  Low-metallicity star formation poses a central problem of cosmology, as it
determines the characteristic mass scale and distribution for the first and
second generations of stars forming in our Universe. Here, we present a
comprehensive investigation assessing the relative impact of metals and
magnetic fields, which may both be present during low-metallicity star
formation. We show that the presence of magnetic fields generated via the
small-scale dynamo stabilises the protostellar disc and provides some degree of
support against fragmentation. In the absence of magnetic fields, the
fragmentation timescale in our model decreases by a factor of ~10 at the
transition from Z=0 to Z>0, with subsequently only a weak dependence on
metallicity. Similarly, the accretion timescale of the cluster is set by the
large-scale dynamics rather than the local thermodynamics. In the presence of
magnetic fields, the primordial disc can become completely stable, therefore
forming only one central fragment. At Z>0, the number of fragments is somewhat
reduced in the presence of magnetic fields, though the shape of the mass
spectrum is not strongly affected in the limits of the statistical
uncertainties. The fragmentation timescale, however, increases by roughly a
factor of 3 in the presence of magnetic fields. Indeed, our results indicate
comparable fragmentation timescales in primordial runs without magnetic fields
and Z>0 runs with magnetic fields.
