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Fast radio bursts (FRBs) are short pulses observed in radio frequenciesusually originating from cosmological distances. The discovery of FRB 200428and its X-ray counterpart from the Galactic magnetar SGR J1935+2154 suggeststhat at least some FRBs can be generated by magnetars. However, the majority ofX-ray bursts from magnetars are not associated with radio emission. The factthat only in rare cases can an FRB be generated raises the question regardingthe special triggering mechanism of FRBs. Here we report a giant glitch fromSGR J1935+2154, which occurred approximately $3.1\pm2.5$\,day before FRB200428, with $\Delta\nu=19.8\pm1.4$ {\rm $\mu$Hz} and$\Delta\dot{\nu}=6.3\pm1.1$\,pHz s$^{-1}$. The corresponding spin-down powerchange rate $\Delta\dot\nu/\dot\nu$ is among the largest in all the detectedpulsar glitches. The glitch contains a delayed spin-up process that is onlydetected in the Crab pulsar and the magnetar 1E 2259+586, a large persistentoffset of the spin-down rate, and a recovery component which is about one orderof magnitude smaller than the persistent one. The temporal coincidence betweenthe glitch and FRB 200428 suggests a physical connection between the two. Theinternally triggered giant glitch of the magnetar likely altered themagnetosphere structure dramatically in favour of FRB generation, whichsubsequently triggered many X-ray bursts and eventually FRB 200428 throughadditional crustal cracking and Alfv\'en wave excitation and propagation.

A giant glitch from the magnetar SGR J1935+2154 before FRB 200428