  Fe3+ ions in sapphire exhibit an Electron Spin Resonance (ESR) which
interacts strongly with high-Q Whispering Gallery (WG) modes at microwave
frequencies. We report the first observation of a third-order paramagnetic
nonlinear susceptibility in such a resonator at cryogenic temperatures, and the
first demonstration of four wave mixing (FWM) using this parametric
nonlinearity. This observation of an all-microwave nonlinearity is an enabling
step towards a host of quantum measurement and control applications which
utilize spins in solids.
