We describe here recent inelastic neutron scattering experiments on the heavy fermion compound URu2Si2 realized in order to clarify the nature of the hidden order (HO) phase which occurs below T_0 = 17.5 K at ambient pressure. The choice was to measure at a given pressure P where the system will go, by lowering the temperature, successively from paramagnetic (PM) to HO and then to antiferromagnetic phase (AF). Furthermore, in order to verify the selection of the pressure, a macroscopic detection of the phase transitions was also achieved in situ via its thermal expansion response detected by a strain gauge glued on the crystal. Just above P_x = 0.5 GPa, where the ground state switches from HO to AF, the Q_0 = (1, 0, 0) excitation disappears while the excitation at the incommensurate wavevector Q_1 = (1.4, 0, 0) remains. Thus, the Q_0 = (1, 0, 0) excitation is intrinsic only in the HO phase. This result is reinforced by studies where now pressure and magnetic field $H$ can be used as tuning variable. Above P_x, the AF phase at low temperature is destroyed by a magnetic field larger than H_AF (collapse of the AF Q_0 = (1, 0, 0) Bragg reflection). The field reentrance of the HO phase is demonstrated by the reappearance of its characteristic Q_0 = (1, 0, 0) excitation. The recovery of a PM phase will only be achieved far above H_AF at H_M approx 35 T. To determine the P-H-T phase diagram of URu2Si2, macroscopic measurements of the thermal expansion were realized with a strain gauge. The reentrant magnetic field increases strongly with pressure. Finally, to investigate the interplay between superconductivity (SC) and spin dynamics, new inelastic neutron scattering experiments are reported down to 0.4 K, far below the superconducting critical temperature T_SC approx 1.3 K as measured on our crystal by diamagnetic shielding.
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