  We report the radio observations of the eclipsing black widow pulsar
J1720-0534, a 3.26 ms pulsar in orbit with a low mass companion of mass 0.029
to 0.034 M$_{\odot}$. We obtain the phase-connected timing ephemeris and
polarization profile of this millisecond pulsar (MSP) using the
Five-hundred-meter Aperture Spherical Radio Telescope (FAST), the Green Bank
Telescope (GBT), and the Parkes Telescope. For the first time from such a
system, an oscillatory polarisation angle change was observed from a particular
eclipse egress with partial depolarization, indicating 10-milliGauss-level
reciprocating magnetic fields oscillating in a length scale of 5000 km
(assuming an orbital inclination angle of 90 degrees) outside the companion's
magnetosphere. The dispersion measure variation observed during the ingresses
and egresses shows the rapid raising of the electron density in the shock
boundary between the companion's magnetosphere and the surrounding pulsar wind.
We suggest that the observed oscillatory magnetic fields originate from the
pulsar wind outside the companion's magnetosphere.
