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Interplay of Superconductivity, Antiferromagnetism, and Pauli Depairing in CeCoIn$_5$

Low temperature magnetization M measurements down to 70~mK have been performed through the superconducting upper critical field H_c2 of CeCoIn5 with the field H parallel to the c axis of the tetragonal crystal. The crossing through the upper critical field H_c2(0) is marked by a sign change in the temperature dependence of M(T). A Fermi liquid law of the magnetization is observed in the superconducting phase while in the paramagnetic state above H_c2 a quasi-linear temperature dependence is obeyed. The specific heat below H_c2 is therefor dominated by the increase of γ(H), the linear term of the specific heat, and is marked by a singularity at H_{c2} (0). No indication of the so called Q-phase was observed below H_c2 (in contrast to the case with H applied in the basal plane).