Magnetic Excitations of Stripes and Checkerboards in the Cuprates

TL;DR

This paper models magnetic excitations in stripe and checkerboard phases of cuprates, linking theoretical predictions to neutron scattering experiments and highlighting the resonance peak's possible origin.

Contribution

It introduces a detailed Heisenberg model analysis of magnetic excitations in stripe and checkerboard phases, connecting theoretical results with experimental neutron scattering data.

Findings

Satellite peaks are significantly suppressed in stripe phases.

Spin wave cones may be unresolved at low energies depending on coupling.

A saddlepoint at (π,π) could explain the resonance peak in experiments.

Abstract

We discuss the magnetic excitations of well-ordered stripe and checkerboard phases, including the high energy magnetic excitations of recent interest and possible connections to the "resonance peak" in cuprate superconductors. Using a suitably parametrized Heisenberg model and spin wave theory, we study a variety of magnetically ordered configurations, including vertical and diagonal site- and bond-centered stripes and simple checkerboards. We calculate the expected neutron scattering intensities as a function of energy and momentum. At zero frequency, the satellite peaks of even square-wave stripes are suppressed by as much as a factor of 34 below the intensity of the main incommensurate peaks. We further find that at low energy, spin wave cones may not always be resolvable experimentally. Rather, the intensity as a function of position around the cone depends strongly on the coupling across the stripe domain walls. At intermediate energy, we find a saddlepoint at $(\pi,\pi)$ for a range of couplings, and discuss its possible connection to the "resonance peak" observed in neutron scattering experiments on cuprate superconductors. At high energy, various structures are possible as a function of coupling strength and configuration, including a high energy square-shaped continuum originally attributed to the quantum excitations of spin ladders. On the other hand, we find that simple checkerboard patterns are inconsistent with experimental results from neutron scattering.