Theory of the hourglass dispersion of magnetic excitations in high-T$_c$ cuprates

TL;DR

This paper presents a comprehensive theory explaining the hourglass-shaped dispersion of magnetic excitations in high-temperature cuprate superconductors across different doping levels, integrating spin fluctuations and local spin rotations.

Contribution

It introduces a unified theoretical framework combining RPA and mode-coupling theory to describe magnetic excitations in cuprates across doping regimes.

Findings

Reproduces the hourglass dispersion observed experimentally at intermediate doping.

Reduces to RPA at large doping and spin wave theory at low doping.

Predicts two excitation branches dispersing upwards and downwards.

Abstract

A theory for the dispersion of collective magnetic excitations in superconducting cuprates is presented with the aim to cover both high and low doping regimes. Besides of spin fluctuations describable in the random phase approximation (RPA) we allow for local spin rotations within a mode-coupling theory. At low temperatures and moderately large correlation lengths we obtain two branches of excitations which disperse up- and downwards exhibiting the hourglass behavior observed experimentally at intermediate dopings. At large and small dopings our theory essentially reduces to the RPA and spin wave theory, respectively.