Vacuum birefringence and the polarized X-ray emission from a radio magnetar
Magnetars are isolated neutron stars with exceptionally strong surface fields exceeding $10^{14}$ G. Their bright X-ray emission probes physical regimes in which quantum electrodynamic (QED) influences radiation propagation. Strong magnetic fields induce polarization-dependent refractive indices in the vacuum; such vacuum birefringence (VB) remains a long-standing but unconfirmed prediction of QED. Here, we report phase- and energy-resolved polarization measurements of the radio-emitting magnetar 1E 1547.0$-$5408 obtained by coordinating X-ray and radio observations from the Imaging X-ray Polarimetry Explorer (IXPE), the Neutron Star Interior Composition ExploreR (NICER), and the Parkes/Murriyang observatory. We detect large polarization degrees (PD) in the thermally-dominant soft X-ray band, reaching phase-averaged values of $65\%$ at 2 keV before substantially decreasing between 2$-$4 keV. At certain rotational phases, the 2$-$3 keV PD rises to nearly $80\%$ while remaining high ($\gtrsim 40\%$) throughout the radio beam crossing. The phase-dependent X-ray and radio polarization angles are both consistent with the rotating vector model, suggesting that the emission geometries track the star's large-scale magnetic field. Collectively, these characteristics challenge standard surface emission models using non-refractive propagation of light to infinity. VB-governed magnetospheric propagation can naturally explain the X-ray polarization signals. Our results represent a significant advance in probing this hallmark prediction of QED, opening a new cosmic window into superstrong-field quantum physics, thereby motivating further observational and theoretical studies concentrating on this domain.