  The structure of neutron-rich Cr isotopes is systematically investigated by
using the spherical shell model. The calculations reproduce well the known
energy levels for the even-even $^{52-62}$Cr and odd-mass $^{53-59}$Cr nuclei,
and predict a lowering of excitation energies around neutron number N=40. The
calculated $B(E2;2_{1}^{+}\to 0_{1}^{+})$ systematics shows a pronounced
collectivity around N=40; a similar characteristic behavior has been suggested
for Zn and Ge isotopes. Causes for the sudden drop of the $9/2_{1}^{+}$ energy
in $^{59}$Cr and the appearance of very low $0_{2}^{+}$ states around N=40 are
discussed. We also predict a new band with strong collectivity built on the
$0_{2}^{+}$ state in the N=40 isotope $^{64}$Cr.
