  We use the integrated polarized radio emission at 1.4 GHz ($\Pi_{\rm
1.4\,GHz}$) from a large sample of AGN (796 sources at redshifts $z<0.7$) to
study the large-scale magnetic field properties of radio galaxies in relation
to the host galaxy accretion state. We find a fundamental difference in
$\Pi_{\rm 1.4\,GHz}$ between radiative-mode AGN (i.e. high-excitation radio
galaxies, HERGs, and radio-loud QSOs) and jet-mode AGN (i.e. low-excitation
radio galaxies, LERGs). While LERGs can achieve a wide range of $\Pi_{\rm
1.4\,GHz}$ (up to $\sim$$30\%$), the HERGs and radio-loud QSOs are limited to
$\Pi_{\rm 1.4\,GHz} \lesssim 15\%$. A difference in $\Pi_{\rm 1.4\,GHz}$ is
also seen when the sample is divided at 0.5% of the total Eddington-scaled
accretion rate, where the weakly accreting sources can attain higher values of
$\Pi_{\rm 1.4\,GHz}$. We do not find any clear evidence that this is driven by
intrinsic magnetic field differences of the different radio morphological
classes. Instead, we attribute the differences in $\Pi_{\rm 1.4\,GHz}$ to the
local environments of the radio sources, in terms of both the ambient gas
density and the magnetoionic properties of this gas. Thus, not only are
different large-scale gaseous environments potentially responsible for the
different accretion states of HERGs and LERGs, we argue that the large-scale
magnetised environments may also be important for the formation of powerful AGN
jets. Upcoming high angular resolution and broadband radio polarization surveys
will provide the high precision Faraday rotation measure and depolarization
data required to robustly test this claim.
