Spin relaxation properties in graphene due to its linear dispersion

Jo, Sanghyun; Ki, Dong–Keun; Jeong, Dongchan; Lee, Hu Jong; Kettemann, Stefan

doi:10.1103/physrevb.84.075453

Cited by 68 publications

(61 citation statements)

References 43 publications

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“…It is reasonable to expect that there are not more magnetic sites than, say, 1 ppm, in "clean" graphene samples investigated for spin relaxation in experiments [6][7][8][9][10][11][12][13]. For this concentration a simple estimate gives a weak spin relaxation rate, similar to what is predicted for spin-orbit coupling mechanisms.…”

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confidence: 71%

Spin Relaxation Mechanism in Graphene: Resonant Scattering by Magnetic Impurities

2014

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We propose that the observed small (100 ps) spin relaxation time in graphene is due to resonant scattering by local magnetic moments. At resonances, magnetic moments behave as spin hot spots: the spin-flip scattering rates are as large as the spin-conserving ones, as long as the exchange interaction is greater than the resonance width. Smearing of the resonance peaks by the presence of electron-hole puddles gives quantitative agreement with experiment, for about 1 ppm of local moments. Although magnetic moments can come from a variety of sources, we specifically consider hydrogen adatoms, which are also resonant scatterers. The same mechanism would also work in the presence of a strong local spin-orbit interaction, but this would require heavy adatoms on graphene or a much greater coverage density of light adatoms. To make our mechanism more transparent, we also introduce toy atomic chain models for resonant scattering of electrons in the presence of a local magnetic moment and Rashba spin-orbit interaction. DOI: 10.1103/PhysRevLett.112.116602 PACS numbers: 72.80.Vp, 72.25.Rb Graphene [1,2] has been considered an ideal spintronics [3,4] material. Its spin-orbit coupling being weak, the spin lifetimes of Dirac electrons are expected to be long, on the order of microseconds [5]. Yet experiments find tenths of a nanosecond [6][7][8][9][10][11][12][13]. This vast discrepancy has been the most outstanding puzzle of graphene spintronics. Despite intense theoretical efforts [14][15][16][17][18][19][20][21], the mechanism for the spin relaxation in graphene has remained elusive. Recently, mesoscopic transport experiments [22] found evidence that local magnetic moments could be the culprits. Here we propose a mechanism of how even a small concentration of such moments can drastically reduce the spin lifetime of Dirac electrons. If the local moments sit at resonant scatterers, such as vacancies [23][24][25] and adatoms [25,26], they can act as spin hot spots [27]: while contributing little to momentum relaxation, they can dominate spin relaxation. Our mechanism is general, but to obtain quantitative results we use model parameters corresponding to hydrogen adatoms which yield both resonant scattering and local moments [26,28,29]. The calculated spin relaxation rates for 1 ppm of local moments, when averaged over electron density fluctuations due to electron-hole puddles, are in quantitative agreement with experiment. Our theory shows that in order to increase the spin lifetime in graphene, local magnetic moments at resonant scatterers need to be chemically isolated or otherwise eliminated.In graphene the presence of local magnetic moments is not obvious, unless the magnetic sites (vacancies or adatoms) [30] are intentionally produced [24,25]. It is reasonable to expect that there are not more magnetic sites than, say, 1 ppm, in "clean" graphene samples investigated for spin relaxation in experiments [6][7][8][9][10][11][12][13]. For this concentration a simple estimate gives a weak spin relaxation rate, similar to wha...

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confidence: 71%

Spin Relaxation Mechanism in Graphene: Resonant Scattering by Magnetic Impurities

2014

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“…In this case the experimental data does show linear trends, but none of the sets intersect with the origin. This cannot be attributed to broadening of the density of states or finite conductivity [9].…”

Section: Eymentioning

confidence: 99%

Long-distance spin transport in high-mobility graphene on hexagonal boron nitride

et al. 2012

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We performed spin transport measurements on boron nitride based single layer graphene devices with mobilities up to 40 000 cm 2 V −1 s −1 . We could observe spin transport over lengths up to 20 µm at room temperature, the largest distance measured so far for graphene. Due to enhanced charge carrier diffusion, spin relaxation lengths are measured up to 4.5 µm. The relaxation times are similar to values for lower quality SiO2 based devices, around 200 ps. We find that the relaxation rate is determined in almost equal measures by the Elliott-Yafet and D'Yakonov-Perel mechanisms.The potential of graphene [1] as an emerging material for spintronics has been established, revealing spin relaxation lengths λ of 2 µm at room temperature [2]. Spins relax over a length λ = √ D s τ s , where D s is the spin diffusion constant and τ s the spin relaxation time. One straightforward way to achieve spin transport over larger distances is to enhance D s by fabricating high mobility devices. On the other hand, τ s is theoretically predicted to range up to hundreds of nanoseconds [3]. However, observations made in the recent years by experimentalists [2, 4-13] do not match up to the high expectations set by theory. Measurements typically indicate τ s to be in the hundred picoseconds range and the discrepancy between theory and experiment and the exact relaxation mechanism remain yet unclear. Some works suggest that spin relaxation is dominated by the Elliott-Yafet (EY) mechanism [4,11,14], where τ s is proportional to the momentum relaxation time τ p and spins lose their information during scattering events. Other efforts indicate that the D'Yakonov-Perel (DP) mechanism is stronger [3,15,16], where τ s is inversely proportional to τ p and spins dephase in between scattering events.In identifying the limiting factors on spin transport in graphene, the substrate deserves special attention. For charge transport it has already been shown that the standard silicon oxide substrate reduces the mobility of charge carriers considerably [17]. The SiO 2 substrate is expected to also affect the spin relaxation in graphene through its roughness, trapped charges and surface phonons [16]. One approach to reduce the substrate roughness and screen impurities is to use epitaxial graphene on silicon carbide [12,18]. However, the presence of localized states is believed to affect spin transport in this system [13]. Alternatively, eliminating the influence of the substrate by suspending the graphene flake yields a 3 orders of magnitude increase in mobility [19,20]. Suspended spintronic graphene devices have been studied and a lower bound for τ s of ∼200 ps was found [10]. Determination of the actual value was however not possible since the presence of local supports for the suspended device was found to dominate the extraction of τ s .Atomically flat hexagonal boron nitride (h-BN) was found to be a much better substrate than SiO 2 for high quality graphene electronics [21][22][23], yielding a 2 orders of magnitude increase in mobility. In this manuscri...

