Magnetic moment fragmentation and dynamical spin ice features in Neodymuim pyrochlores

Neodymium pyrochlores show rich, complex and exotic physical phenomena. The Nd³⁺ ions have a well-isolated ground state doublet with octupolar-dipolar symmetry and they interact with each other via highly anisotropic exchange interactions. We have studied two members of this family Nd₂Zr₂O₇ and Nd₂Hf₂O₇. Both show long-range all-in-all-out antiferromagnetic order revealing broken gauge symmetry in the ground state. The lowest energy excitations form a flat, gapped mode with a pinch-point structure factor suggesting a proximate gauge symmetry leading to dynamical spin ice. At higher energies there are dispersive spin-wave modes which touch the flat mode, at the pinch points. They have a pinch point pattern of their own which is rotated with respect to that of the flat mode and which give rise to half-moon features in constant energy slices. The coexistence of long-range magnetic order, the pinch-point mode and half-moon features originate from fragmentation of the Nd³⁺ magnetic moment into divergence-free and divergence-full parts. Finally at temperatures just above the Neel temperature, the pinch point mode becomes gapless and the spin-waves broaden suggesting a spinon continuum.