Incommensurate spin dynamics in underdoped cuprate perovskites

摘要

The incommensurate magnetic response observed in normal-state cuprateperovskites is interpreted based on the projection operator formalism and thet-J model of Cu-O planes. In agreement with experiment the calculateddispersion of maxima in the susceptibility has the shape of two parabolas withupward and downward branches which converge at the antiferromagnetic wavevector. The maxima are located at the momenta $({1/2},{1/2}\pm\delta)$,$({1/2}\pm\delta,{1/2})$ and at $({1/2}\pm\delta,{1/2}\pm\delta)$,$({1/2}\pm\delta,{1/2}\mp\delta)$ in the lower and upper parabolas,respectively. The upper parabola reflects the dispersion of magneticexcitations of the localized Cu spins, while the lower parabola arises due to adip in the spin-excitation damping at the antiferromagnetic wave vector. Formoderate doping this dip stems from the weakness of the interaction between thespin excitations and holes near the hot spots. The frequency dependence of thesusceptibility is shown to depend strongly on the hole bandwidth and dampingand varies from the shape observed in YBa$_2$Cu$_3$O$_{7-y}$ to that inherentin La$_{2-x}$Sr$_x$CuO$_4$.