Unveiling competing fluctuations at an unconventional quantum critical point

Quantum critical points (QCPs) are widely accepted as a source of a diverse set of collective quantum phases of matter. This unusually rich behavior originates from the interplay of fermiology, exchange interactions, and electronic correlations. A key issue is how the competition between various degrees of freedom is resolved and reflected in the observed physical properties. Here we show, through inelastic neutron scattering measurements, how competing interactions mask the behavior of a QCP in CeCu$_{6-x}$Ag$_{x}$. In particular, the inelastic neutron scattering measurements reveal a butterfly shaped pattern of scattering that is composed of at least two fluctuations to different ordered states. When the critical fluctuations are separated and analyzed, they conform to the predictions of the Hertz-Millis-Moriya theory of a QCP and offer an explanation to the long standing puzzle of why the magnetic field tuned and compositionally tuned QCPs appear to be different in one of the archetypal examples of metallic quantum criticality, CeCu$_{6-x}$Au$_{x}$.