Low-damping sub-10-nm thin films of lutetium iron garnet grown by molecular-beam epitaxy

We analyze the structural and magnetic characteristics of (111)-oriented lutetium iron garnet (Lu$_3$Fe$_5$O$_{12}$) films grown by molecular-beam epitaxy, for films as thin as 2.8 nm. Thickness-dependent measurements of the in- and out-of-plane ferromagnetic resonance allow us to quantify the effects of two-magnon scattering, along with the surface anisotropy and the saturation magnetization. We achieve effective damping coefficients of $11.1(9) \times 10^{-4}$ for 5.3 nm films and $32(3) \times 10^{-4}$ for 2.8 nm films, among the lowest values reported to date for any insulating ferrimagnetic sample of comparable thickness.