  The origin of magnetic fields in clusters of galaxies is still a matter of
debate. Observations for intracluster magnetic fields over a wide range of
redshifts are crucial to constrain possible scenarios for the origin and
evolution of the fields. (Differences of Faraday rotation measures (RMs) of an
embedded double radio sources, i.e. a pair of lobes of mostly Fanaroff--Riley
type II radio galaxies, are free from the Faraday rotation contributions from
the interstellar medium inside the Milky Way and the intergalactic medium
between radio galaxies and us, and hence provide a novel way to estimate
average magnetic field within galaxy clusters.) We have obtained a sample of
627 pairs whose RMs and redshifts are available in the most updated RM
catalogues and redshift databases. The RM differences of the pairs are derived.
The statistically large RM differences for pairs of redshifts $z>0.9$ indicate
that intracluster magnetic fields is as strong as about 4~$\mu$G. Such strong
magnetic fields in the intracluster medium at the half age of the Universe,
comparable to intracluster field strength in nearby galaxy clusters, pose a
challenge on the theories for origin of cosmic magnetic fields.
