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Trends in Heavy Fermion Matter

A brief review on major advances in heavy fermion physics is presented including the Ce metal phase diagram, the huge effective mass detected in CeAl3, and the successive discoveries of unconventional superconductivity in CeCu2Si2 and three U based compounds, UBe13, UPt3 and URu2Si2. In order to track the origin of the huge effective mass, the case of intermediate valence compounds is discussed with emphasis of the differences between Yb and Ce materials. The formation of the effective mass is analyzed by two regular- and singular-part contributions. Examples are given for both, antiferromagnetic (CeRu2Si2 series) and ferromagnetic tricriticalities (UGe2). Pressure and magnetic-field studies on the ferromagnetic superconductor URhGe illustrate the role of the singular effective mass enhancement on the superconducting pairing. The discovery of the Ce-115 material gives the opportunity to study deeply the interplay of antiferromagnetism and superconductivity. This is clearly demonstrated by field re-entrance AF inside the SC phase just below the superconducting upper critical field (Hc2) for CeCoIn5 or on both side of Hc2 within a restricted pressure window for CeRhIn5. The present status of the search for the hidden-order parameter of URu2Si2 is given and we emphasize that it may correspond to a lattice unit-cell doubling which leads to a drastic change in the band structure and spin dynamic, with the possibility of competition between multipolar ordering and antiferromagnetism.