  We report the first discovery of pulse phase modulating optical depths at the
iron K-edge in accretion-powered X-ray pulsars, from Suzaku observations. A
significant modulating optical depth of the iron K-edge is detected for Vela
X-1 and GX 1+4. Similar trends are seen in GX 301-2 and OAO 1657-415, though
with poor statistical significance. The observed iron K-edge exhibits a maximum
optical depth, when the X-ray continuum dims, and there is no significant pulse
phase variation in the ionization state of iron. The revealed changes in the
optical depth with pulse phase can be explained as being due to the accreting
matter captured by the magnetic field lines of the pulsar, which co-rotates
with the neutron star spin and is responsible for photoelectric absorption.
Based on the above interpretation, we propose that the accreting matter within
the Alfv\'en radius contains iron with an ionization state of Fe$_{\rm
V\hspace{-0.1em}I-X\hspace{-0.1em}I}$ with a particle density of $10^{17}$
cm$^{-3}$ and has a shape flattened along the azimuthal direction, such as an
accretion curtain.
