sections. Yttrium iron garnet (YIG) is extensively used for SW devices [11][12][13] because of its low intrinsic Gilbert damping, [14][15][16][17][18][19] but other materials with low Gilbert damping have been proposed, including Permalloy [20,21] and Heusler alloys. [22] However, films of low anisotropy materials such as YIG and Permalloy are typically magnetized in plane due to the dominant shape anisotropy and require a substantial external outof-plane magnetic field to saturate the film. This motivates the search for a magnetic material with a low Gilbert damping and a low out-of-plane saturation field, or ideally with a perpendicular magnetic anisotropy (PMA) that promotes an out-of-plane remanent magnetization, in order to realize integrated FV SW devices.The net magnetic anisotropy includes contributions from magnetocrystalline anisotropy, magnetoelastic anisotropy, and shape anisotropy. [9] In epitaxial films, magnetoelastic anisotropy can be tuned via the lattice mismatch with the substrate. Although YIG has only a modest magnetostriction, PMA was reported for 20 nm thick epitaxial YIG on a Sm 3 Ga 5 O 12 (SmGG) buffer layer on a rare-earth-substituted gadolinium gallium garnet (SGGG) substrate and for SGGG/SmGG/40 nm thick YIG/SmGG, [23] in which the top SmGG suppresses strain relaxation. The top SmGG was essential to obtain PMA in >40 nm thick YIG, but such overlayers lead to spacing loss which would decrease the efficiency of SW excitations using an antenna. Seed and buffer layers also lead to a more complex growth and patterning process. PMA has also been obtained in several single-layer rare-earth-substituted garnet films as a result of magnetoelastic anisotropy, [24][25][26][27] but the substitution of rare earth ions for Y in the iron garnet system tends to increase the Gilbert damping. [28,29] In these reports, there were no detailed discussions of the relation between the magnetoelastic anisotropy and the propagation properties of FV SWs.In this work, the effect of epitaxial mismatch on the net anisotropy and damping of YIG is described. By changing the magnetoelastic anisotropy, the field required for saturating the YIG out of plane can be reduced, facilitating the development of FV SW devices. Three epitaxial YIG films were prepared on gadolinium gallium garnet (GGG), SGGG, and neodymium gallium garnet (NGG) substrates directly (without any buffer layers). These substrates have the same crystalline structure but different lattice constants, yielding different lattice strain and Single-crystalline yttrium iron garnet (YIG) films are grown on gadolinium gallium garnet (GGG), rare-earth-substituted GGG, and neodymium gallium garnet (NGG) substrates, and their crystalline structures, surface morphologies, magnetic and magneto-optical properties, spin wave (SW) spectra of the forward volume (FV) mode, and damping parameters are characterized. YIG grown on NGG shows the smallest out-of-plane effective anisotropy field of 1080 Oe among the three samples because of its larger magnetoelastic anisotropy...