Bulk electron spin polarization generated by the spin Hall current

Physical Review B - Condensed Matter and Materials Physics

Volumn 74, Issue 4, 2006, Pages

  Korenev, V L ^a  

^a IOFFE INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746321401     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.74.041308     Document Type: Article

References (30)

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26. The equilibrium spin currents J iγ eq are excluded automatically from Eqs. 1 4. Indeed, for Rashba interaction [E. I. Rashba, J. Supercond. JOUSEH 0896-1107 10.1007/s10948-005-3349-8 18, 137 (2005)] J iγ eq εiγz Qiγ. The spin currents in a form Jiγ = const* Qiγ do not contribute to spin polarization because of identity εβjγ Qji Qiγ =0, which is valid for any second rank tensor.
27. In practice, however, this "theorem" will not work in low symmetry crystals, too. Introducing to the RHS of Eq. 1 of any change of spin not related with the linear in p spin-orbit coupling violates Eq. 4. For example, these are the Larmor precession in external magnetic field and spin relaxation not related with linear in p terms (the cubic in p terms, spin-flip during impurity scattering process, hyperfine interaction, exchange interaction with holes, etc). Thus the KKM approach resolves naturally the spin accumulation problem following from the "theorem." An expanded version of this Letter can be found in V. L. Korenev, cond-mat/0512566 (unpublished), which contains the discussion of spin accumulation problem and the details omitted in this version.
28. Another definition of spin current is proposed by J. Shi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.076604 96, 076604 (2006). Authors combine the precessional term and the divergence of the conventional spin current term into a single one to define the divergence of new spin current. One can see that it leads to the regrouping of terms in Eq. 1 thus leaving the final solution of Eq. 1 unchanged.
29. For example, the cancellation cannot be interpreted as nonexistence [A. Khaetskii, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.056602 96, 056602 (2006)] of the "intrinsic" spin current. It is the total spin current that is cancelled out. The intrinsic spin current exists but the KKM spin current compensates it. As a result, the nonzero spin density is developed leading to the "equilibrium" polarization ρT. We neglect the intrinsic spin current and mean spin ρT. Indeed, simple estimation can be done by formula ρT =α kdr 4T (Refs.) where the spin-orbit constant α=λ U 2.5× 10-10 eV cm, drift quasi-momentum kdr =mbE6× 104 cm-1 (at room temperature b=8000 cm2 Vs
30. [M. Shur, GaAs Devices and Circuits (Plenum, NY, 1987)]). It gives ρT 1.5× 10-4 that is 10 times less than the estimation ρ2× 10-3 given by Eq. 10.