Yttrium iron garnet (${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$) is a prototypical ferrimagnetic insulator widely used in spin-wave and magnonic devices owing to its extremely low magnetic damping and long magnon propagation length, and recent experiments suggest that lattice vibrations can influence magnetic properties, motivating a microscopic understanding of how phonons modify exchange interactions. In this work, phonon-driven tuning of exchange interactions in ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ is investigated from a mode-resolved perspective based on first-principles calculations. We focus on how optical phonons modify the dominant superexchange pathways and how lattice distortions affect the Fe-O-Fe bond geometry that governs the exchange interaction. To this end, phonon modes are computed from density functional theory, and the exchange interactions are evaluated from a Wannier-based tight-binding model and mapped onto a spin Hamiltonian, while displaced structures along individual infrared-active modes are used to quantify their impact on the magnetic interactions.

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• Exchange interaction
• Magnons
• Phonons
• Magnetic systems
• First-principles calculations