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Role of commensurate and incommensurate low-energy excitations in the paramagnetic to hidden-order transition of URu$_2$Si$_2$

We report low-energy inelastic neutron scattering data of the paramagnetic (PM) to hidden-order (HO) phase transition at $T_0=17.5\,{\rm K}$ in URu$_2$Si$_2$. While confirming previous results for the HO and PM phases, our data reveal a pronounced wavevector dependence of low-energy excitations across the phase transition. To analyze the energy scans we employ a damped harmonic oscillator model containing a fit parameter $1/Γ$ which is expected to diverge at a second-order phase transition. Counter to expectations the excitations at $\vec{Q}_1=(1.44,0,0)$ show an abrupt step-like suppression of $1/Γ$ below $T_0$, whereas excitations at $\vec{Q}_0=(1,0,0)$, associated with large-moment antiferromagnetism (LMAF) under pressure, show an enhancement and a pronounced peak of $1/Γ$ at $T_0$. Therefore, at the critical HO temperature $T_0$, LMAF fluctuations become nearly critical as well. This is the behavior expected of a super-vector order parameter with nearly degenerate components for the HO and LMAF leading to nearly isotropic fluctuations in the combined order-parameter space.