Spin relaxation and the Elliott-Yafet parameter in W(001) ultrathin films: Surface states, anisotropy, and oscillation effects

Long, Nguyễn Hoàng; Mavropoulos, Phivos; Zimmermann, Bernd; Heers, Swantje; Bauer, David; Blügel, Stefan; Mokrousov, Yuriy

doi:10.1103/physrevb.87.224420

Cited by 8 publications

(22 citation statements)

References 49 publications

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“…For one thing we found 30 that the free-electron-like Fermi surface of the noble metals, when projected in the surface Brillouin zone of the ultrathin film, cuts through the Brillouin zone edge producing spin-flip hot spots that have only been reported in the case of multivalent metals 18 so far. Additionally we analyzed the surface states in the case of W(001) films 29 and found that the Rashba character can strongly contribute to spin relaxation; we also saw an oscillatory behavior of the spin relaxation as a function of the film thickness. In both cases 29,30 we also found a considerable anisotropy of the EYP as well as spin-relaxation rate with respect to the angle between the injected spin polarization and the film normal.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally we analyzed the surface states in the case of W(001) films 29 and found that the Rashba character can strongly contribute to spin relaxation; we also saw an oscillatory behavior of the spin relaxation as a function of the film thickness. In both cases 29,30 we also found a considerable anisotropy of the EYP as well as spin-relaxation rate with respect to the angle between the injected spin polarization and the film normal.…”

Section: Introductionmentioning

confidence: 99%

“…In these systems, however, there are no surface states at the Fermi surface, which cause a pronounced oscillatory behavior of the EYP as found in W(001) films. 29 Yet the influence from the stacking symmetry along z-direction, i.e. ...ABAB... in fcc (001) films and ...ABCABC... in fcc (111) fims, could give rise the fluctuation of the EYP as seen in Pt(001) and Pt(111).…”

Section: A Elliott-yafet Parametermentioning

confidence: 99%

“…In a recent paper 29 we analyzed the EYP for bcc W(001) and discussed in detail its dependence on the film thickness. Remarkably, we found that owing to the surface states at the Fermi surface, the EYP of W(001) exhibits an oscillatory behavior with respect to the film thickness, which we traced back to the interaction of surface states at the two surfaces of the film together with the stacking of the bcc structure.…”

Section: A Elliott-yafet Parametermentioning

confidence: 99%

“…Importantly, Rashba surface states 26,27 can be formed around the Fermi level and they were shown to enhance the spin-flip relaxation rate. 23,28,29 Thin film is a keyword for reducing the size of spintronics devices. It also gives a flexibility in manipulating electron spins in the spin Hall experiments.…”

Section: Introductionmentioning

confidence: 99%

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Spin relaxation and spin Hall transport in5dtransition-metal ultrathin films

et al. 2014

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The spin relaxation induced by the Elliott-Yafet mechanism and the extrinsic spin Hall conductivity due to the skew-scattering are investigated in 5d transition-metal ultrathin films with self-adatom impurities as scatterers. The values of the Elliott-Yafet parameter and of the spin-flip relaxation rate reveal a correlation with each other that is in agreement with the Elliott approximation. At 10-layer thickness, the spin-flip relaxation time in 5d transition-metal films is quantitatively reported about few hundred nanoseconds at atomic percent which is one and two orders of magnitude shorter than that in Au and Cu thin films, respectively. The anisotropy effect of the Elliott-Yafet parameter and of the spin-flip relaxation rate with respect to the direction of the spin-quantization axis in relation to the crystallographic axes is also analyzed. We find that the anisotropy of the spin-flip relaxation rate is enhanced due to the Rashba surface states on the Fermi surface, reaching values as high as 97% in 10-layer Hf(0001) film or 71% in 10-layer W(110) film. Finally, the spin Hall conductivity as well as the spin Hall angle due to the skew-scattering off self-adatom impurities are calculated using the Boltzmann approach. Our calculations employ a relativistic version of the first-principles full-potential Korringa-Kohn-Rostoker Green function method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: A Elliott-yafet Parametermentioning

confidence: 99%

Section: A Elliott-yafet Parametermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spin relaxation and spin Hall transport in5dtransition-metal ultrathin films

et al. 2014

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Ab initio electron-defect interactions using Wannier functions

Park

Zhou

et al. 2020

npj Comput Mater

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Computing electron-defect (e-d) interactions from first principles has remained impractical due to computational cost. Here we develop an interpolation scheme based on maximally localized Wannier functions (WFs) to efficiently compute e-d interaction matrix elements. The interpolated matrix elements can accurately reproduce those computed directly without interpolation, and the approach can significantly speed up calculations of e-d relaxation times and defect-limited charge transport. We show example calculations of vacancy defects in silicon and copper, for which we compute the e-d relaxation times on fine uniform and random Brillouin zone grids (and for copper, directly on the Fermi surface) as well as the defect-limited resistivity at low temperature. Our interpolation approach opens doors for atomistic calculations of charge carrier dynamics in the presence of defects.

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Spin-orbit coupling in elemental two-dimensional materials

et al. 2019

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The fundamental spin-orbit coupling and spin mixing in graphene and rippled honeycomb lattice materials silicene, germanene, stanene, blue phosphorene, arsenene, antimonene, and bismuthene is investigated from first principles. The intrinsic spin-orbit coupling in graphene is revisited using multi-band k · p theory, showing the presence of non-zero spin mixing in graphene despite the mirror symmetry. However, the spin mixing itself does not lead to the the Elliott-Yafet spin relaxation mechanism, unless the mirror symmetry is broken by external factors. For other aforementioned elemental materials we present the spin-orbit splittings at relevant symmetry points, as well as the spin admixture b 2 as a function of energy close to the band extrema or Fermi levels. We find that spin-orbit coupling scales as the square of the atomic number Z, as expected for valence electrons in atoms. For isolated bands, it is found that b 2 ∼ Z 4 . The spin-mixing parameter also exhibits giant anisotropy which, to a large extent, can be controlled by tuning the Fermi level. Our results for b 2 can be directly transferred to spin relaxation time due to the Elliott-Yafet mechanism, and therefore provide an estimate of the upper limit for spin lifetimes in materials with space inversion center.

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Spin relaxation and the Elliott-Yafet parameter in W(001) ultrathin films: Surface states, anisotropy, and oscillation effects

Cited by 8 publications

References 49 publications

Spin relaxation and spin Hall transport in5dtransition-metal ultrathin films

Spin relaxation and spin Hall transport in5dtransition-metal ultrathin films

Ab initio electron-defect interactions using Wannier functions

Spin-orbit coupling in elemental two-dimensional materials

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