  Gamow-Teller (GT) strength distributions of Mg isotopes are investigated
within a framework of the deformed quasi-particle random phase
approximation(DQRPA). We found that the N=20 shell closure in $^{28 \sim 34}$Mg
was broken by the prolate shape deformation originating from the {\it
fp}-intruder states. The shell closure breaking gives rise to a shift of
low-lying GT excited states into high-lying states. Discussions regarding the
shell evolution trend of single particle states around N=20 nuclei are also
presented with the comparison to other approaches.
