  In this work we interpret and discuss the time variable rotation measure (RM)
found, for the first time over a 1-yr period, in the core region of a blazar.
These results are based on a one-year, multi-frequency (15, 24, and 43 GHz)
Very Long Baseline Array (VLBA) monitoring of the TeV blazar Markarian 421 (Mrk
421). We investigate the Faraday screen properties and its location with
respect to the jet emitting region. Given that the 43 GHz radio core flux
density and the RM time evolution suggest a similar trend, we explore the
possible connection between the RM and the accretion rate. Among the various
scenarios that we explore, the jet sheath is the most promising candidate for
being the main source of Faraday rotation. During the one-year observing period
the RM trend shows two sign reversals, which may be qualitatively interpreted
within the context of the magnetic tower models. We invoke the presence of two
nested helical magnetic fields in the relativistic jet with opposite
helicities, whose relative contribution produce the observed RM values. The
inner helical field has the poloidal component ($B_{\rm p}$) oriented in the
observer's direction and produces a positive RM, while the outer helical field,
with $B_{\rm p}$ in the opposite direction, produces a negative RM. We assume
that the external helical field dominates the contribution to the observed RM,
while the internal helical field dominates when a jet perturbation arises
during the second observing epoch. Being the intrinsic polarization angle
parallel to the jet axis, a pitch angle of the helical magnetic field
$\phi\gtrsim 70^\circ$ is required. Additional scenarios are also considered to
explain the observed RM sign reversals.
