  By combining experimental measurements of the quasiparticle and dynamical
magnetic properties of optimally electron-doped Pr$_{0.88}$LaCe$_{0.12}$CuO$_4$
with theoretical calculations we demonstrate that the conventional fermiology
approach cannot possibly account for the magnetic fluctuations in these
materials. In particular, we perform tunneling experiments on the very same
sample for which a dynamical magnetic resonance has been reported recently and
use photoemission data by others on a similar sample to characterize the
fermionic quasiparticle excitations in great detail. We subsequently use this
information to calculate the magnetic response within the conventional
fermiology framework as applied in a large body of work for the hole-doped
superconductors to find a profound disagreement between the theoretical
expectations and the measurements: this approach predicts a step-like feature
rather than a sharp resonance peak, it underestimates the intensity of the
resonance by an order of magnitude, it suggests an unreasonable temperature
dependence of the resonance, and most severely, it predicts that most of the
spectral weight resides in incommensurate wings which are a key feature of the
hole-doped cuprates but have never been observed in the electron-doped
counterparts. Our findings strongly suggest that the magnetic fluctuations
reflect the quantum-mechanical competition between antiferromagnetic and
superconducting orders.
