Magnetic sensitivity of the microwave cryogenic sapphire oscillator

The Cryogenic Sapphire Oscillator is today recognized for its unprecedented frequency stability, mainly coming from the exceptional physical properties of its resonator made in a high quality sapphire crystal. With these instruments, the fractional frequency measurement resolution, currently of the order of 1e-16, is such that it is possible to detect very small phenomena like residual resonator environmental sensitivities. Thus, we highlighted an unexpected magnetic sensitivity of the Cryogenic Sapphire Oscillator (CSO) at low magnetic field. The fractional frequency sensitivity has been preliminary evaluated to 1e-13/Gauss, making this phenomenon a potential cause of frequency stability limitation. In this paper we report the experimental data related to the magnetic sensitivity of the quasi-transverse magnetic Whispering Gallery (WGH) modes excited in sapphire crystals differing from their paramagnetic contaminants concentration. The magnetic behavior of the WGH modes does not follow the expected theory combining the Curie law and the Zeeman effect affecting the Electron Spin Resonance of the paramagnetic ions present in the crystal.