Single Crystal Diffuse Neutron Scattering Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce\(_2\)Zr\(_2\)O\(_7\): No Apparent Octupolar Correlations Above \(T = 0.05\) K

The insulating magnetic pyrochlore Ce\(_2\)Zr\(_2\)O\(_7\) has gained attention as a quantum spin ice candidate with dipole-octupole character that arises from the crystal electric field ground state doublet for the Ce\(^{3+}\) Kramers ion. This permits both spin ice phases based on magnetic dipoles and those based on more-exotic octupoles. This work reports low-temperature neutron diffraction measurements on single crystal Ce\(_2\)Zr\(_2\)O\(_7\) with \(Q\)-coverage both at low \(Q\) where the magnetic form factor for dipoles is near maximal and at high \(Q\) covering the region where the magnetic form factor for Ce\(^{3+}\) octupoles is near maximal. This study was motivated by recent powder neutron diffraction studies of other Ce-based dipole-octupole pyrochlores, Ce\(_2\)Sn\(_2\)O\(_7\) and Ce\(_2\)Hf\(_2\)O\(_7\), which each showed temperature-dependent diffuse diffraction at high \(Q\) that was interpreted as arising from octupolar correlations. Our measurements use an optimized single crystal diffuse scattering instrument that allows us to screen against strong Bragg scattering from Ce\(_2\)Zr\(_2\)O\(_7\). The temperature-difference neutron diffraction reveals a low-\(Q\) peak consistent with dipolar spin ice correlations reported in previous work, and an alternation between positive and negative net intensity at higher \(Q\). These features are consistent with our numerical-linked-cluster calculations using pseudospin interaction parameters previously reported for Ce\(_2\)Zr\(_2\)O\(_7\), Ce\(_2\)Sn\(_2\)O\(_7\), and Ce\(_2\)Hf\(_2\)O\(_7\). Importantly, neither the measured data nor any of the NLC calculations show evidence for increased scattering at high \(Q\) resulting from octupolar correlations. We conclude that at the lowest attainable temperatures for our measurement (\(T = 0.05\) K), octupolar correlations are not present in Ce\(_2\)Zr\(_2\)O\(_7\) on the level of our observation threshold of \(\sim\) 0.1\(\%\) of the low-\(Q\) dipole scattering.