Unconventional Superconductivity in CeCoIn 5 Studied by the Specic Heat and Magnetization Measurements Shugo IKEDA 1 , Hiroaki SHISHIDO 1 , Miho NAKASHIMA 1 , Rikio SETTAI 1 , Dai AOKI 1; * , Yoshinori HAGA 2 , Hisatomo HARIMA 3 , Yuji AOKI 4 , Takahiro NAMIKI 4 , Hideyuki SATO 4 and Yoshichika O ¯ NUKI 1;2 1 Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043 2 Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195 3 The Institute of Scientic and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047 4 Graduate School of Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo 192-0309 (Received May 1, 2001) We measured the low-temperature specic heat in magnetic elds up to 80 kOe, together with the magnetization for the heavy-fermion superconductor CeCoIn 5 with the transition temperature T c ¼ 2:25 K. CeCoIn 5 is a strong-coupling superconductor with a large jump in the specic heat C=C n ðT c Þ¼ 4:7. The heavy-fermion state is signicantly formed below 1 K, reaching at least 1070 mJ/K 2 mol in magnetic elds. This large electronic specic heat coecient at 0.25 K is, however, reduced with increasing magnetic eld, ranging from 1070 mJ/K 2 mol at 50 kOe to 820 mJ/K 2 mol at 80 kOe. The upper critical eld H c2 at 0 K is estimated to be 116 kOe for H k½100 and 49.5 kOe for H k½001. The present anisotropy of H c2 is well explained by the anisotropic eective mass, but the magnitude of H c2 is reduced strongly by the paramagnetic eect for both eld directions. KEYWORDS: CeCoIn 5 , specic heat, superconductivity, heavy fermion The 4f electrons of rare earth compounds exhibit a variety of characteristics including spin and valence uctuations, heavy fermions and anisotropic supercon- ductivity. 1) In these compounds, both the Ruderman{ Kittel{Kasuya{Yosida (RKKY) interaction and the Kondo eect compete with each other. The former enhances the long-range magnetic order, where the 4f electrons with the magnetic moments are treated as localized electrons and the indirect f {f interaction is mediated by the conduction electrons with spins. On the other hand, the latter quenches the magnetic moments of the localized-4f electrons by the spin polarization of the conduction electrons, consequently producing renorma- lized quasiparticles with a large mass, so-called heavy fermions. The heavy-fermion state is basically understood as follows. The 4f levels of the Ce ions are generally split into three crystalline electric eld (CEF) doublets at high temperatures because the 4f electrons in the Ce compounds are almost localized in nature. At low temperatures, the magnetic entropy of the ground-state doublet in the 4f levels, R ln 2, is expressed by integrating the magnetic specic heat C m in the form of C m =T over the temperature. When the magnetic specic heat C m is changed into the electronic specic heat T via the many-body Kondo eect, the heavy- fermion state is formed below the Kondo temperature T K : ¼ R ln 2=T K ’ 10 4 =T K (mJ/K 2 mol). 2) In fact, the electronic specic heat coecient and the Kondo temperature are 1600 mJ/K 2 mol and 5 K in CeCu 6 , and 350 mJ/K 2 mol and 20 K in CeRu 2 Si 2 , respectively. Recently it was reported that CeIrIn 5 and CeCoIn 5 are heavy-fermion superconductors. 3{5) The transition tem- peratures T c (and the value) are 0.4 K (680 mJ/ K 2 mol), and 2.3 K (300{1000 mJ/K 2 mol), respectively. Here, the value in CeCoIn 5 is about 300 mJ/K 2 mol at T c but increases with decreasing temperature, reaching about 1000 mJ/K 2 mol at 0.1 K, which was obtained by the specic heat measurement in a magnetic eld. 3) The specic heat result also indicates that CeCoIn 5 is a strong-coupling superconductor with C=C n ðT c Þ¼ 4:5 and the specic heat in the superconducting state follows a power law of T 2 -dependence in a narrow temperature range from 0.1 to 0.7 K. 3,5) Here, C is a jump in the specic heat at T c , and C n ðT c Þ is the specic heat in the normal state at T ¼ T c . The present C=C n ðT c Þ value is extremely large compared to the BCS value of 1.43, and the data suggest the existence of a line node in the superconducting energy gap. CeRhIn 5 , however, orders antiferromagnetically below T N ¼ 3:8 K, whereas super- conductivity was observed under pressure, p> 1:6 GPa. 6) These characteristic properties are closely related to the unique tetragonal crystal structure (P4/mmm #123 D 1 4h ) with alternating layers of CeIn 3 and TIn 2 (T: Co, Rh and Ir), stacked sequentially along the [001] direction (c-axis). Recently, we claried that this unique crystal structure brings about quasi-two dimensional Fermi surfaces in CeIrIn 5 and CeCoIn 5 , which were determined by de Haas-van Alphen experiments. 7,8) Both com- pounds are compensated metals with equal volumes of electron and hole Fermi surfaces. The Fermi surfaces consist of a cylindrical band 15-electron Fermi surface and a complicated band 14-hole Fermi surface stretching along [001]. To clarify the electronic state in both the normal and superconducting mixed states of CeCoIn 5 , we carried out * Present address: DRFMC-SPSMS, CEA, 38054 Grenoble Cedex 9, France. Journal of the Physical Society of Japan Vol. 70, No. 8, August, 2001, pp. 2248{2251 2248 LETTERS