  Various ground state properties are explored for full isotonic(isotopic)
chain of neutron number N(proton number Z)$=$40 using different families of
Relativistic Mean-Field theory. Several properties such as nucleon separation
energies, pairing energies, deformation, radii and nucleon density
distributions are evaluated and compared with the experimental data as well as
those from other microscopic and macroscopic models. N$=$40 isotonic chain
presents ample of support for the neutron magicity and articulates double
magicity in recently discovered $^{60}$Ca and $^{68}$Ni. Our results are in
close conformity with recently measured value of charge radius of $^{68}$Ni [S.
Kaufmann \textit{et al.}, Phys. Rev. Lett. 124, 132502 (2020)] which supports
the N$=$40 magicity. Contrarily, Zr isotopes (Z$=$40) display variety of shapes
leading to the phenomenon of shape transitions and shape co-existence. The role
of 3s$_{1/2}$ state, which leads to central depletion if unoccupied, is also
investigated. $^{56}_{16}$S and $^{122}_{40}$Zr are found to be doubly bubble
nuclei.
