The abnormally large collectivity of neutron-rich magnesium isotopes in the “island of inversion” has not been well understood. It has been commented that the unexpectedly large deformations observed in the magnesium isotopes are attributed to the neutron f7/2 intruder orbits involved remarkably even in the ground states, which points to nuclear force directly. Recently, a new isospin-dependent Nilsson potential was suggested to improve the calculations of the ground states of magnesium isotopes. With the improved Nilsson potential, in the present work we investigate the collectivity of excited states by using the projected shell model. To avoid the collapse of the BCS pairing, which occurs in weak pairing, we improved pairing calculations by using the Lipkin-Nogami approach. The collectivity and the erosion of the N = 20 shell in neutron-rich magnesium isotopes are discussed by calculating spectra and electric quadrupole transitions. The gyromagnetic factors are calculated and compared with existing data to get insight into the configurations of collective states at different spins. A two-quasineutron Kπ = 6+ state in 38Mg is predicted to be a possible isomer with an excitation energy lower than the I π = 6+ member of the ground-state band.