It was shown soon after Sinova's article that this system was not robust to disorder. First order corrections to the spin Hall conductivity very exactly cancel out the zeroth order conductivity [Raimondi and Schwab, PRB 71 (2005)] and quantum corrections are zero [Chalaev and Loss, PRB 71 (2005)], meaning a total disappearance of the spin Hall effect. But what if the disordered impurities have a magnetic moment (or a spin)? Magnetic impurities break time reversal invariance, so the effect of this type of disorder is different.
We noticed through an analytical linear response calculation of the optical spin Hall conductivity that there is a singularity in the static limit. Numerically we find that the spin Hall conductivity keeps close to its clean value (-e/8pi), but large fluctuations were observed. To get the average value shown in the figure above we needed about 700 disorder configurations with 64 twisted boundary conditions for each configuration.