  The dynamics of the plasma in the inner regions of an accretion disk around
accreting millisecond X-ray pulsars is controlled by the magnetic field of the
neutron star. The interaction between an accretion disk and a strong magnetic
field is not well-understood, particularly at low accretion rates (the
so-called ``propeller regime'). This is due in part to the lack of clear
observational diagnostics to constrain the physics of the disk-field
interaction. Here we associate the strong ~1 Hz modulation seen in the
accreting millisecond X-ray pulsar NGC 6440 X-2 with an instability that arises
when the inner edge of the accretion disk is close to the corotation radius
(where the stellar rotation rate matches the Keplerian speed in the disk). A
similar modulation has previously been observed in another accreting
millisecond X-ray pulsar (SAX J1808.4-3658) and we suggest that the two
phenomena are related and that this may be a common phenomenon among other
magnetized systems. Detailed comparisons with theoretical models suggest that
when the instability is observed, the interaction region between the disk and
the field is very narrow -- of the order of 1 km. Modelling further suggests
that there is a transition region (~1-10 km) around the corotation radius where
the disk-field torque changes sign from spin up to spin down. This is the first
time that a direct observational constraint has been placed on the width of the
disk-magnetosphere interaction region, in the frame of the trapped-disk
instability model.
