I would like to test a model on experimental data (major loop + first-order reversals + minor loops), but I hardly manage to find public databases ... Can anyone help me? Thanks!
You can find in handbooks (see below) such parameters as exchange stiffness, magnetic anisotropy constants, magnetization saturation, magnetoelastic/magnetostriction constants etc. - then you can apply some simplified model and to compare it with your experiment. Exactly what you are asking - I've never seen. And the reason is that excluding several analytically simple magnetization reversal mechanisms (Stoner Wohlfarth, curling, fanning etc.) a hysteresis loop of a bulk ferromagnet is somehow dependent on almost all physical parameters describing it: shape, quality of the surface, defects in volume and on surface, crystallite size, texture, internal stresses, and others including even conductivity in special cases. There is also well-know Brown paradox - then even for ideally prepared sample, where almost all of the mentioned parameters are known - you still have a considerable discrepancy between calculation and experiment.
K. H. J. Buschow, Handbook of Magnetic Materials (North-Holland, 2002).
H. Kronmüller and S. S. P. Parkin, Handbook of magnetism and advanced magnetic materials : 5 volume set (John Wiley & Sons, Hoboken, NJ, 2007).
A. Hubert and R. Schдfer, Magnetic domains : the analysis of magnetic microstructures (Springer, Berlin ; New York, 1998).
G. Bertotti, Hysteresis in magnetism : for physicists, materials scientists, and engineers (Academic Press, San Diego, 1998)
Although you might find general hysteresis loops, you will not find a database with first-order reversal curves (FORCs). The best I can suggest is to cooperate with a lab which has this kind of capability - for instance Wolfson Centre for Magnetics, at Cardiff University, UK:
http://wolfson.engineering.cf.ac.uk/
Their measurements of FORCs were a basis for several paper in modelling of hysteresis loops (search for Prof. Zirka in IEEE Trans. Magnetics, for instance).