  Gamma-ray bursts (GRBs), both long and short, are explosive events whose
inner engine is generally expected to be a black hole or a highly magnetic
neutron star (magnetar) accreting high density matter. Recognizing the nature
of GRB central engines, and in particular the formation of neutron stars (NSs),
is of high astrophysical significance. A possible signature of NSs in GRBs is
the presence of a plateau in the early X-ray afterglow. Here we carefully
select a subset of long and short GRBs with a clear plateau, and look for an
additional NS signature in their prompt emission, namely a transition between
accretion and propeller in analogy with accreting, magnetic compact objects in
other astrophysical sources. We estimate from the prompt emission the minimum
accretion luminosity below which the propeller mechanism sets in, and the NS
magnetic field and spin period from the plateau. We demonstrate that these
three quantities obey the same universal relation in GRBs as in other accreting
compact objects switching from accretion to propeller. This relation provides
also an estimate of the radiative efficiency of GRBs, which we find to be
several times lower than radiatively efficient accretion in X-ray binaries and
in agreement with theoretical expectations. These results provide additional
support to the idea that at least some GRBs are powered by magnetars surrounded
by an accretion disc.
