Low temperature magnetization data obtained for titanium (III) doped caesium gallium alum show a spectacular deviation from Brillouin behavior with the magnetization highly dependent on the strength of the applied field at a given value of B/T. This arises from unprecedented higher-order contributions to the magnetization and these measurements afford the determination of the Zeeman coefficients to third order. This anomalous magnetic behavior is a manifestation of Jahn-Teller coupling giving rise to low-lying vibronic states which mix into the ground state through the magnetic field.