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

Abstract

The Ce$_2$X$_2$O$_7$ (X=Sn, Hf, Zr) family of cubic pyrochlores has emerged as one of the most promising classes of Quantum Spin Ice candidates. However, understanding their microscopic exchange Hamiltonian and spin correlations has been hampered by varying sample quality, and poor signal-to-noise in the existing neutron data due to a small Ce$^{3+}$ magnetic dipole moment. In this work, we overcome these challenges and report single-crystal diffuse neutron scattering from hydrothermally grown Ce$_2$Sn$_2$O$_7$ -- the highest quality crystals obtained to date for the Ce$_2$X$_2$O$_7$ family. In contrast to the broad diffuse scattering observed in Ce$_2$Hf$_2$O$_7$ and Ce$_2$Zr$_2$O$_7$, we find highly structured diffuse scattering from Ce$_2$Sn$_2$O$_7$ featuring strong intensities along the Brillouin zone boundaries. The observed $\mathbf{Q}$-dependence disagrees with predictions of the nearest neighbour XYZ model commonly used for Ce$_2$X$_2$O$_7$, but is remarkably similar to the diffuse scattering observed in \textit{classical} Dipolar Spin Ice. Our study highlights the importance of further neighbour interactions in determining the low energy physics of the Ce-pyrochlores, and calls for a revision of the current theoretical framework to incorporate their effects.

Figures (3)

• Figure 1: Ce$_2$Sn$_2$O$_7$ diffuse neutron scattering in the (a,c) HHL and (b,d) HK0 plane at (a,b) 50 mK and (c,d) 800 mK. A 12 K background has been subtracted from all the data. The data in (a,c)/(b,d) is obtained by integrating the diffuse intensity in the [H,-H,0]/[0,0,L] direction with $-0.2<\mathrm{H}<0.2$/$-0.2<\mathrm{L}<0.2$, and has been symmetrized in accordance with the $Fd\Bar{3}m$ space group. The white lines denote the Brillouin zone boundaries of the primitive FCC lattice.
• Figure 2: Powder-averaged diffuse scattering intensity as a function of $|\mathbf{Q}|$ at 50 mK and 800 mK obtained by performing an orientational average of the symmetrized single crystal data in the [H+0.5,H-0.5,L] plane (inset). To avoid the Ce$_2$Sn$_2$O$_7$ nuclear Bragg peaks, we used an integration range of $0.3<\mathrm{H}<0.7$ in the [H,-H,0] direction. A 12 K background has been subtracted from both the single crystal and powder-averaged data. Powder rings due to aluminum sample can of the dilution insert and the copper sample mount have also been masked out in the data.
• Figure 3: (a-d) Diffuse scattering in the [H,H,L] plane in (a) Ce$_2$Sn$_2$O$_7$ at 50mK, (b) Ce$_2$Zr$_2$O$_7$ at 50mK, (c) Nd$_2$Zr$_2$O$_7$ at 450mK and (d) Dy$_2$Ti$_2$O$_7$ at 300mK. A high temperature background at 12 K/5 K/20 K has been subtracted from (a)/(b)/(c), but not (d). (a) is the same as Fig. \ref{['Ce2Sn2O7large']} (a). (b) is part of the CORELLI data set previously published in Ref. EvanSmith_PRX_2025_Ce2Zr2O7. (c) and (d) are adapted from Ref. PRL_BellaLake_2020_Nd2Zr2O7 and Ref. Bramwell_PRL_2008, with permissions from the American Physical Society. (e,f) Diffuse scattering intensity as a function of momentum transfer along (e) [0,0,L] and (f) [H,H, 2.375] in Ce$_2$Sn$_2$O$_7$ (blue open circle) and Dy$_2$Ti$_2$O$_7$ (red solid square), with intensity scales shown on the left and right vertical axes, respectively. The directions of the momentum transfers are shown as black solid lines in (d). The Ce$_2$Sn$_2$O$_7$ data in (e) and (f) are obtained by slicing the single crystal data in (a) with an integration range of $-0.2 < \mathrm{H} < 0.2$ along [H,H,0] and $2.2 < \mathrm{L} < 2.55$ along [0,0,L], respectively. The Dy$_2$Ti$_2$O$_7$ data have been adapted from Ref. Fennell_PRB_2004 with permissions from the American Physical Society.