  In rotating neutron stars the existence of the Coriolis force allows the
presence of the so-called Rossby oscillations (r-modes) which are know to be
unstable to emission of gravitational waves. Here, for the first time, we
introduce the magnetic damping rate in the evolution equations of r-modes. We
show that r-modes can generate very strong toroidal fields in the core of
accreting millisecond pulsars by inducing differential rotation. We shortly
discuss the instabilities of the generated magnetic field and its long
time-scale evolution in order to clarify how the generated magnetic field can
stabilize the star.
