Although many electrons are moving by orbital motions and spin orientations around a nuclei, only two electrons with up and down spins can occupy one orbit. Therefore, most of the magnetic moments originated from spins cancel each other and does not contribute to the magnetic moment of a solid. In the case of transition elements whose d-orbit is not fully occupied and rare earth elements whose p-orbit is not fully occupied, magnetic moment appear due to the spins. According to Hund's rule, electron are occupied so that the total spin becomes maximum. In other words, the number of up-spins increases from 1 to 5 according to the atomic number, thereafter, total spin amount decreases as up-spin and down-spin cancel each other when two electrons occupy one orbit. The reason why the actual metal never has such a high magnetization of 5 Bohr magnetron is that the d-electrons are shared by many atoms in crystals as free electron. Thus, the maximum magnetization obtained from FeCo is 2.4 Bohr electron, which is less than half of the Bohr magnetron of an atom.

Types of magnetism

　As describes above, the elements whose d-orbit or f-orbit are not fully occupied exhibit magnetic moments, but the magnetism of solids depends on how these atomic magnetic moments are aligned in crystals. Here, only four types of magnetism that are important in applications of magnetic materials are shown in Fig. 2. The magnetic moments of atoms are ordered in the crystals shown in Fig. 2 (a) - (c). This is because of a quantum mechanics effect called "exchange interaction" that work in short distance of the order of atomic distance. In the ferromagnetic material in Fig. 2(a), the exchange force cause alignment of magnetic moments in one direction, causing spontaneous magnetic moment in material. The most materials treated in magnetic engineering is ferromagnetic materials, and the magnetic engineering is the discipline to study how ferromagnetic materials can be applied for various industrial applications. On the other hand, if the exchange force cause antiparallel ordering of atomic spins in a crystal, the magnetic moments are cancelled in the crystal and spontaneous magnetization is lost. This type of materials are called "anitiferromagnetic material". The anitiferromagnetic materials are often used to pin the magnetization of thin ferromagnetic films by the exchange coupling between a ferromagnetic/antiferromagnetic layers. When the amount of magnetic moments of antiparallelly ordered magnetic moments is different, the material exhibits spontaneous magnetization. This type of materials are called "ferromagnetic material". Most materials do not have any order of magnetic moment, in which case the orientations of magnetic moments are random, thus no spontaneous magnetization appear. These are called "paramagnetism", which show only small magnetization when magnetic field is applied due to the orientation of atomic magnetic moments. So the susceptibility of paramagnetism materials is orders of magnetized smaller than those for ferromagnetic and ferrimagnets. Since most of materials show paramagnetism, the materials that can be used in magnetic engineering is pretty limited. Since magnetic order is disturbed by thermal agitation, ferromagnets, antiferromagnets and ferrimagnets loose their magnetic order at high temperature at magnetic transition temperature called "Curie or Neel temperatures". When the size of ferromagnetic particles become smaller than a few nanometer, the magnetic moments are thermally fluctuated and they become paramagnetic even at room temperature. This state is called superparamagnetism.