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. Focussing 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 Nd${}_2$Zr${}_2$O${}_7$. 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 Ce${}_2$Sn${}_2$O${}_7$.

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• Quantum Spin Ice Response to a Magnetic Field in the Dipole-Octupole Pyrochlore Ce${}_2$Zr${}_2$O${}_7$
• $\mu$SR Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce${}_2$Zr${}_2$O${}_7$
• Order-by-disorder without quantum zero-point fluctuations in the pyrochlore Heisenberg ferromagnet with Dzyaloshinskii-Moriya interactions
• A pseudofermion functional renormalization group study of dipolar-octupolar pyrochlore magnets
• Finite Temperature Dynamics in 0-Flux and $\pi$-Flux Quantum Spin Ice: Self-Consistent Exclusive Boson Approach
• Exploiting polarization dependence in two dimensional coherent spectroscopy: examples of Ce${}_2$Zr${}_2$O${}_7$ and Nd${}_2$Zr${}_2$O${}_7$
• Dipolar-octupolar correlations and hierarchy of exchange interactions in Ce${}_2$Hf${}_2$O${}_7$
• Spin ice in a general applied magnetic field: Kasteleyn transition, magnetic torque and rotational magnetocaloric effect
• Thermodynamics of the dipole-octupole pyrochlore magnet Ce${}_2$Hf${}_2$O${}_7$ in applied magnetic fields
• Field-temperature phase diagram of the enigmatic Nd${}_2$(Zr${}_{1-x}$Ti${}_x$)${}_2$O${}_7$ pyrochlore magnets
• Programmable order by disorder effect and underlying phases through dipolar quantum simulators