  The continuous flow of gas and dark matter across scales in the cosmic web
can generate correlated dynamical properties of haloes and filaments (and the
magnetic fields they contain). With this work, we study the halo spin
properties and orientation with respect to filaments, and the morphology of the
magnetic field around these objects, for haloes with masses in the range
1e8-1e14 Msun and filaments up to 8 Mpc long. Furthermore, we study how these
properties vary in presence, or lack thereof, of different (astro)physical
processes and with different magnetic initial conditions. We perform
cosmological magnetohydrodynamical simulations with the Eulerian code Enzo and
we develop a simple and robust algorithm to study the filamentary connectivity
of haloes in three dimensions. We investigate the morphological and magnetic
properties and focus on the alignment of the magnetic field along filaments:
our analysis suggests that the degree of this alignment is partially dependent
on the physical processes involved, as well as on magnetic initial conditions.
We discuss the contribution of this effect on a potential attempt to detect the
magnetic field surrounding these objects: we find that it introduces a bias in
the estimation of the magnetic field from Faraday rotation measure techniques.
Specifically, given the strong tendency we find for extragalactic magnetic
fields to align with the filaments axis, the value of the magnetic field can be
underestimated by a factor 3, because this effect contributes to making the
line-of-sight magnetic field (for filaments in the plane of the sky) much
smaller than the total one.
