Atomic moment

Basic magnetic properties of metallic systems and materials are treated by Gignoux in [3.1]. Extensive data on magnetic properties of metals can be found in [3.2]. Magnetic properties of ferrites are treated by Guillot in [3.3]. Extensive data on magnetic and other properties of oxides and related compounds can be found in [3.4] and [3.5]. 

The suitability of a metal or oxide to be used as a magnetic material is determined by its mean atomic 

---

Shape anisotropy is related to the magnetostatic energy of a magnet. A needle-shaped sample tends to line the atomic moments along the needle axis and a disk-shaped sample tends to line these moments parallel to the disk surface. 

Recently it was pointed out by Zener7 that the atomic moments, in parallel orientation, might react with the electrons in the conduction band in such a way as to uncouple some of the pairs, producing a set of conduction electrons occupying individual orbitals, and with spins parallel to the spins of the atomic electrons. Zener assumed that the conduction band for the transition metals is formed by the 4.s orbitals of the atoms, and that there is somewhat less than one conduction electron per atom in iron, cobalt, and nickel. Like Slater, he attributed the atomic magnetic moments to the partially filled 3d subshell. 

Quantitative calculations can be made on the basis of the assumption that the density of levels in energy for the conduction band is given by the simple expression for the free electron in a box, and the interaction energy e of a dsp hybrid conduction electron and the atomic moment can be calculated from the spectroscopic values of the energy of interaction of electrons in the isolated atom. The results of this calculation for iron are discussed in the following section. 

The calculated energy of interaction of an atomic moment and the Weiss field (0.26 uncoupled conduction electrons per atom) for magnetic saturation is 0.135 ev, or 3070 cal. mole-1. According to the Weiss theory the Curie temperature is equal to this energy of interaction divided by 3k, where k is Boltzmann s constant. The effect of spatial quantization of the atomic moment, with spin quantum number S, is to introduce the factor (S + 1)/S that is, the Curie temperature is equal to nt S + l)/3Sk. For iron, with 5 = 1, the predicted value for the Curie constant is 1350°K, in rough agreement with the experimental value, 1043°K. 

An obvious refinement of the simple theory for cobalt and nickel and their alloys can be made which leads to a significant increase in the calculated value of the Curie temperature. The foregoing calculation for nickel, for example, is based upon the assumption that the uncoupled valence electrons spend equal amounts of time on the nickel atoms with / = 1 and the nickel atoms with J = 0. However, the stabilizing interaction of the spins of the valence electrons and the parallel atomic moments would cause an increase in the wave function for the valence electrons in the neighborhood of the atoms with / = 1 and the parallel orientation. This effect also produces a change in the shape of the curve of saturation magnetization as a function of temperature. The details of this refined theory will be published later. 

The atomic electrostatic moments of an atom are obtained by integration over its charge distribution. As the multipole formalism separates the charge distribution into pseudoatoms, the atomic moments are well defined. 

In the multipole-model description, the charge density is a sum of atom-centered density functions. The moments of the entire distribution are obtained as the sum over the individual atomic moments plus contributions due to the shift to a common origin. 

The condition for localized electrons with spontaneous atomic moments is U > w that for itinerant electrons with no spontaneous moment is Un < w. The intermediate case Un = w is of considerable theoretical interest. In the case of iron oxides, a U5 = 3 eV ensures a localized 3 d majority-spin configuration at both Fe " and Fe " ions since the cubic-field splitting Ag < Ag, is small enough to leave the ions in the high-spin state. However, localization of the minority-spin electron, particularly in the mixed Fe / Fe " state, does not necessarily follow. Similarly, a much smaller U4 will be seen to make U4 = w for Fe " in the perovskites A Fe03. 

---