Half moons are pinch points with dispersion

TL;DR

This paper unifies the phenomena of pinch points and half moons in spin liquids, showing that half moons are pinch points on dispersing bands, supported by simulations and experimental data on Nd$_2$Zr$_2$O$_7$.

Contribution

It introduces a unified framework linking pinch points and half moons, revealing half moons as pinch points on dispersing excitation bands in spin liquids.

Findings

Half moons are pinch points on dispersing bands.

Simulations show evolution of bands into spin liquid states.

Theory reproduces experimental features in Nd$_2$Zr$_2$O$_7$.

Abstract

"Pinch points," singular features observed in (quasi-)elastic neutron scattering, are a widely discussed hallmark of spin liquids with an emergent gauge symmetry. Much less attention has been paid to "half moons," distinctive crescent patterns at finite energy, which have been observed in experiments on a number of pyrochlore magnets, and in a wide range of model calculations. Here we unify these two phenomena within a single framework, paying particular attention to the case of ordered, or field-saturated states, where pinch points and half moons can be found in bands of excitations above a gap. We find that half moons are nothing other than pinch points inscribed on a dispersing band. Molecular dynamics simulations of the kagome lattice antiferromagnet are used to explore how these bands evolve into the ground state and excitations of a classical spin liquid. We explicitly demonstrate that this theory can reproduce the pinch points and half moons observed in Nd$_2$Zr$_2$O$_7$.