Change of rotation measure during eclipse of a black widow PSR J2051$-$0827

Black widows are millisecond pulsars ablating their companions. The material blown from the companion blocks the radio emission, resulting in radio eclipses. The properties of the eclipse medium are poorly understood. Here, we present direct evidence of the existence of magnetic fields in the eclipse medium of the black widow PSR J2051$-$0827 using observations made with the Five-hundred-meter Aperture Spherical radio Telescope (FAST). We detect a regular decrease in rotation measure (RM) in the egress of eclipse, changing from $60\,\rm rad\,m^{-2}$ to $-28.7\,\rm rad\,m^{-2}$. The RM gradually changes back to normal when the line-of-sight moves away from the eclipse. The estimated line-of-sight magnetic field strength in the eclipse medium is $\sim 0.1$ G. The RM reversal could be caused by a change of the magnetic field strength along the line of sight due to binary orbital motion. The RM reversal phenomenon has also been observed in some repeating fast radio bursts (FRBs), and the study of spider pulsars may provide additional information about the origin of FRBs.