A search for flavour changing neutral current (FCNC) processes in top-quark decays by the ATLAS Collaboration is presented. Data collected from pp collisions at the LHC at a centre-of-mass energy of sqrt(s) = 7 TeV during 2011, corresponding to an integrated luminosity of 2.1 fb^-1, were used. A search was performed for top-quark pair-production events, with one top quark decaying through the t->Zq FCNC (q=u,c) channel, and the other through the Standard Model dominant mode t->Wb. Only the decays of the Z boson to charged leptons and leptonic W-boson decays were considered as signal. Consequently, the final-state topology is characterised by the presence of three isolated charged leptons, at least two jets and missing transverse momentum fr...