. The results are obtained for driving electric field of 1 kV/cm and 2 kV/cm. The scattering mechanisms incorporated in our simulations include the acoustic phonon scattering, the optical phonon scattering, impurity and spin flip scattering along the lines of [8], [27], [35], [36], [37], [38]. The time step chosen is 0.005 fs, and the particles are evolved for 3 × 10
Conclusion
In this work, we studied the spin relaxation in bilayer α-, β-, and γ-ac GNRs subjected to external electric and magnetic field. The electrons were injected with initial polarization along the z axis which is perpendicular to the graphene plane. The spin relaxation length depends on the type of acGNR and the external electric and magnetic fields. We found that the spin relaxation length increases with increased width for β-, and γ ac GNR while it is nearly same for all widths for α–ac GNR. The
Acknowledgements
The authors thank the Department of Science and Technology of the Government of India for partially funding this project.
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