Dielectric Properties of Single Crystal Calcium Tungstate
This investigation employed microwave whispering gallery mode (WGM) analysis to characterize the dielectric properties of a cylindrical, single-crystal sample of calcium tungstate (CaWO$_4$). Through investigation of quasi-transverse\hyp{}magnetic and quasi-transverse\hyp{}electric mode families, we can assess loss mechanisms and relative permittivity from room temperature down to cryogenic conditions. We report the biaxial permittivity values of $\epsilon_{||} = 9.029 \pm 0.009$ and $\epsilon_{\perp} = 10.761 \pm 0.01$ at $295$ K, and $\epsilon_{||} = 8.794 \pm 0.009$ and $\epsilon_{\perp} = 10.440 \pm 0.01$ at $4$ K. Components are denoted with respect to the c\hyp{}axis of the crystal unit cell. The parallel component agrees well with the published literature at MHz frequencies; however, the perpendicular component is $4.8$\% lower. The WGM technique offers greater precision, with accuracy limited primarily by the uncertainty in the crystal's dimensions. WGMs also serve as sensitive probes of lattice dynamics, enabling monitoring of temperature-dependent loss mechanisms. At room temperature, the measured loss tangents were $\tan\delta_{||}^{295,\mathrm{K}} = (4.1 \pm 1.4) \times 10^{-5}$ and $\tan\delta_{\perp}^{295,\mathrm{K}} = (3.64 \pm 0.92) \times 10^{-5}$. Upon cooling to 4 K, the loss tangents improved by approximately two orders of magnitude, reaching $\tan\delta_{||}^{4,\mathrm{K}} = (1.56 \pm 0.52) \times 10^{-7}$ and $\tan\delta_{\perp}^{4,\mathrm{K}} = (2.05 \pm 0.79) \times 10^{-7}$. These cryogenic values are higher than those reported in prior studies, likely due to a magnetic loss channel associated with an unidentified paramagnetic spin ensemble. These findings have implications for the use of CaWO$_4$ in applications such as spin-based quantum systems and cryogenic bolometry, highlighting the potential of WGMs for novel sensing applications.