We present detailed imaging of Faraday rotation and depolarization for the radio galaxies 0206+35, 3C 270, 3C 353 and M 84, based on Very Large Array observations at multiple frequencies in the range 1365 to 8440 MHz. All of the sources show highly anisotropic banded rotation measure (RM) structures with contours of constant RM perpendicular to the major axes of their radio lobes. All except M84 also have regions in which the RM fluctuations have lower amplitude and appear isotropic. We give a comprehensive description of the banded RM phenomenon and present an initial attempt to interpret it as a consequence of interactions between the sources and their surroundings. We show that the material responsible for the Faraday rotation is in front of the radio emission and that the bands are likely to be caused by magnetized plasma which has been compressed by the expanding radio lobes. We present a simple model for the compression of a uniformly magnetized external medium and show that RM bands of approximately the right amplitude can be produced, but only for special initial conditions. A two‐dimensional magnetic structure in which the field lines are a family of ellipses draped around the leading edge of the lobe can produce RM bands in the correct orientation for any source orientation. We also report the first detections of rims of high depolarization at the edges of the inner radio lobes of M 84 and 3C 270. These are spatially coincident with shells of enhanced X‐ray surface brightness, in which both the field strength and the thermal gas density are likely to be increased by compression. The fields must be tangled on small scales.

Aims. The goal of this work is to constrain the strength and structure of the magnetic field associated with the environment of the radio source 3C 449 by using observations of Faraday rotation, which we model with a structure function technique, and by comparison with numerical simulations. We assume that the magnetic field is a Gaussian isotropic random variable and that it is embedded in the hot intra-group plasma surrounding the radio source. Methods. For this purpose, we present detailed rotation measure images for the polarized radio source 3C 449, previously observed with the Very Large Array at seven frequencies between 1.365 and 8.385 GHz. All of the observations are consistent with pure foreground Faraday rotation. We quantify the statistics of the magnetic-field fluctuations by deriving rotation measure structure functions, which we fit using models derived from theoretical power spectra. We quantify the errors due to sampling by making multiple twodimensional realizations of the best-fitting power spectrum. We also use depolarization measurements to estimate the minimum scale of the field variations. We then develop three-dimensional models with a gas density distribution derived from X-ray observations and a random magnetic field with this power spectrum. By comparing our simulations with the observed Faraday rotation images, we can determine the strength of the magnetic field and its dependence on density, as well as the outer scale of the magnetic turbulence. Results. The rotation measure and depolarization data are consistent with a broken power-law magnetic-field power spectrum, with a break at about 11 kpc and slopes of 2.98 and 2.07 at smaller and larger scales respectively. The maximum and minimum scales of the fluctuations are ≈65 and ≈0.2 kpc, respectively. The average magnetic field strength at the cluster centre is 3.5 ± 1.2 μG, decreasing linearly with the gas density within ≈16 kpc of the nucleus. At larger distances, the dependence of field on density appears to flatten, but this may be an effect of errors in the density model. The magnetic field is not energetically important.