Spin Coulomb drag in the two-dimensional electron liquid

We calculate the spin-drag transresistivity rho(up arrowdown arrow)(T) in a two-dimensional electron gas at temperature T in the random-phase approximation. In the low-temperature regime we show that, at variance with the three-dimensional low-temperature result [rho(up arrowdown arrow)(T) similar to T-2], the spin transresistivity of a two-dimensional spin unpolarized electron gas has the form rho(up arrowdown arrow)(T) similar to T-2 ln T. In the spin-polarized case the familiar form rhoup arrowdown arrow(T) = AT(2) is recovered, but the constant of proportionality, A, diverges logarithmically as the spin-polarization tends to zero. In the high-temperature regime we obtain rho(up arrowdown arrow)(T) = -((h) over bar /e(2))(pi(2)Ry*/k(B)T) (where Ry* is the effective Rydberg energy) independent of the density. Again, this differs from the three-dimensional result, which has a logarithmic dependence on the density. Two important differences between the spin-drag transresistivity and the ordinary Coulomb-drag transresistivity are pointed out. (i) The ln T singularity at low temperature is smaller, in the Coulomb-drag case, by a factor e(-4kFd), where k(F) is the Fermi wave vector and d is the separation between the layers. (ii) The collective mode contribution to the spin-drag transresistivity is negligible at all temperatures. Moreover, the spin-drag effect is, for comparable parameters, larger than the ordinary Coulomb-drag effect.