Multicritical Phenomena of Superconductivity and Antiferromagnetism in Organic Conductor $κ$-(BEDT-TTF)$_2$X

We study theoretically the multicritical phenomena of the superconductivity (SC) and antiferromagnetism (AF) in organic conductors $\kappa$-BEDT salts. This system is in the strong coupling regime both for the SC and the AF, and the critical fluctuation is observed within the temperature region $T-T_c \lesssim 10{\rm K}$. The phase diagram and the experimental data on NMR relaxation rate $1/T_1$ is analysed in terms of the renormalization group (RG) method, and the following results are obtained; (i) the bicritical phenomenon observed experimentally indicates the rotational symmetry, i.e., SO(5) symmetry, within the 5-dimensional order paramter space of the SC and the AF. (ii) the critical exponent $x$ for the divergence of $1/T_1$ is well explained by the formula $ x = \nu (z - 1 - \eta)$ with the dynamical exponent $z = 3/2$ for the AF region while $z = \phi/\nu \sim 1.84 $ at the bicritical point. These results strongly suggest that the origin of the SC is common with the AF and its symmetry is d-wave.