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 Nd2Zr2O7.
Introduction.A central challenge in the study of frustrated magnets is to identify features which can be used to distinguish between different types of magnetic states, in the absence of conventional long-range magnetic order [1, 2]. In this context, any robust feature observed in more than one system is of potential interest as a witness to the underlying physics. A prime example is provided by "pinch points" -singular, bowtie-like motifs in the spin structure factor, characteristic of "Coulombic" phases with an emergent gauge symmetry [3][4][5][6][7]. Pinch points have famously been observed in neutron-scattering experiments on spin ice [8], a wide range of other pyrochlore magnets [9, 10], and in simulations of, e.g., kagome-lattice antiferromagnets [11][12][13].
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