There is growing evidence that a clear distinction between magnetars and radio pulsars may not exist, implying the population of neutron stars that exhibit both radio pulsations and bursting activities could be potentially large. In this situation, new insights into the burst mechanism could be gained by combining the temporal behavior of radio pulsations. We present a general model for radio suppression by relativistic $e^{pm}$ plasma outflows at the onset of magnetar flares. A sudden ejection of magnetic energy into the magnetosphere would generate a fireball plasma, which is promptly driven to expand at relativistic speed. This would make the plasma cutoff frequency significantly higher than the rest frame radio frequency, resulting in the suppression of radio waves. We analytically show that any GHz radio emission arising from the magnetosphere is suppressed for $sim100 {rm s}$, depending on the total fireball energy. On the other hand, thermal radiation is expected from the hot spot(s) on the stellar surface created by an inflow of dense plasma, which could be the origin of short bursts. Since our hypothesis predicts radio suppression in coincidence with short bursts, this could be an indirect method to constrain the occurrence rate of short bursts at the faint end that remain undetected by X-ray detectors. Furthermore, ultra-fast gamma-ray flashes from the fireball photosphere is also expected as a smoking gun, although the onboard detection is challenging due to its extremely short duration $simmu$s. Finally, our model is applied to the radio pulsar with magnetar-like activities, PSR J1119-6127 in light of recent observations. Implications for fast radio bursts and the possibility of plasma lensing are also discussed.
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