The quantum origins of moment fragmentation in Nd2Zr2O7
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.