Ultrastable cryogenic sapphire dielectric microwave resonators

Measurements of the properties of cryogenic sapphire resonators with various concentrations of paramagnetic ions are reported, and a new way of achieving self-compensation of temperature fluctuations for such resonators mounted inside conducting shields is described. It is shown that frequency-temperature self-compensation, in which the T⁴ temperature dependence of the sapphire dielectric constant compensates the effect of the T^-1 Curie law of paramagnetic impurities, can be achieved at convenient operating temperatures around 6 K. Samples with a few ppm of chromium and iron impurity ions display strong influence on mode frequency and Q of nearby spin resonances at 11.45 GHz (Cr³⁺) and 12.05 GHz (Fe³⁺) and fail to compensate above the spin resonances. In samples with much reduced chromium and iron concentrations, an ion with a very high frequency paramagnetic resonance (such as Ti³⁺) has been exploited to obtain essentially frequency-independent self-compensation