  The polarization of photons emitted by astrophysical sources might be altered
as they travel through a dark matter medium composed of ultra light axion-like
particles (ALPs). In particular, the coherent oscillations of the ALP
background in the galactic halo induce a periodic change on the polarization of
the electromagnetic radiation emitted by local sources such as pulsars.
Building up on previous works, we develop a new, more robust, analysis based on
the generalised Lomb-Scargle periodogram to search for this periodic signal in
the emission of the Crab supernova remnant observed by the QUIJOTE MFI
instrument and 20 galactic pulsars from the Parkes Pulsar Timing Array (PPTA)
project. We also carefully take into account the stochastic nature of the axion
field, an effect often overlooked in previous works. This refined analysis
leads to the strongest limits on the axion-photon coupling for a wide range of
dark matter masses spanning $10^{-23}\text{ eV}\lesssim m_a\lesssim10^{-19}
\text{ eV}$. Finally, we survey possible optimal targets and the potential
sensitivity to axionic dark-matter in this mass range that could be achieved
using pulsar polarimetry in the future.
