Strain-Tunable Magnetic Compensation Temperature of Epitaxial Tb$_3$Fe$_5$O$_{12}$ Thin Films

High-quality rare-earth iron garnet (ReIG) Tb$_3$Fe$_5$O$_{12}$ (TbIG) thin films are epitaxially grown on a series of (111)-oriented garnet substrates with various lattice constants. The coherent growth induces a substrate-dependent in-plane tensile or compressive strain in the TbIG film. Measurements of the anomalous Hall-like effect (AHLE) in TbIG/Pt heterostructures show that the compensation temperature of TbIG films monotonically changes with the film strain. The strain results in a variation of the distances between magnetic atoms in the TbIG crystal and therefore the corresponding exchange interactions. The latter is explicitly calculated as a function of the lattice strain based on density functional theory, reproducing the observed experimental results. This work provides a versatile way to optimize ReIG-based spin-orbit torque devices.