Theory for the spin susceptibility in the pseudogap regime of the underdoped cuprates: Effect of phase fluctuations

We present a theory for the temperature and frequency dependence of the spi n susceptibility chi" in the presence of superconducting phase fluctuations . Our scenario, which is based on the spin-fermion model provides an explan ation for the presence of a resonance peak above T-1 as observed by inelast ic neutron scattering experiments in the underdoped cuprates. Within the sa me framework we show that the (CU)-C-63 spin-lattice relaxation time T-1 di rectly probes the strength of phase fluctuations. A comparison of our theor etical results with the experimental NMR data on underdoped Bi-2212 suggest s that phase fluctuations exist only in limited temperature range above T-c in agreement with recent experiments by Corson et al.