Field re-entrant hidden-order phase under pressure in URu ₂Si₂

We succeeded in growing high quality single crystals of URu ₂Si₂ and performed thermal expansion measurements under pressure. Applying a magnetic field along the [001] direction in the tetragonal structure, the so-called hidden-order phase reappears after the suppression of the antiferromagnetic phase above the critical pressure P_x. We determined the pressure-temperature-field phase diagram for the paramagnetic, hidden-order and antiferromagnetic states for the H ∥ [001] direction. We also present the temperature dependence of the upper critical field H _c2 for and H ∥ [001] and [100] determined by the AC specific heat measurements, corresponding to the bulk superconductivity in a high quality single crystal.