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Growth of nm-thick yttrium iron garnet films and ferromagnetic resonance (FMR) linewidth properties in the films are reported. The films were grown on gadolinium gallium garnet substrates by pulsed laser deposition (PLD). Films in the 5–35 nm thickness range showed a (111) orientation and a surface roughness between 0.1 and 0.3 nm. The 10 nm films showed a 10 GHz FMR linewidth of about 6 Oe and a damping constant of 3.2 × 10-4. The FMR linewidth increases with both the surface roughness and the surface Fe deficiency. Thicker films exhibit a smaller FMR linewidth and a lower damping constant.