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 1as = 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 \u2192 Zq FCNC (q = u, c) channel, and the other through the Standard Model dominant mode t \u2192 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 ...