Pinch points and half-moons in dipolar-octupolar Nd$_2$Hf$_2$O$_7$

TL;DR

This paper investigates the complex magnetic excitations in Nd2Hf2O7, revealing coexistence of static order, pinch points, and dispersive modes, confirming theories about divergence-full and divergence-free components in spin ice systems.

Contribution

It demonstrates the coexistence of divergence-full and divergence-free magnetic features in Nd2Hf2O7, experimentally confirming theoretical predictions about half-moon and pinch point excitations.

Findings

Observation of static long-range magnetic order.

Detection of flat, gapped pinch point excitations.

Identification of dispersive modes with half-moon patterns.

Abstract

While it is established that the pinch point scattering pattern in spin ice arises from an emergent coulomb phase associated with magnetic moment that is divergence-free, more complex Hamiltonians can introduce a divergence-full part. If these two parts remain decoupled, they give rise to the co-existence of distinct features. Here we show that the moment in ${\rm Nd_2Hf_2O_7}$ forms a static long-range ordered ground state, a flat, gapped pinch point excitation and dispersive excitations. These results confirm recent theories which predict that the dispersive modes, which arise from the divergence-full moment, host a pinch point pattern of their own, observed experimentally as `half-moons'.