Paramagnetic susceptibility and permittivity measurements at microwave frequencies in cryogenic sapphire resonators

We present high-resolution measurements of the temperature-dependence of mode frequency for three monocrystalline microwave sapphire dielectric resonators at liquid helium temperatures. In two resonators the susceptibility is independent of frequency and displays a non-Curie law behaviour. This can be interpreted as arising from a van Vleck temperature-independent contribution to the paramagnetic susceptibility of the and ions involved. We also report measurements of the combined dependence of thermal expansion and permittivity on temperature in the range 2 - 20 K and show that this is about 50% larger in all three resonators than the value calculated from the presently accepted thermal expansion coefficient of sapphire.