  The even-Z odd-N neutron-halo nuclei, which are the possible lightest
neutron-halo nuclei heavier than $^{37}$Mg, are explored by studying the
shell-structure unique in weakly-bound neutrons for spherical or deformed
shape. It is pointed out that due to the narrowed N=50 spherical energy-gap and
a few resulting close-lying neutron one-particle levels, 1g$_{9/2}$,
3s$_{1/2}$, and 2d$_{5/2}$, for spherical shape, nuclei with some weakly-bound
neutrons filling in those levels may be deformed and have a good chance to show
deformed s-wave halo. Promising candidates are $^{71}_{24}$Cr$_{47}$,
$^{73}_{24}$Cr$_{49}$, $^{75}_{24}$Cr$_{51}$ and $^{77}_{26}$Fe$_{51}$ in the
case that those nuclei lie inside the neutron drip-line. An interesting
possibility of the deformed p-wave or s-wave halo is suggested also for the
nucleus $^{53}_{18}$Ar$_{35}$.
