  Accreting millisecond pulsars show significant variability of their pulse
profiles, especially at low accretion rates. On the other hand, their X-ray
spectra are remarkably similar with not much variability over the course of the
outbursts. For the first time, we have discovered that during the 2008 outburst
of SAX J1808.4-3658 a major pulse profile change was accompanied by a dramatic
variation of the disc luminosity at almost constant total luminosity. We argue
that this phenomenon is related to a change in the coupling between the neutron
star magnetic field and the accretion disc. The varying size of the pulsar
magnetosphere can influence the accretion curtain geometry and affect the shape
and the size of the hotspots. Using this physical picture, we develop a
self-consistent model that successfully describes simultaneously the pulse
profile variation as well as the spectral transition. Our findings are
particularly important for testing the theories of accretion onto magnetized
neutron stars, better understanding of the accretion geometry as well as the
physics of disc-magnetosphere coupling. The identification that varying hotspot
size can lead to pulse profile changes has profound implications for
determination of the neutron star masses and radii.
