  We map a quantum Rabi ring, consisting of $N$ cavities arranged in a ring
geometry, into an effective magnetic model containing the XY exchange and the
Dzyaloshinskii Moriya (DM) interactions. The analogue of the latter is induced
by an artificial magnetic field, which modulates photon hopping between
nearest-neighbor cavities with a phase. The mean-field behavior of both systems
is almost identical, facilitating the description of the different phases in
the quantum optical model through simple arguments of competing magnetic
interactions. For the square geometry ($N=4$) the rich phase diagram exhibits
three superradiant phases denoted as ferro-superradiant, antiferro-superradiant
and chiral superradiant. In particular, the DM interaction is responsible for
the chiral phase in which the energetically degenerate configurations of the
order parameters are similar to the in-plane magnetizations of skyrmions with
different helicities. The antiferro-superradiant phase is suppressed in the
triangle geometry ($N=3$) as geometric frustration contributes to stabilize the
chiral phase even for small values of the DM interaction. The chiral phases for
odd and even $N$ show a different scaling behavior close to the phase
transition. The equivalent behavior on both systems opens the possibility of
simulating chiral magnetism in a few-body quantum optical platform, as well as
understanding one system using the insights gained from the other.
