  We use inelastic neutron scattering to study the temperature dependence of
the spin excitations of a detwinned superconducting YBa$_2$Cu$_3$O$_{6.45}$
($T_c=48$ K). In contrast to earlier work on YBa$_2$Cu$_3$O$_{6.5}$ ($T_c=58$
K), where the prominent features in the magnetic spectra consist of a sharp
collective magnetic excitation termed ``resonance'' and a large
($\hbar\omega\approx 15$ meV) superconducting spin gap, we find that the spin
excitations in YBa$_2$Cu$_3$O$_{6.45}$ are gapless and have a much broader
resonance. Our detailed mapping of magnetic scattering along the
$a^\ast$/$b^\ast$-axis directions at different energies reveals that spin
excitations are unisotropic and consistent with the ``hourglass''-like
dispersion along the $a^\ast$-axis direction near the resonance, but they are
isotropic at lower energies. Since a fundamental change in the low-temperature
normal state of YBa$_2$Cu$_3$O$_{6+y}$ when superconductivity is suppressed
takes place at $y\sim0.5$ with a metal-to-insulator crossover (MIC), where the
ground state transforms from a metallic to an insulating-like phase, our
results suggest a clear connection between the large change in spin excitations
and the MIC. The resonance therefore is a fundamental feature of metallic
ground state superconductors and a consequence of high-$T_c$ superconductivity.
