Magnetization processes

The domain picture is a good one for ferromagnetic solids, when the domain size is much greater than the domain wall width. Domain wall motion and domain rotation are the two basic magnetization processes in any multidomain solid. Consider a multidomain ellipsoidal specimen with no magnetocrystalline anisotropy. This was the basis of the discussion of the demagnetizing. When the field is applied along the easy axis, the effect is to move the domain walls in such a way as to grow the parallel domains and shrink the antiparallel domains. The average magnetization M_av = M[(V_p − V_ap)/ (V_p + V_ap)] increases with increasing applied field in such a way that H = H' − NM_av = 0. The external susceptibility due to domain wall motion is χ_ext= M_av/H' = 1/N.
The other magnetization process, magnetization rotation, applies when the applied field H' has a component perpendicular to the anisotropy axis. If K_u is the effective anisotropy of whatever origin, the external susceptibility is μ₀M²_s /2K_u. The magnetization attains saturation when the applied field equals the anisotropy field, 2K_u/μ₀M_s .