Nonlocal formulation of spin Coulomb drag

The spin Coulomb drag (SCD) effect occurs in materials and devices where charged carriers with different spins exchange momentum via Coulomb scattering. This causes frictional forces between spin-dependent currents that lead to intrinsic dissipation, which may limit spintronics applications. A nonlocal formulation of SCD is developed which is valid for strongly inhomogeneous systems such as nanoscale spintronics devices. This nonlocal formulation of SCD is successfully applied to linewidths of intersubband spin plasmons in semiconductor quantum wells, where experiments have shown that the local approximation fails.

Figure 1

Schematic illustration of two volume elements of inhomogeneous spin-up and spin-down electron velocity distributions, indicated by blue and red streamlines, respectively. The volume elements interact via Coulomb forces; the resulting exchange of momentum leads to the SCD effect.

Figure 2

Electronic excitations in a 20-nm $n$-doped quantum well with $N_s=2.3\times {10}^{11}{\mathrm{cm}}^{-2}$ (Ref. 15). The intrasubband and first intersubband particle-hole (p-h) continua are shaded in light blue and yellow, respectively; the charge and spin plasmon dispersions are indicated by ${\Omega }_c$ and ${\Omega }_s$. The two insets show a pair of inter- and intrasubband p-h excitations, respectively, which form the dominant spin-plasmon decay channel.