Magnetic frustration leads to the emergence of diverse exotic behaviors, and the study of their theories and phenomenology is crucial. For example, sophisticated understanding has been established for models with underlying U(1) symmetry and the associated pinch-point features in their spin-spin correlations.
However, this turned out to be only half the story. Attached to the pinch points, there exists another highly universal feature in the shape of two “half moons” in a wide range of frustrated magnetic models and recent experiments on Nd₂Zr₂O₇.
In this work we establish its theoretical interpretation, which turned out to be a hidden side of the pinch-points. It is a result of decomposition and decoupling of the emergent magnetic field in the system, which leads to an extra pinch point on the dispersive band. The half moons are essentially the pinch points seen on a constant energy cross-section.

This work was published as “Half moons are pinch points with dispersion”, Han Yan, Rico Pohle and Nic Shannon, Phys. Rev. B, 98 140402(R) (2018). It was also singled out as an Editor’s Suggestion, and for inclusion in Kalaidascope.