  Spin-liquid states are often described as the antithesis of magnetic order.
Recently, however, it has been proposed that in certain frustrated magnets the
magnetic degrees of freedom may "fragment" in such a way as to give rise to a
coexistence of spin liquid and ordered phases. Recent neutron-scattering
results [S. Petit, E. Lhotel, B. Canals, M. Ciomaga Hatnean, J. Ollivier, H.
Muttka, E. Ressouche, A. R. Wildes, M. R. Lees, and G. Balakrishnan, Nat. Phys.
12, 746 (2016)] suggest that this scenario may be realized in the pyrochlore
magnet Nd2Zr2O7. These observations show the characteristic pinch-point
features of a Coulombic spin liquid occurring alongside the Bragg peaks of an
"all-in-all-out" ordered state. Here we explain the quantum origins of this
apparent magnetic moment fragmentation, within the framework of a quantum model
of nearest-neighbor exchange, appropriate to Nd2Zr2O7. This model is able to
capture both the ground-state order and the pinch points observed at finite
energy. The observed fragmentation arises due to the combination of the unusual
symmetry properties of the Nd3+ ionic wave functions and the structure of
equations of motion of the magnetic degrees of freedom. The results of our
analysis suggest that Nd2Zr2O7 is proximate to a U(1) spin-liquid phase and is
a promising candidate for the observation of a Higgs transition in a magnetic
system.
