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

Abstract

We present a theory for the temperature and frequency dependence of the spin susceptibility ${\chi }^{″}$ in the presence of superconducting phase fluctuations. Our scenario, which is based on the spin-fermion model provides an explanation for the presence of a resonance peak above $T_c,$ as observed by inelastic neutron scattering experiments in the underdoped cuprates. Within the same framework we show that the ${}^{63}\mathrm{Cu}$ spin-lattice relaxation time $T_1$ directly probes the strength of phase fluctuations. A comparison of our theoretical results with the experimental NMR data on underdoped Bi-2212 suggests that phase fluctuations exist only in limited temperature range above $T_c$ in agreement with recent experiments by Corson et al.