By performing combined resistivity and calorimetric experiments under pressure, we have determined a precise temperature-pressure ͑T , P͒ phase diagram of the heavy fermion compound URu 2 Si 2 . It will be compared with previous diagrams determined by elastic neutron diffraction and strain gauge techniques. At first glance, the low-pressure ordered phase referred to as hidden order is dominated by Fermi-surface nesting, which has strong consequences on the localized spin dynamics. The high-pressure phase is dominated by large moment antiferromagnetism ͑LMAF͒ coexisting with at least dynamical nesting needed to restore on cooling a local moment behavior. ac calorimetry confirms unambiguously that bulk superconductivity does not coexist with LMAF. URu 2 Si 2 is one of the most spectacular examples of the dual itinerant and local character of uranium-based heavy fermion compounds.

We report on detailed ac calorimetry measurements under high pressure and magnetic field of CeRhIn5. Under hydrostatic pressure the antiferromagnetic order vanishes near p ⋆ c = 2 GPa due to a first order transition. Superconductivity is found for pressures above 1.5 GPa inside the magnetic ordered phase. However, the superconductivity differ from the pure homogeneous superconducting ground state above 2 GPa. The application of an external magnetic field H ab induces a transition inside the superconducting state above p ⋆ c which is strongly related to the re-entrance of the antiferromagnetism with field. This field-induced supplementary state vanishes above the quantum critical point in this system. The analogy to CeCoIn5 is discussed.The discovery of the cerium heavy fermion CeM In 5 (M = Co, Ir, Rh) systems opened a new route to investigate the interplay of magnetic fluctuations, unconventional superconductivity (SC) and antiferromagnetic order (AF) in strongly correlated electron systems in the vicinity of a quantum phase transition (QPT). While CeCoIn 5 and CeIrIn 5 are unconventional superconductors at ambient pressure (p)with most probably d-wave symmetry below T c = 2.2 K and T c = 0.4 K and suited very close to a QPT, CeRhIn 5 offers the possibility to tune a heavy fermion system from AF to SC as function of pressure [1,2,3]. At ambient pressure CeRhIn 5 orders antiferromagnetically below the Néel temperature T N = 3.8 K in an incommensurate helical structure with propagation vector Q = (1/2, 1/2, 0.297) and a staggered moment of about 0.8 µ B [4]. Neutron scattering experiments under pressure showed that this magnetic structure is almost unchanged under pressure up to the highest investigated pressure of 1.7 GPa [5]. SC has been reported for pressures above 0.9 GPa on the basis of resistivity measurements. Nuclear-quadrupole resonance (NQR) measurements in combination with ac susceptibility have shown that SC and AF coexist on a microscopic scale in the pressure range from p = 1.6 − 1.75 GPa [6]. The spin-lattice relaxation rate shows at low temperature an unexpected 1/T 1 ∝ T dependence which gives evidence for a gap-less nature of the low-lying excitations. A pure superconducting ground-state with line nodes in the gap is attained for p > 2 GPa and 1/T 1 ∝ T 3 has been reported [7]. Previous detailed specific heat measurements under hydrostatic pressure give evidence that the magnetic transition disappears by a first order transition at p The application of an external magnetic field H offers a second parameter to influence the competition between AF and SC. Recently it was shown that a magnetic QCP can be achieved in CeCoIn 5 by the application of a magnetic field of the order of the upper critical field H c2 (0) [10,11]. H c2 (T ) in this compound is strongly Pauli limited and the transition becomes first order at low temperatures [12,13,14]. At high magnetic field near H c2 (0) a new superconducting phase was observed which may be the first example of a Fulde-Ferrel-Ovchinnikov-Larkin (FFLO) state...

We report on the synthesis of superconducting single crystals of FeSe and their characterization by x-ray diffraction, magnetization and resistivity. We have performed ac susceptibility measurements under high pressure in a hydrostatic liquid argon medium up to 14 GPa and we find that T(C) increases up to 33-36 K in all samples, but with slightly different pressure dependences on different samples. Above 12 GPa no traces of superconductivity are found in any sample. We have also performed a room temperature high pressure x-ray diffraction study up to 12 GPa on a powder sample, and we find that, between 8.5 and 12 GPa, the tetragonal PbO structure undergoes a structural transition to a hexagonal structure. This transition results in a volume decrease of about 16% and is accompanied by the appearance of an intermediate, probably orthorhombic, phase.