The interplay between epitaxial strain, magnetic compensation, Curie temperature, and anisotropy in ferrimagnetic insulators remains a central question with both fundamental and technological significance. Here, we present a comparative theoretical study of strain effects on ${\mathrm{Gd}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ (GIG) thin films grown along [001] and [111] orientations. Using density functional theory and an ab initio-based effective Hamiltonian, we study the evolution of the magnetic compensation temperature ($T_M$), Curie temperature ($T_C$), and perpendicular magnetic anisotropy (PMA) under epitaxial strain. Our results show a linear enhancement of both $T_M$ and $T_C$ under compressive strain, with (001)-oriented films exhibiting a notably higher strain sensitivity than (111)-oriented counterparts. PMA was also found to have a nearly linear strain dependence with a strong orientation dependence, and to reverse when Gd $4f$ electrons were treated as core states—hinting at a possible strong temperature dependence of PMA. Our results offer clarity to experimental variability in $T_M$ and provide a microscopic basis for tailoring magnetic compensation, Curie temperature and anisotropy in rare-earth-based spintronics.

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• Ferrimagnetism
• Magnetic anisotropy
• Magnetic interactions
• Magnetism
• Ferrimagnets
• Density functional theory
• Monte Carlo methods