Quantum Spin Ice Response to a Magnetic Field in the Dipole-Octupole Pyrochlore Ce${}_2$Zr${}_2$O${}_7$

Abstract

We report new heat capacity measurements on single crystal Ce${}_2$Zr${}_2$O${}_7$ down to $\sim$ 0.1 K in a magnetic field along the $[1,\bar{1},0]$ direction. These new measurements show that the broad hump in the zero-field heat capacity moves higher in temperature with increasing field strength and is split into two humps by the $[1,\bar{1},0]$ field at $\sim$ 2 T. These separate features are due to the decomposition of the pyrochlore lattice into effectively decoupled chains for fields in this direction: one set of chains ($\alpha$-chains) is polarized by the field while the other ($\beta$-chains) remains free. Our theoretical modelling suggests that the $\beta$-chains are close to a critical state, with nearly-gapless excitations. We also report new elastic and inelastic neutron scattering measurements on single crystal Ce${}_2$Zr${}_2$O${}_7$ in $[1,\bar{1},0]$ and $[0,0,1]$ magnetic fields at temperatures down to 0.03 K. The elastic scattering behaves consistently with the formation of independent chains for a $[1,\bar{1},0]$ field, while the $[0,0,1]$ field produces a single field-induced magnetic Bragg peak at $(0,2,0)$ and equivalent wavevectors, indicating a polarized spin ice for fields above $\sim$ 3 T. For both $[1,\bar{1},0]$ and $[0,0,1]$ fields, our inelastic neutron scattering results show an approximately-dispersionless continuum of scattering that increases in both energy and intensity with increasing field strength. By modelling the complete set of experimental data using numerical linked cluster and semiclassical molecular dynamics calculations, we demonstrate the dominantly multipolar nature of the exchange interactions in Ce${}_2$Zr${}_2$O${}_7$ and the smallness of the parameter $\theta$ which controls the mixing between dipolar and octupolar degrees of freedom. These results support previous estimates of the microscopic exchange parameters.

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• Kitaev Quantum Spin Liquids
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• Emergent photons and fractionalized excitations in a quantum spin liquid
• Distinguishing thermodynamics and spectroscopy for octupolar U(1) spin liquid of Ce-pyrochlores
• 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${}_7$
• Theory of rare-earth Kramers magnets on a Shastry-Sutherland lattice: dimer phases in presence of strong spin-orbit coupling
• Signatures of spinon dynamics and phase structure of dipolar-octupolar quantum spin ices in two-dimensional coherent spectroscopy
• Thermodynamics of the dipole-octupole pyrochlore magnet Ce${}_2$Hf${}_2$O${}_7$ in applied magnetic fields
• Two-Peak Heat Capacity Accounts for $R\ln (2)$ Entropy and Ground State Access in the Dipole-Octupole Pyrochlore Ce${}_2$Hf${}_2$O${}_7$
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