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“…In SLG the spin-relaxation rate decreases with increasing the carrier density [5][6][7][8], in BLG the spin-relaxation rate increases [7,8]. Since the diffusivity in the investigated samples decreases with increasing the electron density, it has been a common practice to assign two different mechanisms to both structures: the Elliott-Yafet mechanism [25,26] to SLG [5,6,9,10] and Dyakonov-Perel mechanism [27] to BLG [7][8][9].…”

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confidence: 99%

“…Unfortunately, spin relaxation in graphene structures has been a baffling problem [3]. While experiments in both single layer graphene (SLG) [4][5][6][7][8][9][10][11] and bilayer graphene (BLG) [7,8] yield spin lifetimes on the 100-1000 ps time scale (the highest values achieved in graphene/h-BN structures [12,13]), theories based on realistic spin-orbit coupling and transport parameters predict lifetimes on the order of microseconds [14][15][16][17][18][19][20][21][22][23][24].While the magnitudes of the spin-relaxation rates of SLG and BLG are similar, the dependence of the rates on the electron density is opposite in the two systems. In SLG the spin-relaxation rate decreases with increasing the carrier density [5][6][7][8], in BLG the spin-relaxation rate increases [7,8].…”

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confidence: 99%

Resonant Scattering by Magnetic Impurities as a Model for Spin Relaxation in Bilayer Graphene

et al. 2015

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We propose that the observed spin relaxation in bilayer graphene is due to resonant scattering by magnetic impurities. We analyze a resonant scattering model due to adatoms on both dimer and nondimer sites, finding that only the former give narrow resonances at the charge neutrality point. Opposite to singlelayer graphene, the measured spin-relaxation rate in the graphene bilayer increases with carrier density. Although it has been commonly argued that a different mechanism must be at play for the two structures, our model explains this behavior rather naturally in terms of different broadening scales for the same underlying resonant processes. Not only do our results-using robust and first-principles inspired parameters-agree with experiment, they also predict an experimentally testable sharp decrease of the spin-relaxation rate at high carrier densities. DOI: 10.1103/PhysRevLett.115.196601 PACS numbers: 72.80.Vp, 72.25.Rb Understanding spin relaxation is essential for designing spintronics devices [1,2]. Unfortunately, spin relaxation in graphene structures has been a baffling problem [3]. While experiments in both single layer graphene (SLG) [4][5][6][7][8][9][10][11] and bilayer graphene (BLG) [7,8] yield spin lifetimes on the 100-1000 ps time scale (the highest values achieved in graphene/h-BN structures [12,13]), theories based on realistic spin-orbit coupling and transport parameters predict lifetimes on the order of microseconds [14][15][16][17][18][19][20][21][22][23][24].While the magnitudes of the spin-relaxation rates of SLG and BLG are similar, the dependence of the rates on the electron density is opposite in the two systems. In SLG the spin-relaxation rate decreases with increasing the carrier density [5][6][7][8], in BLG the spin-relaxation rate increases [7,8]. Since the diffusivity in the investigated samples decreases with increasing the electron density, it has been a common practice to assign two different mechanisms to both structures: the Elliott-Yafet mechanism [25,26] to SLG [5,6,9,10] and Dyakonov-Perel mechanism [27] to BLG [7][8][9].The main problem with that assignment is quantitative. Spin-orbit coupling in graphene [28] is too weak to yield such a small spin-relaxation time. An explicit first-principles calculation [23] predicts that one would need 0.1% of adatoms to give a 100 ps spin lifetime. Recently a new mechanism for SLG was proposed [29] (see also Ref.[30]), based on resonant scattering off local magnetic moments. It gives the observed spin-relaxation times with as little as 1 ppm of local magnetic moments and also agrees with the experimental behavior for SLG of decreasing the spinrelaxation rate with increasing electron density. Where do these local moments come from? It was theoretically predicted that adatoms such as hydrogen [31,32], but also chemisorbed organic molecules [33] can be responsible. Experimentally it was demonstrated that hydrogen adatoms indeed induce local moments [34,35], but even untreated graphene flakes were shown to exhibit 20 ppm spin 1=2 para...

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Spin relaxation properties in graphene due to its linear dispersion

Cited by 68 publications

References 43 publications

Spin Relaxation Mechanism in Graphene: Resonant Scattering by Magnetic Impurities

Spin Relaxation Mechanism in Graphene: Resonant Scattering by Magnetic Impurities

Long-distance spin transport in high-mobility graphene on hexagonal boron nitride

Resonant Scattering by Magnetic Impurities as a Model for Spin Relaxation in Bilayer Graphene

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