Complex Permittivity of Gadolinium Gallium Garnet From 8.2 to 12.4 GHz

This letter reports the measured complex permittivity of gadolinium gallium garnet (GGG) from 8.2 to 12.4 GHz using a transmission/reflection method in a rectangular waveguide. A modification of the Nicolson–Ross–Weir method, valid for nonmagnetic materials, yields an average relative dielectric constant of 11.99 and loss tangent of ${5.2\times 10^{-3}}$ across the band. The measured relative dielectric constant agrees well with near-dc and terahertz measurements. A statistical error analysis quantifying systematic and nonsystematic errors indicates a standard deviation of 0.77$\%$ and 17$\%$ for the relative dielectric constant and loss tangent, respectively. The measured loss tangent of GGG indicates that microwave spin-wave transducers operating in the magnetostatic regime (wavelength larger than 100 $\mu$m at 1 GHz and larger than 10 $\mu$m at 10 GHz) will need to consider dielectric losses in addition to ohmic losses, while transducers operating near and in the exchange regime will be dominated by ohmic loss. If on-chip matching networks are required, it is recommended to use a low-order network and as thin a GGG substrate as possible to reduce the power dissipated in the network.