ISOTOPE EFFECT IN SPIN FLUCTUATION MODELS

We have studied the d-wave superconducting transition temperature T-c and the isotope effect in the spin fluctuation models. We found that t he isotope exponent alpha is at least one order order of magnitude sma ller than typical observed values in the cuprates with models coupling to harmonic phonon degrees of freedom and reasonable limits on coupli ng strength and phonon spectra. Models with coupling to non-linear tun neling modes in a strongly anharmonic multi-well lattice potential and realistic coupling strengths have effectively larger isotopic mass de pendences and may therefore account for the observed magnitudes of alp ha.