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Inelastic neutron scattering for Nd$_{2-x}$Ce$_x$CuO$_{4+\delta}$ nearoptimal doping ($x \approx 0.155$, $T_{c} = 25 \mathrm{K}$) reveals that thedynamic magnetic susceptibility at the antiferromagnetic zone center exhibitstwo characteristic energies in the superconducting state: $\omega_1 \approx 6.4\mathrm{meV}$ and $\omega_2 \approx 4.5 \mathrm{meV}$. These two magneticenergies agree $quantitatively$ with the $B_{1g}$ / $B_{2g}$ and $A_{1g}$features previously observed in electronic Raman scattering, where the formeris believed to indicate the maximum electronic gap and the origin of thesmaller $A_{1g}$ feature has remained unexplained. The susceptibility changeupon cooling into the superconducting state is inconsistent with previousclaims of the existence of a magnetic resonance mode near 10 meV, butconsistent with a resonance at $\omega_2$.

Two characteristic energies in the low-energy antiferromagnetic response  of the electron-doped high-temperature superconductor  Nd$_{2-x}$Ce$_x$CuO$_{4+\delta}$