Probing Superexchange Interactions in Spin Ice Ho$_2$Ti$_2$O$_7$ Thin Films

We report on a study of the structural and magnetic properties of strained Ho$_2$Ti$_2$O$_7$ thin films. Structural characterization via lab-based and synchrotron x-ray diffraction confirms the epitaxial growth of our films and shows a critical thickness slightly below 50 nm. Neutron scattering maps of our films show a $Q = 0$ structure indicating that the spin ice physics is preserved in the films. Magnetization measurements with a field applied in the film plane confirm this and show markedly linear behavior in the $\chi T~ vs. \ 1/T$ curve for $2~\text{K} \leq T \leq 5~\text{K}$ similar to that previously observed by others in single crystals. Furthermore, for fields applied along the [111] direction, out of the film plane, we observe a more parabolic behavior, which is treated as two linear regions with an interesting slope change around 3 K that could be a signature of the transition to the paramagnetic `hot' phase reported by others in single crystals. From the linear regions we extract the value for nearest neighbor superexchange interactions (J$_S$) between the Ho ions. We find similar values compared to reported bulk values for the interaction strength, again signaling the preservation of spin ice physics in strained thin films.