  The origin of large-scale and coherent magnetic fields in astrophysical discs
is an important and long standing problem. Researchers commonly appeal to a
turbulent dynamo, sustained by the magneto-rotational instability (MRI), to
supply the large-scale field. But research over the last decade in particular
has demonstrated that various non-ideal MHD effects can impede or extinguish
the MRI, especially in protoplanetary disks. In this paper we propose a new
scenario, by which the magnetic field is generated and sustained via the
gravitational instability (GI). We use 3D stratified shearing box simulations
to characterise the dynamo and find that it works at low magnetic Reynolds
number (from unity to ~100) for a wide range of cooling times and boundary
conditions. The process is kinematic, with a relatively fast growth rate ($<
0.1 \Omega$), and it shares some properties of mean field dynamos. The magnetic
field is generated via the combination of differential rotation and spiral
density waves, the latter providing compressible horizontal motions and
large-scale vertical rolls. At greater magnetic Reynolds numbers the build up
of large-scale field is diminished and instead small-scale structures emerge
from the breakdown of twisted flux ropes. We propose that GI may be key to the
dynamo engine not only in young protoplanetary discs but also in some AGN and
galaxies.
