Spin fluctuation-induced superconductivity in two and three dimensional systems

The strong coupling theory of unconventional superconductivity due to spin fluctuations around the antiferromagnetic instability, previously developed for two dimensional (square lattice) systems is extended to three dimensional (simple cubic lattice) systems. The values for T-c are found to be similar for the 2- and 3-dimensional systems provided the band widths and the spin fluctuation parameters take similar values. The dependences of T-c on various parameters are investigated. In both dimensions the value of T-c is most sensitive to the frequency spread of antiferromagnetic fluctuations; the larger the frequency spread the higher T-c. In the light of the present results a systematic scaling analysis is given for the values of T-c for possible spin fluctuation-induced superconductors including high-T-c cuprates, heavy electron- and organic superconductors, etc.