Unconventional superconductivity and other previously unknown phases of matter exist in the vicinity of a quantum critical point (QCP): a continuous phase change of matter at absolute zero. Intensive theoretical and experimental investigations on itinerant systems have shown that metallic ferromagnets tend to develop via either a first-order phase transition or through the formation of intermediate superconducting or inhomogeneous magnetic phases. Here, through precision low-temperature measurements, we show that the Grüneisen ratio of the heavy fermion metallic ferromagnet YbNi(4)(P(0.92)As(0.08))(2) diverges upon cooling to T = 0, indicating a ferromagnetic QCP. Our observation that this kind of instability, which is forbidden in d-electron metals, occurs in a heavy fermion system will have a large impact on the studies of quantum critical materials.

Abstract. We report measurements of the pressure-dependent superconducting transition temperature Tc and electrical resistivity of the heavy-fermion compound CeCoIn 5 . Pressure moves CeCoIn 5 away from its proximity to a quantum-critical point at atmospheric pressure. Experimental results are qualitatively consistent with theoretical predictions for strong-coupled, d-wave superconductivity in an anisotropic 3D superconductor. Although heavy-fermion superconductivity has been known for over two decades, a microscopic theory of this broken-symmetry state has remained elusive. Experiments have established, however, that the unconventional superconductivity in heavyfermion compounds most likely is mediated by magnetic fluctuations, which also are responsible for enhancing the effective mass of itinerant quasiparticles by two to three orders of magnitude. [1,2,3] In spite of 20 years of searching, there has been, until very recently, only one example of a Ce-based heavy-fermion compound, CeCu 2 Si 2 , that is superconducting at atmospheric pressure. [4] In contrast, several examples of Cebased heavy-fermion antiferromagnets have been found in which superconductivity appears as their Néel temperature is tuned toward T = 0 with the application of pressure. [5,6,7,8] This recent series of discoveries re-enforces the belief not only that a magnetic interaction is responsible for superconductivity in these materials but also that heavy-fermion superconductivity may be favored at a particular 'soft-spot' in phase space, i.e., near a quantum-critical point

We have studied the temperature-pressure phase diagram of CeCoSi by electrical-resistivity experiments under pressure. Our measurements revealed a very unusual phase diagram. While at low pressures no dramatic changes and only a slight shift of the Neel temperature T-N (approximate to 10 K) are observed, at about 1.45 GPa a sharp and large anomaly, indicative of the opening of a spin-density wave gap, appears at a comparatively high temperature T-S approximate to 38 K. With further increasing pressure, T-S shifts rapidly to low temperatures and disappears at about 2.15 GPa, likely continuously in a quantum critical point, but without evidence for superconductivity. Even more surprisingly, we observed a clear shift of T-S to higher temperatures upon applying a magnetic field. We discuss two possible origins for T-S : magnetic ordering of Co and a metaorbital type of transition of Ce

We review magnetic, superconducting and non-Fermi-liquid properties of the structurally layered heavy-fermion compounds CenMmIn3n+2m (M=Co, Rh, Ir). These properties suggest d-wave superconductivity and proximity to an antiferromagetic quantum-critical point.