A search for flavour-changing neutral interactions involving the top quark, the Higgs boson and an up-type quark q (q = c, u) is presented. The proton-proton collision data set used, with an integrated luminosity of 139 fb−1, was collected at (Formula presented.) TeV by the ATLAS experiment at the Large Hadron Collider. Both the decay process t → qH in tt ̄ production and the production process pp → tH, with the Higgs boson decaying into two photons, are investigated. No significant excess is observed and upper limits are set on the t → cH and the t → uH branching ratios of 4.3 × 10−4 and 3.8 × 10−4, respectively, at the 95% confidence level, while the expected limits in the absence of signal are 4.7 × 10−4 and 3.9 × 10−4. Combining this search with ATLAS searches in the H → τ+τ− and H → bb ̄ final states yields observed (expected) upper limits on the t → cH branching ratio of 5.8 × 10−4 (3.0 × 10−4) at the 95% confidence level. The corresponding observed (expected) upper limit on the t → uH branching ratio is 4.0 × 10−4 (2.4 × 10−4).
