Non-Fermi-liquid behavior in Ce(Ru$_{1-x}$Fe$_x$)$_2$Ge$_2$: cause and effect

We present inelastic neutron scattering measurements on the intermetallic compounds Ce(Ru$_{1-x}$Fe$_x$)$_2$Ge$_2$ ($x$=0.65, 0.76 and 0.87). These compounds represent samples in a magnetically ordered phase, at a quantum critical point and in the heavy-fermion phase, respectively. We show that at high temperatures the three compositions have the identical response of a local moment system. However, at low temperatures the spin fluctuations in the critical composition are given by non-Fermi-liquid dynamics, while the spin fluctuations in the heavy fermion system show a simple exponential decay in time. In both compositions, the lifetime of the fluctuations is determined solely by the distance to the quantum critical point. We discuss the implications of these observations regarding the possible origins of non-Fermi-liquid behavior in this system.