I have a permanent magnet and I just finish building myself a gaussmeter. However it shows me that every magnet I measure has a higher gauss level for the south then the north. Do magnet have different magnetic field strength for south and north pole, ? it could also be my gaussmeter...
Have you checked the linearity? I think I would try to compare the signal to a current that produced the magnetic field with a gapped inductor, with the probe in the gap, and the inductor fed with AC. A scope Lissajous pattern would display the linearity very simply.
Any magnetic structure that concentrates the magnetic flux of a coil into an air gap.
You place the flux probe in the air gap. The presence of the air gap tends to reduce lots of any nonlinearity (between instantaneous current and instantaneous flux) caused by the magnetic properties of the core material in the rest of the flux path, while using that core material to reduce the amperes it takes to reach a given flux level (that is below the saturation flux of the core material).
A pair of E cores with a gap between the middle pair of legs and a coil bedside that gap on each middle leg would be an example of such a structure. Another would be a toroidal core with a slot cut in it (to make an air gap). But even placing the probe between a pair of solenoidal coils wound around straight bars of permeable material would produce a significant increase in flux, compared to air core coils, especially if the cores extend out the ends of the coils by at least the coil length. A pair of bundles of iron welding rods (or cut pieces of coat hangers or floral wire) could form such cores.