  In the present-day Universe, magnetic fields pervade galaxy clusters, with
strengths of a few microGauss obtained from Faraday Rotation. Evidence for
cluster magnetic fields is also provided by Megaparsec-scale radio emission,
namely radio halos and relics. These are commonly found in merging systems and
are characterized by a steep radio spectrum. It is widely believed that
magneto-hydrodynamical turbulence and shock-waves (re-)accelerate cosmic rays,
producing halos and relics. The origin and the amplification of magnetic fields
in clusters is not well understood. It has been proposed that turbulence drives
a small-scaledynamo that amplifies seed magnetic fields (primordial and/or
injected by galactic outflows, as active galactic nuclei, starbursts, or
winds). At high redshift, radio halos are expected to be faint, due to the
Inverse Compton losses and dimming effect with distance. Moreover, Faraday
Rotation measurements are difficult to obtain. If detected, distant radio
halosprovide an alternative tool to investigate magnetic field amplification.
Here, we report LOFAR observations which reveal diffuse radio emission in
massive clusters when the Universe was only half of its present age, with a
sample occurrence fraction of about 50%. The high radio luminosities indicate
that these clusters have similar magnetic field strengths to those in nearby
clusters, and suggest that magnetic field amplification is fast during the
first phases ofcluster formation.
