Magnetic collective mode in underdoped cuprates: a phenomenological analysis

Abstract

The dynamical spin susceptibility as relevant for underdoped cuprates is analysed within the memory-function (MeF) approach. A phenomenological damping function combined with a $T$-independent sum rule is used to describe the anomalous normal state and the resonant peak in the superconducting state, in particular its position and its relative intensity to the normal state. The relation with the random-phase approximation is discussed. The MeF method is generalized to the bilayer system in order to compare with inelastic neutron scattering experiments on YBa$_2$Cu$_3$O$_{6+x}$ which alows also for a quantitative comparison. In this context the problem of missing integrated spectral intensity within the experimentally accessible energy window is also discussed.