What are the magnetic properties of electrons

What is magnetism?

Magnetism was already known in ancient times. We encounter it in many natural phenomena and technical applications, starting with the geomagnetic field with its effects such as the aurora or navigation with the magnetic compass, through the electric motors to the high-temperature superconductors.

Horseshoe magnet

In magnetism, a distinction is made between the physically very different manifestations of dia-, para- and ferromagnetism, the latter only occurring in condensed matter. The properties referred to as “magnetic” in normal usage are mostly of a ferromagnetic nature. The ferromagnetic properties are discussed below using examples.

Ferromagnetism is of great technical importance. For example, it plays a very important role in electric generators, transformers or relays as well as in data storage and data processing. There are still enormous possibilities here in terms of energy saving and miniaturization. This is one reason why ferromagnetism has once again become an extremely exciting and active field of research in recent years. The second reason is that new physical effects, some of which are also of great technological interest, such as giant magnetoresistance or magnetic circular dichroism, have recently been discovered. Finally, the third reason is that a number of new manufacturing and analytical processes have been developed with which new “bespoke” materials can be created and examined in detail.

Magnetic field lines

How does ferromagnetism come about? It has its origin in the fact that individual atoms with not closed electron shells behave like small bar magnets, i.e. like magnetic dipoles. The “strength” of the atomic dipole is called the atom's magnetic moment. This magnetic moment is made up of two contributions. One comes from the self-rotation of the electrons, the spin. The other contribution is generated by the movement of the electrons around the atomic nucleus, which often has an orbital angular momentum and thus a magnetic moment. Therefore a distinction is made between magnetic spin moments and magnetic orbital moments. Both magnetic moments of an atom interact with each other, they are coupled with each other due to the spin-orbit interaction. Under certain circumstances the magnetic moments of the individual atoms couple with each other and then all point in the same direction. This is caused by a special force, the exchange interaction, which can be explained with the laws of quantum mechanics. Materials in which this alignment occurs are called ferromagnets because the effect first occurs with iron (Latin: ferrum) was observed. The macroscopic magnetic moment, which is characteristic of a solid, results from the vectorial sum of all atomic magnetic moments and is called magnetization.

However, the atomic magnetic moments are modified by the complex interplay of electrons in condensed matter and the bond conditions in the crystal. While the spins do not immediately notice the enormous electrical fields that prevail in a crystal, the electrically charged electrons, which have an orbital angular momentum, “feel” these fields on their spatially extended orbit. As a result, the orbital moment - and via the spin-orbital coupling, the entire magnetic moment - aligns itself in such a way that the energy of the electrons is as low as possible. The magnetic properties of a solid therefore depend on its crystal structure via the local electric fields. Under certain circumstances, quantum mechanical effects can lead to a partial extinction of the orbital angular momentum. Then the spin-orbit interaction is very small and the spins, which now essentially determine the magnetic moment, are very easily oriented in the direction of an applied external field. This can be seen with ordinary soft iron. Anisotropic crystals, whose physical properties are direction-dependent, show a different behavior. The stronger the directional dependence or anisotropy, as it occurs in particular at inner and outer interfaces, at crystal defects, chemical and structural inhomogeneities, the less completely the orbital angular momentum is extinguished. The stronger the coupling of the magnetic moments to the lattice and the greater the spatial variation of the magnetic properties of the crystal. As with a bar magnet, the direction of magnetization of the solid is then rigidly fixed and can only be influenced with very high external magnetic fields. Such materials are called hard magnetic.

As mentioned, the atomic magnetic moments in the ferromagnetic material try to collectively arrange themselves in parallel due to their direct magnetic interaction. However, this is not the most favorable state in terms of energy, since the macroscopic solid would then cause large magnetic fields. A non-magnetized state, seen from the outside, is more favorable, as is the case, for example, with soft iron without the presence of an external field. This happens because tiny areas are formed with magnetic moments in the same direction, which are called domains or Weiss areas. The magnetizations of the individual domains are oriented towards each other in such a way that they compensate each other and then the overall magnetization disappears. The size of the domains, which ranges from a few millimeters to well below a micrometer, and their structure depend sensitively on the size of the atomic moments and their coupling to the crystal structure. The domain structure is therefore an important “fingerprint” of the magnetic system and largely determines its macroscopic properties.