Microwave Studies of Single Crystal TeO2 at Cryogenic Temperatures

We use whispering-gallery-mode analysis to characterise the microwave dielectric properties of single-crystal TeO$_2$ at cryogenic temperatures and compare its loss performance with other low-loss dielectric materials. Finite-element modelling is combined with measurements at room temperature, 4 K, and 20 mK to develop accurate cryogenic simulations and extract the anisotropic dielectric permittivities, giving $\varepsilon_\parallel=25.75\pm0.08$ and $\varepsilon_\perp=20.90\pm0.07$. Loss measurements reveal quality factors as high as $9\times10^6$ and minimum loss tangents approaching $3\times10^{-8}$, placing TeO$_2$ among promising low-loss dielectrics for cryogenic microwave applications. Electron-spin-resonance spectroscopy further indicates a clean spin environment, while identifying distinct spin systems consistent with the known properties of the crystal.