Neutron scattering investigation of the spin ice state in ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$

${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ has been advanced as an ideal spin ice material. We present a neutron scattering investigation of a single-crystal sample of ${}^{162}\mathrm{Dy}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. The scattering intensity has been mapped in zero applied field in the $h,h,l$ and $h,k,0$ planes of reciprocal space at temperatures between 0.05 and $20\mathrm{K}$. The measured diffuse scattering has been compared with that predicted by the dipolar spin ice model. The comparison is good, except at the Brillouin-zone boundaries where extra scattering appears in the experimental data. It is concluded that the dipolar spin ice model provides a successful basis for understanding ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, but that there are issues which remain to be clarified.

Figure 1

Top: a unit cell of the pyrochlore lattice which consists of four interpenetrating face centered cubic (fcc) Bravais sublattices. Two spins related by an fcc translation are shown with antiferromagnetic correlation. Correlations of this type give rise to the zone-boundary scattering observed experimentally. Bottom: the spin ice state on a single tetrahedron (bottom). A macroscopic spin ice state is constructed by stacking such local arrangements on the lattice.

Figure 2

(Color online) ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$: Diffuse scattering in the $h,h,l$ plane measured at $20\mathrm{K}$ (top left), $1.3\mathrm{K}$ (top right), and $0.3\mathrm{K}$ (bottom left, with zone boundaries illustrated). The sharp, intense spots are nuclear Bragg reflections with no magnetic intensity. The map at $20\mathrm{K}$ was recorded using an average scattering angle of $\varphi =48°$ which gives stronger arc-shaped artefacts for small $\mid \mathbf{Q}\mid$ values compared to $\varphi =32°$. The result of the Monte Carlo simulation of the dipolar spin ice model at $0.3\mathrm{K}$ is shown at bottom right.

Figure 3

(Color online) ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at $0.05\mathrm{K}$: experimental scattering intensity in the $h,k,0$ plane (left), compared with that calculated from Monte Carlo simulations (right).

Figure 4

${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at $0.03\mathrm{K}$: comparison of experimental and Monte Carlo data for $h,k,0$ and $h,h,l$ planes. The comparison in the $h,k,0$ plane is shown at top left using a slice along $3,k,0$. The Monte Carlo data was compared to the experimental data by adjusting an overall intensity scale parameter and single backward parameter in order to give the best fit. The comparisons for the $h,h,l$ plane are slices along $h,h,0$ (top right), $0,0,l$ (bottom left), and along $h,h,2.3$ (bottom right). For slices 2 and 3 the Monte Carlo data were compared using an overall intensity scale parameter and sloping backward, slice 4 was compared with an overall intensity scale parameter and constant background. The slice positions in the scattering plane are indicated in the insets, and for the $h,h,l$ plane by numbers 2–4. Shaded areas in the slices are Bragg peaks from the sample and were excluded from the fitting.