  In millisecond pulsars the existence of the Coriolis force allows the
development of the so-called Rossby oscillations (r-modes) which are know to be
unstable to emission of gravitational waves. These instabilities are mainly
damped by the viscosity of the star or by the existence of a strong magnetic
field. A fraction of the observed millisecond pulsars are known to be inside
Low Mass X-ray Binaries (LMXBs), systems in which a neutron star (or a black
hole) is accreting from a donor whose mass is smaller than 1 $M_\odot$. Here we
show that the r-mode instabilities can generate strong toroidal magnetic fields
by inducing differential rotation. In this way we also provide an alternative
scenario for the origin of the magnetars.
