Supplementary mMaterial

Figures S1- S4 can be found in the supplementary material. Figure S1 visually represents the different strain types in RIG thin films resulting from lattice mismatch between the substrates and films. Figure S2 presents the rocking curves, out-of-plane magnetization hysteresis measurements, and AFM images. Figure S3 includes the XRD, RSM, and spin wave transmission data for LuIG/SGGG thin films, where the film thickness exceeds the critical thickness. Figure S4 illustrates the distribution of potential energy in bonds as a function of interatomic spacing. Additionally, the methods for calculating strain-induced magnetic anisotropy are discussed. Note S5 demonstrates the calculation of strain-induced anisotropy field, HA, and effective perpendicular anisotropy field, HPMAeff. Supplementary note S6 and Figure S6 demonstrate the ESR linewidth broadening in RIG thin films. Supplementary note S7 and Figure S7 demonstrate the estimation of magnetocrystalline anisotropy from the angle-resolved in-plane ESR measurements.