  Magnetars, the most strongly magnetised neutron stars, are among the most
promising targets for X-ray polarimetry. The Imaging X-ray Polarimetry Explorer
(IXPE), the first satellite devoted to exploring the sky in polarised X-rays,
has observed four magnetars to date. A proper interpretation of IXPE results
requires the development of new atmospheric models that can take into proper
account the effects of the magnetised vacuum on par with those of the plasma.
Here we investigate the effects of mode conversion at the vacuum resonance on
the polarisation properties of magnetar emission by computing plane-parallel
atmospheric models under varying conditions of magnetic field
strength/orientation, effective temperature and allowing for either complete or
partial adiabatic mode conversion. Complete mode conversion results in a switch
of the dominant polarisation mode, from the extraordinary (X) to the ordinary
(O) one, below an energy that decreases with increasing magnetic field
strength, occurring at $\approx 0.5\, \mathrm{keV}$ for a magnetic field
strength of $B=10^{14}\, \mathrm{G}$. Partial adiabatic mode conversion results
in a reduced polarisation degree when compared with a standard plasma
atmosphere. No dominant mode switch occurs for $B=10^{14}\, \mathrm{G}$ while
there are two switches for lower fields of $B=3\times10^{13}\, \mathrm{G}$.
Finally, by incorporating our models in a ray-tracing code, we computed the
expected polarisation signal at infinity for different emitting regions on the
star surface and for different viewing geometries. The observability of QED
signatures with IXPE and with future soft X-ray polarimeters as REDSoX is
discussed.
