Dipolar spin ice regime proximate to an all-in-all-out N\'{e}el ground state in the dipolar-octupolar pyrochlore Ce$_2$Sn$_2$O$_7$
The dipolar-octupolar (DO) pyrochlores, R$_2$M$_2$O$_7$ (R = Ce, Sm, Nd), are key players in the search for realizable novel quantum spin liquid (QSL) states as a large parameter space within the DO pyrochlore phase diagram is theorized to host QSL states of both dipolar and octupolar nature. We present neutron diffraction measurements on newly synthesized hydrothermally-grown Ce$_2$Sn$_2$O$_7$ powders that show a broad signal at low scattering vectors, reminiscent of a dipolar spin ice. This is strikingly different from previous neutron diffraction on powder samples grown from solid-state synthesis, which found diffuse scattering at high scattering vectors associated with magnetic octupoles. This raises the question about subtle crystalline structural differences and in particular the potential role of disorder that is present in the different samples. We quantify any differences through complementary neutron structure refinement and atomic PDF measurements but detect no oxidation or other crystallographic disorder in the hydrothermally-grown samples. To interpret the new diffuse scattering, we characterize the exchange interaction parameters in the near-neighbor XYZ model Hamiltonian associated with DO pyrochlores by fitting quantum numerical linked cluster expansions (NLCE) to heat capacity and magnetic susceptibility measurements, and classical Monte Carlo calculations to the diffuse neutron diffraction of the newly synthesized Ce$_2$Sn$_2$O$_7$ samples. This places Ce$_2$Sn$_2$O$_7$'s ground state within the ordered dipolar all-in-all-out (AIAO) N\'{e}el phase with quantum Monte-Carlo calculations showing a transition to long-range order at temperatures below those accessed experimentally. We conclude that new hydrothermally-grown Ce$_2$Sn$_2$O$_7$ samples host a finite-temperature proximate dipolar spin ice phase, above the expected transition to AIAO N\'{e}el order.