Test for pairing symmetry based on spin fluctuations in the organic superconductor kappa-(BEDT-TTF)2X

We propose that the superconducting pairing symmetry of organic superconductors kappa-(BEDT-TTF)2X can be determined by measuring the position in momentum space of the incommensurate peaks of the spin susceptibility. Using the weak coupling BCS theory and including the many-body effects via the random-phase approximation for the Hubbard model on an anisotropic triangular lattice, we show that the position of these peaks is uniquely determined by the pairing symmetry of the superconducting state and the geometry of the Fermi surface. We demonstrate the different incommensurate patterns of spin responses for d(x(2)-y(2-)) and d(xy)-like pairing states. In addition, we find that there is no spin resonance mode in the reasonable range of parameters discussed.