We report on the measurement of new low-lying states in the neutron-rich 81,82,83,84Zn nuclei via in-beam γ -ray spectroscopy. These include the View the MathML source41+→21+ transition in 82Zn, the View the MathML source21+→0g.s.+ and View the MathML source41+→21+ transitions in 84Zn, and low-lying states in 81,83Zn were observed for the first time. The reduced View the MathML sourceE(21+) energies and increased View the MathML sourceE(41+)/E(2+1) ratios at N=52N=52, 54 compared to those in 80Zn attest that the magicity is confined to the neutron number N=50N=50 only. The deduced level schemes are compared to three state-of-the-art shell model calculations and a good agreement is observed with all three calculations. The newly observed 2+2+ and 4+4+ levels in 84Zn suggest the onset of deformation towards heavier Zn isotopes, which has been incorporated by taking into account the upper sdg orbitals in the Ni78-II and the PFSDG-U models