  The role of the pseudospin symmetry in the inversion of the ground-state spin
in Cu isotopes is investigated within the covariant density functional theory
(CDFT). The density functional PC-PK1 gives a good agreement with the observed
ground-state properties of the odd-A $^{69-79}$Cu. In particular, the inversion
of the ground-state spin at $A=75$ is reproduced nicely, which can be explained
by the level crossing between the proton pseudospin partners $\pi 2p_{3/2}$ and
$\pi 1f_{5/2}$. It is found that the pseudospin symmetry plays a dominant role
in the evolution of the energy splittings between the pseudospin partners. By
comparing with the results of the nonrelativistic DFTs, our studies suggest
that the pseudospin symmetry is essential to the shell evolution around this
region.
