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

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 $\mathrm{N}{\mathrm{d}}_2\mathrm{H}{\mathrm{f}}_2{\mathrm{O}}_7$ 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'.

arXiv comment8 pages, 5 figures

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