Signature of hidden order in heavy fermion superconductor ${\text{URu}}_2{\text{Si}}_2$: Resonance at the wave vector ${\text{Q}}_0=\left(\mathrm{1,0,0}\right)$

Simultaneous neutron scattering and thermal expansion measurements on the heavy-fermion superconductor ${\text{URu}}_2{\text{Si}}_2$ under hydrostatic pressure of 0.67 GPa have been performed in order to detect the successive paramagnetic, hidden order, and large moment antiferromagnetic phases on cooling. The temperature dependence of the sharp low energy excitation at the wave vector ${\mathbf{Q}}_{\mathbf{0}}=\left(\mathrm{1,0,0}\right)$ shows clearly that this resonance is a signature of the hidden order state. In the antiferromagnetic phase, this resonance disappears. The higher energy excitation at the incommensurate wave vector ${\mathbf{Q}}_{\mathbf{1}}=\left(\mathrm{1.4,0,0}\right)$ persists in the antiferromagnetic phase but increases in energy.

Figure 1

(Color online) $\left(T,P\right)$ phase diagram of ${\text{URu}}_2{\text{Si}}_2$ from resistivity (circles) and ac calorimetry (triangles) measurements (Ref. 19) with the low-pressure HO phase and the high-pressure AF phase. Bulk superconductivity state is suppressed at $P_x$ when antiferromagnetism appears. The open triangles correspond to the present determination of $T_0$ and $T_x$ at $P=0.67\text{GPa}$.

Figure 2

(Color online) Thermal evolution of the magnetic Bragg peak intensity at ${\mathbf{Q}}_{\mathbf{0}}=\left(\mathrm{1,0,0}\right)$ (dashed line) and of the thermal expansion ${\alpha }_a$ (solid line) of ${\text{URu}}_2{\text{Si}}_2$ at $P=0.67\text{Pa}$. ${\text{I}}_M$ corresponds to the count at the top of the magnetic Bragg peak ${\mathbf{Q}}_{\mathbf{0}}$ per 10 min, the background subtracted. The inset is a zoom of $I_M$ and ${\alpha }_a$ in the HO phase.

Figure 3

(Color online) Energy scan at ${\mathbf{Q}}_{\mathbf{0}}$ in the PM $\left(T=20.1\text{K}\right)$, HO $\left(T=13.9\text{K}\right)$, and AF $\left(T=1.5\text{K}\right)$ phases. Only electronic background has been subtracted. The curves are guides for the eyes.

Figure 4

(Color online) Energy scan at ${\mathbf{Q}}_{\mathbf{1}}$ in the PM $\left(T=20.1\text{K}\right)$, HO $\left(T=13.9\text{K}\right)$, and AF $\left(T=1.5\text{K}\right)$ phases. An energy scan measured at $T=1.8\text{K}$ at the wave vector $\mathbf{Q}=\left(\mathrm{1.3,0,0}\right)$ has been used as background and subtracted to the energy scans measured at ${\mathbf{Q}}_{\mathbf{1}}$. The curves are guides for the eyes.

Figure 5

(Color online) Integration of the dynamic susceptibility $I_{{\Delta }_0}\left(Q_0\right)$ from $E=0.6\text{meV}\to E=2.5\text{meV}$ (black circles). The dashed blue curve is a guide for the eyes. Thermal expansion in red (solid line). If the HO persists down to 0 K, its contribution, measured at $P=0$ in Ref. 25, is the extrapolated green dotted line.