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We use inelastic neutron scattering to study the temperature dependence ofthe 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 sharpcollective magnetic excitation termed ``resonance'' and a large($\hbar\omega\approx 15$ meV) superconducting spin gap, we find that the spinexcitations in YBa$_2$Cu$_3$O$_{6.45}$ are gapless and have a much broaderresonance. Our detailed mapping of magnetic scattering along the$a^\ast$/$b^\ast$-axis directions at different energies reveals that spinexcitations are unisotropic and consistent with the ``hourglass''-likedispersion along the $a^\ast$-axis direction near the resonance, but they areisotropic at lower energies. Since a fundamental change in the low-temperaturenormal state of YBa$_2$Cu$_3$O$_{6+y}$ when superconductivity is suppressedtakes place at $y\sim0.5$ with a metal-to-insulator crossover (MIC), where theground state transforms from a metallic to an insulating-like phase, ourresults suggest a clear connection between the large change in spin excitationsand the MIC. The resonance therefore is a fundamental feature of metallicground state superconductors and a consequence of high-$T_c$ superconductivity.

Quantum Spin Excitations through the metal-to-insulator crossover in $Y Ba_2 Cu_3 O_{6+y}$