  We present Faraday rotation data for radio sources in the centers of the
Abell clusters A400 and A2634. These clusters contain large (> 100 kpc), tailed
radio sources, each attached to the central cD galaxy. These clusters do not
have strong cooling cores. Our data extend previous work on rotation measure in
cluster centers to larger scales and non-cooling clusters. The rotation
measure, and thus the magnetic field, is ordered on scales 10-20 kpc in both
clusters. The geometry of the rotation measure appears to be determined by the
distribution of the X-ray emitting gas, rather than by the radio tails
themselves. We combine our data with previously published X-ray and radio data
in order to analyze the magnetic fields in all 12 clusters whose central radio
sources have been imaged in rotation measure. We find that the fields are
dynamically significant in most clusters. We argue that the Faraday data
measure fields in the intracluster medium, rather than in a skin of the radio
source. Finally, we consider the nature and maintenance of the magnetic fields
in these clusters, and conclude that either the cluster-wide field exists at
similar levels, or that a weaker cluster-wide field is amplified by effects in
the core.
