A statistical Model for Ferromagnetism

Abstract

Considering exchange and Fermi energy of a system of electrons together with magnetostatic, magnetostrictive and anisotropy forces, the internal energy of a magnetized system can be expressed as a function of its magnetization. As indicated by Slater, the entropy of the system is also a function of magnetization, so that the free energy can be expressed approximately as an even fourth degree polynomial in the magnetization in the absence of an external field. Plotting the free energy vs. magnetization, the curve has either one minimum, or two minima separated by a maxima. The former condition corresponds to the para-, the latter to ferromagnetism.

Introduction of an external magnetic field adds a linear term to the free and internal energy functions.

The shift in position of the minima can be calculated, and is used to compute the corresponding net magnetization of the system.

The hysteresis curve can be explained by the existence of the maximum in the internal energy curve, which tends to prevent the system from settling to equilibrium at the lower of the two relative minimum. Increasing the external field eventually causes the higher of the two relative minima to fuse with the maximum into a point of inflection, at which point the entire system will settle in equilibrium around the one remaining minimum. The external field at which this happens is the coercivity.

Other elements of the hysteresis loop are explained similarly.