Observationally, magnetic fields reach equipartition with thermal energy and
cosmic rays in the interstellar medium of disk galaxies such as the Milky Way.
However, thus far cosmological simulations of the formation and evolution of
galaxies have usually neglected magnetic fields. We employ the moving-mesh code
\textsc{Arepo} to follow for the first time the formation and evolution of a
Milky Way-like disk galaxy in its full cosmological context while taking into
account magnetic fields. We find that a prescribed tiny magnetic seed field
grows exponentially by a small-scale dynamo until it saturates around z=4
with a magnetic energy of about 10% of the kinetic energy in the center of
the galaxy's main progenitor halo. By z=2, a well-defined gaseous disk forms
in which the magnetic field is further amplified by differential rotation,
until it saturates at an average field strength of \sim 6 \mug in the disk
plane. In this phase, the magnetic field is transformed from a chaotic
small-scale field to an ordered large-scale field coherent on scales comparable
to the disk radius. The final magnetic field strength, its radial profile and
the stellar structure of the disk compare well with observational data. A minor
merger temporarily increases the magnetic field strength by about a factor of
two, before it quickly decays back to its saturation value. Our results are
highly insensitive to the initial seed field strength and suggest that the
large-scale magnetic field in spiral galaxies can be explained as a result of
the cosmic structure formation process.Comment: 5 pages, 4 figures, accepted to ApJ
