We show that the r-mode instability can generate strong toroidal fields in the core of accreting millisecond quark stars by inducing differential rotation. We follow the spin frequency evolution on a long time scale taking into account the magnetic damping rate in the evolution equations of r-modes. The maximum spin frequency of the star is only marginally smaller than in the absence of the magnetic field. The late-time evolution of the stars which enter the r-mode instability region is instead rather different if the generated magnetic fields are taken into account: they leave the millisecond pulsar region and they become radio pulsars.
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