Observation of Dipolar Spin-ice--like Correlations in the Quantum Spin Ice Candidate Ce$_2$Sn$_2$O$_7$

We report diffuse scattering measurements on the dipolar-octupolar pyrochlore, Ce$_2$Sn$_2$O$_7$, to elucidate its magnetic correlations within the correlated paramagnetic regime above its ordering temperature, $\mathrm{T_N}\sim 40~$mK. The magnetic transition at $\mathrm{T_N}$, observed in recent specific heat measurements, has been interpreted within the nearest-neighbor XYZ model as a transition into an all-in-all-out (AIAO) magnetic order. However, the observed diffuse scattering above $\mathrm{T_N}$ argues against an AIAO magnetic order by exhibiting $no$ short-range order at the AIAO wave-vectors, inconsistent with the nearest neighbor model. Instead, the observed diffuse scattering strongly resembles that observed in classical dipolar spin ice, Dy$_2$Ti$_2$O$_7$, and suggests the presence of short-range correlated structures such as chains, or clusters in the low energy manifold of Ce$_2$Sn$_2$O$_7$, favored by further neighbor interactions. We discuss how chain-like states qualitatively account for the observed H-T phase diagram under a [1,1,0]-field.