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We present wideband (1 − 6.5 GHz) polarimetric observations, obtained with the Karl G. Jansky Very Large Array, of the merging galaxy cluster MACS J0717.5+3745, which hosts one of the most complex known radio relic and halo systems. We used both rotation measure synthesis and QU-fitting to find a reasonable agreement of the results obtained with these methods, particularly when the Faraday distribution is simple and the depolarization is mild. The relic is highly polarized over its entire length (850 kpc), reaching a fractional polarization > 30% in some regions. We also observe a strong wavelength-dependent depolarization for some regions of the relic. The northern part of the relic shows a complex Faraday distribution, suggesting that this region is located in or behind the intracluster medium (ICM). Conversely, the southern part of the relic shows a rotation measure very close to the Galactic foreground, with a rather low Faraday dispersion, indicating very little magnetoionic material intervening along the line of sight. Based on a spatially resolved polarization analysis, we find that the scatter of Faraday depths is correlated with the depolarization, indicating that the tangled magnetic field in the ICM causes the depolarization. We conclude that the ICM magnetic field could be highly turbulent. At the position of a well known narrow-angle-tailed galaxy (NAT), we find evidence of two components that are clearly separated in the Faraday space. The high Faraday dispersion component seems to be associated with the NAT, suggesting the NAT is embedded in the ICM while the southern part of the relic lies in front of it. If true, this implies that the relic and this radio galaxy are not necessarily physically connected and, thus, the relic may, in fact, not be powered by the shock re-acceleration of fossil electrons from the NAT. The magnetic field orientation follows the relic structure indicating a well-ordered magnetic field. We also detected polarized emission in the halo region; however, the absence of significant Faraday rotation and a low value of Faraday dispersion suggests the polarized emission that was previously considered as the part of the halo does, in fact, originate from the shock(s).

The joint analysis of the Dispersion and Faraday Rotation Measure from distant, polarised Fast Radio Bursts may be used to put constraints on the origin and distribution of extragalactic magnetic fields on cosmological scales. While the combination of Dispersion and Faraday Rotation Measure can in principle give the average magnetic fields along the line-of-sight, in practice this method must be used with care because it strongly depends on the assumed magnetisation model on large cosmological scales. Our simulations show that the observation of Rotation Measures with $\geq 1-10 ~\rm rad/m^2$ in $\sim 10^2$ Fast Radio Bursts will be able to discriminate between extreme scenarios for the origin of cosmic magnetic fields, independent of the exact distribution of sources with redshift. This represent a strong case for incoming (e.g. ALERT, CHIME) and future (e.g. with the Square Kilometer Array) radio polarisation surveys of the sky., 8 pages, 10 figures, MNRAS accepted, in press. A color-blind friendly version can be downloaded here https://storage.googleapis.com/wzukusers/user-14759165/documents/5b5586d8d71601wxVuGn/frb-magnetic-fields-6.pdf