Hierarchy of energy scales and field-tunable order by disorder in dipolar-octupolar pyrochlores

Abstract

Dipolar-octupolar pyrochlore magnets in a strong external magnet field applied in the [110] direction are known to form a "chain"state, with subextensive degeneracy. Magnetic moments are correlated along one-dimensional chains carrying effective Ising degrees of freedom which are noninteracting on the mean-field level. Here we investigate this phenomenon in detail, including the effects of quantum fluctuations. We identify two distinct types of chain phases, both featuring distinct subextensive, classical ground-state degeneracy. Focusing on one of the two kinds, we discuss lifting of the classical degeneracy by quantum fluctuations. We map out the ground-state phase diagram as a function of the exchange couplings, using linear spin wave theory and real-space perturbation theory. We find a hierarchy of energy scales in the ground-state selection, with the effective dimensionality of the system varying in an intricate way as the hierarchy is descended. We derive an effective two-dimensional anisotropic triangular lattice Ising model with only three free parameters which accounts for the observed behavior. Connecting our results to experiment, they are consistent with the observation of a disordered chain state in Nd2Zr2O7. We also show that the presence of two distinct types of chain phases has consequences for the field-induced breakdown of the apparent U(1) octupolar quantum liquid phase recently observed in Ce2Sn2O7.