Universal Intrinsic Spin-Hall Effect

Universal Intrinsic Spin-Hall Effect

February 2, 2008 | Jairo Sinova, Dimitrie Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, A.H. MacDonald
A new effect in semiconductor spintronics, the universal intrinsic spin-Hall effect, is described. This effect leads to dissipationless spin currents in paramagnetic spin-orbit coupled systems. In high mobility two-dimensional electron systems with substantial Rashba spin-orbit coupling, a spin current perpendicular to the charge current is intrinsic. The intrinsic spin-Hall conductivity has a universal value for zero quasiparticle spectral broadening. The effect arises from the time dependence of the effective magnetic field experienced by the spin due to its motion in momentum space. For the Rashba Hamiltonian, the effect can be understood using the Bloch equation for a spin-1/2 particle. The dynamics of an electron spin in the presence of time-dependent Zeeman coupling are described by the Bloch equation. The spin current is polarized perpendicular to the two-dimensional plane and flows in the planar direction perpendicular to the charge current direction. The spin-Hall conductivity is calculated using the Kubo formula approach. For a given momentum, the spinor originally points in the azimuthal direction. An electric field in the x-direction changes the y-component of the momentum-dependent effective field. The z-component of the spin direction for an electron in a state with momentum p is found to be proportional to -eħ²pyEx/(2λp³). Summing over all occupied states, the linear response of the z-spin-polarization component vanishes, but the spin-current in the y-direction is finite. The spin-Hall conductivity is found to be independent of the Rashba coupling strength and the 2DES density when both bands are occupied. The intrinsic spin-Hall effect is compared to the extrinsic character of the effect discussed by Hirsch. The universality of the intrinsic spin-Hall effect is not robust against disorder and will be reduced when the disorder broadening is larger than the spin-orbit coupling splitting. The effect is applicable to any paramagnetic material with strong spin-orbit coupling, including hole-doped bulk semiconductors. The work was supported by various grants and institutions.A new effect in semiconductor spintronics, the universal intrinsic spin-Hall effect, is described. This effect leads to dissipationless spin currents in paramagnetic spin-orbit coupled systems. In high mobility two-dimensional electron systems with substantial Rashba spin-orbit coupling, a spin current perpendicular to the charge current is intrinsic. The intrinsic spin-Hall conductivity has a universal value for zero quasiparticle spectral broadening. The effect arises from the time dependence of the effective magnetic field experienced by the spin due to its motion in momentum space. For the Rashba Hamiltonian, the effect can be understood using the Bloch equation for a spin-1/2 particle. The dynamics of an electron spin in the presence of time-dependent Zeeman coupling are described by the Bloch equation. The spin current is polarized perpendicular to the two-dimensional plane and flows in the planar direction perpendicular to the charge current direction. The spin-Hall conductivity is calculated using the Kubo formula approach. For a given momentum, the spinor originally points in the azimuthal direction. An electric field in the x-direction changes the y-component of the momentum-dependent effective field. The z-component of the spin direction for an electron in a state with momentum p is found to be proportional to -eħ²pyEx/(2λp³). Summing over all occupied states, the linear response of the z-spin-polarization component vanishes, but the spin-current in the y-direction is finite. The spin-Hall conductivity is found to be independent of the Rashba coupling strength and the 2DES density when both bands are occupied. The intrinsic spin-Hall effect is compared to the extrinsic character of the effect discussed by Hirsch. The universality of the intrinsic spin-Hall effect is not robust against disorder and will be reduced when the disorder broadening is larger than the spin-orbit coupling splitting. The effect is applicable to any paramagnetic material with strong spin-orbit coupling, including hole-doped bulk semiconductors. The work was supported by various grants and institutions.
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Understanding Universal intrinsic spin Hall effect.