  Low-frequency quadrupole vibrational modes in deformed $^{36,38,40}$Mg close
to the neutron drip line are studied by means of the quasiparticle-random-phase
approximation based on the coordinate-space Hartree-Fock-Bogoliubov formalism.
Strongly collective $K^{\pi}=0^{+}$ and $2^{+}$ excitation modes carrying 10-20
Weisskopf units in the intrinsic isoscalar quadrupole transition strengths are
obtained at about 3 MeV. There are two reasons for the enhancement of the
transition strengths. First, the quasiparticle wave functions generating these
modes possess spatially very extended structure. The asymptotic selection rules
characterizing the $\beta$ and $\gamma$ vibrations in stable deformed nuclei
are thus strongly violated. Second, the dynamic pairing effects act strongly to
enhance the collectivity of these modes. It is suggested that the lowest
$K^{\pi}=0^{+}$ collective mode is a particularly sensitive indicator of the
nature of pairing correlations in deformed nuclei close to the neutron drip
line.
