Semiclassical Boltzmann theory of spin Hall effects in giant Rashba systems
Cong Xiao
Front. Phys. ›› 2018, Vol. 13 ›› Issue (2) : 137202
Semiclassical Boltzmann theory of spin Hall effects in giant Rashba systems
For the spin Hall effect arising from strong band-structure spin–orbit coupling, a semiclassical Boltzmann theory reasonably addressing the intriguing disorder effect called side-jump has not yet been developed. This paper describes such a theory in which the key ingredient is the spin-current counterpart of the semiclassical side-jump velocity (introduced in the context of the anomalous Hall effect). Applying this theory to spin Hall effects in a two-dimensional electron gas with giant Rashba spin–orbit coupling, largely enhanced spin Hall angle is found in the presence of magnetic impurities when only the lower Rashba band is partially occupied.
spin Hall effect / semiclassical Boltzmann theory / side jump / Rashba spin–obit coupling
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For instance, one can verify that the semi-classical framework described in Ref. [11] cannot produce any extrinsic contribution to the SHE of the conventional spin current polarized in the zdirection in a disordered Rashba 2DEG [Eqs. (2)–(7) in that paper]. |
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In the present paper we do not consider side-jump induced by spin–orbit scattering. A semi-classical treatment of this case can be found in: P. M. Levy, H. Yang, M. Chshiev, and A. Fert, Spin Hall effect induced by Bi impurities in Cu: Skew scattering and side-jump, Phys. Rev. B88, 214432(2013) |
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The reason why the side-jump AHE and SHE induced by band-structure spin–orbit coupling is defined as the sum of these three semi-classical contributions was detailed in Ref. [2]. Simply, there are at least two motivations: one is the equivalence described in Ref. [26] and the other is that all these three contributions belong to the disorder-induced interband-coherence effect (see Refs. [2, 3, 7, 9]). |
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In the context of AHE induced by band-structure spinorbit coupling, it has been established that the disorderinduced interband-coherence contribution (side-jump) calculated in the semi-classical Boltzmann theory is equivalent to the ladder vertex correction in the weakdisorder limit to the bubble of the anomalous Hall conductivity in the nonchiral basis (szbasis for the Rashba model). The present calculations suggest that this equivalence is also valid for the spin Hall conductivity of the conventionally defined spin current. In fact, this equivalence has been employed in the statement of Ref. [1]. |
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