Neutron Scattering Study of URu$_{2-x}$Re$_x$Si$_2$ with $x$ = 0.10: Driving Order towards Quantum Criticality

We report inelastic neutron scattering measurements in the hidden order state of URu$_{2-x}$Re$_x$Si$_2$ with $x$ = 0.10. We observe that towards the ferromagnetic quantum critical point induced by the negative chemical pressure of Re-doping, the gapped incommensurate fluctuations are robust and comparable in intensity to the parent material. As the Re doping moves the system toward the quantum critical point, the commensurate spin fluctuations related to hidden order weaken, display a shortened lifetime and slow down. Halfway to the quantum critical point, the hidden order phase survives, albeit weakened, in contrast to its destruction by hydrostatic pressure and by positive chemical pressure from Rh-doping.