Accessing Few-Layer CrI$_3$ Magnetoelasticity Through Bulk Single Crystals
The persistence of ferromagnetic long-range order in monolayers of the van der Waals semiconductor CrI$_3$ opens new routes for spintronic applications based on two-dimensional quantum magnets. In the fabrication of such devices, the constituent materials inevitably experience anisotropic strain, which modifies their intrinsic electronic properties. At the same time, strain can serve as a powerful tuning parameter, driving the material to desired regimes. While several theoretical studies have investigated the effect of biaxial in-plane strain on CrI$_3$ numerically, experiments are widely limited to the application of hydrostatic pressure. Here, we perform high-resolution magnetostriction experiments on bulk CrI$_3$ samples, and \textit{ab-initio}-based magnetoelastic calculations, to elucidate the role of uniaxial lattice strain on the magnetic properties. Our data show that magnetostriction in CrI$_3$ is unexpectedly sensitive to surface effects, which enables us to investigate the influence of in-plane and out-of-plane strain separately, in both the bulk ferromagnetic (BFM) phase emerging at $T_{\rm C}=61\,\mathrm{K}$ and the surface antiferromagnetic (SAFM) phase below $T^* \simeq 50\,\mathrm{K}$. In particular, we quantify the uniaxial strain dependence of the surface interlayer coupling $J^{\rm SAFM}_{\perp}$ and the surface spin-flip field $B^*$, which drastically exceed the strain effects in the BFM phase by a factor of $\sim 30$. The large magnetostrictive response allows us to study the magnetoelastic coupling in few-layer CrI$_3$ through experiments on bulk single crystals, without requiring exfoliation.