Incommensurate spin dynamics in underdoped cuprate perovskites

TL;DR

This paper models incommensurate spin dynamics in underdoped cuprate perovskites using the t-J model, explaining experimental susceptibility dispersion with two parabolas and analyzing the effects of doping, hole bandwidth, and damping.

Contribution

It provides a theoretical interpretation of incommensurate magnetic response in cuprates based on the projection operator formalism and the t-J model, matching experimental dispersion features.

Findings

Dispersion of susceptibility maxima forms two parabolas converging at the antiferromagnetic wave vector.

The upper parabola is related to localized Cu spin excitations.

The lower parabola arises from a dip in spin-excitation damping near the wave vector.

Abstract

The incommensurate magnetic response observed in normal-state cuprate perovskites is interpreted based on the projection operator formalism and the t-J model of Cu-O planes. In agreement with experiment the calculated dispersion of maxima in the susceptibility has the shape of two parabolas with upward and downward branches which converge at the antiferromagnetic wave vector. 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 magnetic excitations of the localized Cu spins, while the lower parabola arises due to a dip in the spin-excitation damping at the antiferromagnetic wave vector. For moderate doping this dip stems from the weakness of the interaction between the spin excitations and holes near the hot spots. The frequency dependence of the susceptibility is shown to depend strongly on the hole bandwidth and damping and varies from the shape observed in YBa$_2$Cu$_3$O$_{7-y}$ to that inherent in La$_{2-x}$Sr$_x$CuO$_4$.