Quantum spin ice response to a magnetic field in the dipole-octupole pyrochlore <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ce</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Zr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>7</mml:mn></mml:msub></mml:mrow></mml:math>

The pyrochlore magnet ${\mathrm{Ce}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ has attracted much attention as a quantum spin ice candidate whose novelty derives in part from the dipolar-octupolar nature of the ${\mathrm{Ce}}^{3+}$ pseudospin-1/2 degrees of freedom it possesses. We report heat capacity measurements on single crystal samples of ${\mathrm{Ce}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ down to $T\ensuremath{\sim}0.1\phantom{\rule{4pt}{0ex}}\mathrm{K}$ in a magnetic field along the $[1,\overline{1},0]$ direction. These 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 separate humps by the $[1,\overline{1},0]$ magnetic field at $\ensuremath{\sim}2\phantom{\rule{0.28em}{0ex}}\mathrm{T}$. 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 ($\ensuremath{\alpha}$ chains) is polarized by the field while the other ($\ensuremath{\beta}$ chains) remains free. This situation is similar to that observed in the classical spin ices ${\mathrm{Ho}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{Dy}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, but with the twist that here the strong transverse exchange interactions produce substantial quantum effects. Our theoretical modeling suggests that the $\ensuremath{\beta}$ chains are close to a critical state, with nearly-gapless excitations. We also report elastic and inelastic neutron scattering measurements on single crystal ${\mathrm{Ce}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ in $[1,\overline{1},0]$ and $[0,0,1]$ magnetic fields at temperatures down to $T=0.03\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. The elastic scattering behaves consistently with the formation of independent chains for a $[1,\overline{1},0]$ field, while the $[0,0,1]$ field produces a single field-induced elastic magnetic Bragg peak at $(0,2,0)$ and equivalent wavevectors, indicating a polarized spin ice state for fields above $\ensuremath{\sim}3\phantom{\rule{4pt}{0ex}}\mathrm{T}$. For both $[1,\overline{1},0]$ and $[0,0,1]$ magnetic 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 modeling 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 ${\mathrm{Ce}}_{2}{\mathrm{Zr}}_{2}{\mathrm{O}}_{7}$ and the smallness of the parameter $\ensuremath{\theta}$, which controls the mixing between dipolar and octupolar degrees of freedom. These results support previous estimates of the microscopic exchange parameters and place strong constraints on the theoretical description of this prominent spin ice candidate.

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