Modern quantum technologies and hybrid quantum systems offer the opportunity to utilize magnons on the level of single excitations. Long lifetimes, low decoherence rates, and a strong coupling rate to other subsystems propose the ferrimagnet yttrium iron garnet (YIG), grown on a gadolinium gallium garnet (GGG) substrate, as a suitable platform to host magnonic quantum states. However, the magnetic damping at cryogenic temperatures significantly increases due to the paramagnetic character and the highly inhomogeneous stray field of GGG, as recent experiments and simulations pointed out. Here, we report on temperature dependent ferromagnetic resonance (FMR) spectroscopy studies in YIG-GGG thin-films with different sample geometries. We experimentally demonstrate how to eliminate the asymmetric stray field-induced linewidth broadening via microstructuring of the YIG film. Additionally, our experiments reveal evidence of a non-Gilbert like behavior of the linewidth at cryogenic temperatures, independent of the inhomogeneous GGG stray field.

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