Figure 7: Reciprocal space mapping of bulk and epitaxial films of spin ices.

Here, Q_x and Q_z are the components of the reciprocal space vector along the [00l] and [hh0] directions, respectively. The plot shows the positions in reciprocal space of the (553) reciprocal lattice point for bulk Y₂Ti₂O₇ (grey dot) and Dy₂Ti₂O₇ (red triangle) based on tabulated lattice parameters³⁸. Both lie along the line for the cubic lattice (dotted line). The experimental data (Fig. 1b) show how the substrate maintained the expected cubic structure (upper black dot), with only a very slightly different lattice constant. The Dy₂Ti₂O₇ film (lower black dot), however, is strained along the [00l] direction – see text for the details. For completeness, the reciprocal (553) reciprocal lattice point for a hypothetical fully relaxed film (blue inverted triangle) is shown, assuming the cubic structure but with lattice constant obtained from the symmetric (440) reflection (Fig. 5). Note that error bars are within the symbol size.