Destabilization of hidden order in URu₂Si₂ under magnetic field and pressure

The mystery of the hidden-order phase in the correlated electron paramagnet URu₂Si₂ is still unsolved. To address this problem, one strategy is to search for clues in the subtle competition between this state and neighbouring magnetically ordered states. It is now well established that long-range antiferromagnetic order can be stabilized in this metal when it is under pressure and that a spin-density wave manifests when a magnetic field is applied along the easy magnetic axis c. However, the full boundaries of the hidden-order phase in the pressure–magnetic-field plane have not been determined so far. Here we present a systematic investigation of URu₂Si₂ under combined high pressures and intense magnetic fields. The boundaries of the hidden-order, antiferromagnetic and spin-density-wave phases are mapped out, indicating an intricate three-dimensional phase diagram. We show that the field-induced spin-density-wave and hidden-order phases disappear in favour of antiferromagnetism at high pressure. Interestingly, a large number of phase boundaries are controlled by the field and pressure dependences of a single parameter. This gives new constraints for theories that model the electronic correlations and ordered phases in URu₂Si₂.