Phonon dynamics in Chromium under pressure: absence of phonon criticality at the approach of the quantum critical point
Fermi surface nesting is key to understanding the origin of the itinerant antiferromagnetic spin density wave in chromium. This magnetic order is accompanied by a charge-density wave, and both density waves disappear above the critical pressure $P_c \approx 10$ GPa at low temperatures, defining a quantum critical point. Whether this pressure-induced quantum phase transition is accompanied by a phonon instability remains an open question. Here, we use inelastic x-ray scattering to track the room-temperature acoustic phonon dispersions at pressures up to $P=15.6$ GPa, well above $P_c$. We focus on the Kohn anomalies near the $H$ and $N$ points of the Brillouin zone, with the $H$ point anomaly lying close to the incommensurate spin-density-wave ordering vector. The phonon branches harden smoothly under pressure, while the positions and wave-vector extents of both anomalies remain essentially unchanged across $P_c$, with no additional critical softening. \textit{Ab initio} calculations likewise show that Fermi surface nesting remains robust above $P_c$. These results indicate that the pressure-induced quantum phase transition is not driven by a phonon instability and support a primarily spin-density-wave-driven mechanism in presence of a robust Kohn anomaly.