  Radio emission from magnetars provides a unique probe of the relativistic,
magnetized plasma within the near-field environment of these ultra-magnetic
neutron stars. The transmitted waves can undergo birefringent and dispersive
propagation effects that result in frequency-dependent conversions of linear to
circularly polarized radiation and vice-versa, thus necessitating
classification when relating the measured polarization to the intrinsic
properties of neutron star and fast radio burst (FRB) emission sites. We report
the detection of such behavior in 0.7-4 GHz observations of the P = 5.54 s
radio magnetar XTE J1810$-$197 following its 2018 outburst. The phenomenon is
restricted to a narrow range of pulse phase centered around the magnetic
meridian. Its temporal evolution is closely coupled to large-scale variations
in magnetic topology that originate from either plastic motion of an active
region on the magnetar surface or free precession of the neutron star crust.
Our model of the effect deviates from simple theoretical expectations for radio
waves propagating through a magnetized plasma. Birefringent self-coupling
between the transmitted wave modes, line-of-sight variations in the magnetic
field direction and differences in particle charge or energy distributions
above the magnetic pole are explored as possible explanations. We discuss
potential links between the immediate magneto-ionic environments of magnetars
and those of FRB progenitors.

High Energy Astrophysical Phenomena