The law of approach to saturation in ferromagnets originating from the magnetocrystalline anisotropy

In this paper, we have investigated the approach to saturation in both Co and Fe single crystals by taking into account the field energy and the magnetocrystalline anisotropy energy and numerically solving the nonlinear equations for equilibrium. And by introducing a new approximation rather than Akulov’s approximation, more accurate, approximate analytical solutions for the nonlinear equations for the field above the magnetocrystalline field have been obtained, which are in good agreement with the numerical results. It has been found that the crystal can reach the saturation as it is magnetized by a field along the easy or hard directions while it will follow the law of approach to saturation by the field applied along the non-easy or non-hard directions. The reason is that depending on the applied field angle the magnetocrystalline anisotropy can make the crystal hard or easy to be magnetized. No paramagnetism-like process occurs, and the a/H, b/H2 and χH terms all originate from the magnetocrystalline anisotropy. With the application of our theory to real ferromagnetic materials, the experimental observations can be understood.