Singularities of various kind are often observed in the magnetization
curve of a ferromagnetic crystal. This is especially true for high ani
sotropy materials, such as the rare earth - intermetallic compounds. E
xamples are the First Order Magnetization Processes (FOMP), which are
discontinuous rotations of the magnetization vector due to high order
anisotropy terms. However, the hard direction anisotropy field of any
ferromagnetic crystal is always a critical field at which it reaches s
aturation. The Singular Point Detection (SPD) technique allows detecti
ng such singularities using polycrystalline samples by the observation
of the successive derivatives d(n)M/dH(n). The shape of the singulari
ty and the order of differentiation ''n'' at which it becomes apparent
depends on the symmetry of the hard axis. The SPD theory has been rec
ently extended to multidomain crystallites on the basis of the Neel ph
ase theory, and utilized for texture studies of permanent magnets. Mor
eover it has been proved to be valid also in the presence of canting b
etween the sublattice moments caused by strong competition between ani
sotropy and exchange; in principle, in the case of ferrimagnetic compo
unds it is possible to detect spin flop transitions both of second and
first order (high FOMP). The application of the SPD approach to the g
eneral problem of the complex susceptibility tensor and its covariant
derivatives can lead to further developments. As an example, the singu
larity observed in the transverse susceptibility of uniaxial materials
is strongly sensitive to the presence of single domain crystallites.