  This Letter presents measurements of the polarization of the top quark in
top-antitop quark pair events, using 4.7 fb^-1 of proton-proton collision data
recorded with the ATLAS detector at the Large Hadron Collider at sqrt(s) = 7
TeV. Final states containing one or two isolated leptons (electrons or muons)
and jets are considered. Two measurements of alpha_l P, the product of the
leptonic spin-analyzing power and the top quark polarization, are performed
assuming that the polarization is introduced by either a CP conserving (CPC) or
a CP violating (CPV) production process. The measurements obtained, alpha_l
P_CPC = -0.035 +/- 0.014 (stat) +/- 0.037 (syst) and alpha_l P_CPV = 0.020 +/-
0.016 (stat) +0.013 -0.017 (syst), are in good agreement with the Standard
Model prediction of negligible top quark polarization.
