  A search for dark matter is conducted in final states containing a photon and
missing transverse momentum in proton$-$proton collisions at $\sqrt{s}$ = 13
TeV. The data, collected during 2015$-$2018 by the ATLAS experiment at the CERN
LHC, correspond to an integrated luminosity of 139 fb$^{-1}$. No deviations
from the predictions of the Standard Model are observed and 95%
confidence-level upper limits between 2.45 fb and 0.5 fb are set on the visible
cross section for contributions from physics beyond the Standard Model, in
different ranges of the missing transverse momentum. The results are
interpreted as 95% confidence-level limits in models where weakly interacting
dark-matter candidates are pair-produced via an s-channel axial-vector or
vector mediator. Dark-matter candidates with masses up to 415 (580) GeV are
excluded for axial-vector (vector) mediators, while the maximum excluded mass
of the mediator is 1460 (1470) GeV. In addition, the results are expressed in
terms of 95% confidence-level limits on the parameters of a model with an
axion-like particle produced in association with a photon, and are used to
constrain the coupling $g_{aZ\gamma}$ of an axion-like particle to the
electroweak gauge bosons.
