FOMP

The magnetocrystalline anisotropy energy of a ferromagnetic crystal can be expressed as a power series of direction cosines of the magnetic moment with respect to the crystal axes. The coefficient of those terms are the anisotropy constant. In general the expansion is limited to few terms. Normally the magnetization curve is continuous respect to applied field up to saturation but, in certain intervals of the anisotropy constant values, irreversible field induced rotations of the magnetization are possible implying first order magnetization transition between equivalent magnetization minima, the so-called first order magnetization process (FOMP).The total energy of an uniaxial magnetic crystal in an applied magnetic field can be written as a summation of the anisotropy term up to six order, neglecting the sixfold planar contribution,Since the FOMP transition represents a singular point in the magnetization curve of a single crystal, we analyze how this singularity is transformed when we magnetize a polycrystalline sample. The result of the mathematical analysis shows the possibility of carrying out the measurement of critical field ( Hcr ) where the FOMP transition takes place in the case of polycrystalline samples.The origin of high anisotropy constant can be found in the interaction of two sublattices (A and B) each of them having a competing high anisotropy energy, i.e. having different easy directions. In particular we can no longer consider the system as a rigid collinear magnetic structure, but we must allow for substantial deviations from the equilibrium configuration present at zero field. Limiting up to fourth order, neglecting the in plane contribution, the anisotropy energy becomes:The problem for cubic crystal system has been approached by Bozorth, and partial results have been obtained by different authors, but exact complete phase diagrams with anisotropy contributions up to sixth and eighth order have only been determined more recently.