A search for the flavour-changing neutral-current decay [Formula: see text] is presented. Data collected by the ATLAS detector during 2012 from proton-proton collisions at the Large Hadron Collider at a centre-of-mass energy of [Formula: see text] TeV, corresponding to an integrated luminosity of 20.3 fb[Formula: see text], are analysed. Top-quark pair-production events with one top quark decaying through the [Formula: see text] ([Formula: see text]) channel and the other through the dominant Standard Model mode [Formula: see text] are considered as signal. Only the decays of the Z boson to charged leptons and leptonic W boson decays are used. No evidence for a signal is found and an observed (expected) upper limit on the [Formula: see text] branching ratio of [Formula: see text] ([Formula: see text]) is set at the 95 % confidence level.