  The electronic structure of the spintronic material Sr$_2$CrReO$_6$ is
studied by means of full-potential linear muffin-tin orbital method. Scalar
relativistic calculations predict Sr$_2$CrReO$_6$ to be half-metallic with a
magnetic moment of 1 $\mu_B$. When spin-orbit coupling is included, the
half-metallic gap closes into a pseudo-gap, and an unquenched rhenium orbital
moment appears, resulting in a significant increase of the total magnetic
moment to 1.28 $\mu_B$. This moment is significantly larger than the
experimental moment of 0.9 $\mu_B$. A possible explanation of this discrepancy
is that the anti-site disorder in Sr$_2$CrReO$_6$ is significantly larger than
hitherto assumed.
