  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.
