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

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