Diamagnetism, paramagnetism and ferromagnetism

Diagram to differentiate between ferro-/para-/diamagnetism

The following diagram can be used to quickly determine whether a material is ferromagnetic, paramagnetic or diamagnetic.

Diamagnetism, paramagnetism and ferromagnetism: forms of magnetisation

When a material is exposed to an external magnetic field, the material becomes magnetised. The direction and strength of this magnetisation is based on the intrinsic properties of the material and is described by the terms diamagnetism, paramagnetism and ferromagnetism. Other types of magnetism (e. g. ferrimagnetism) are known, but those will not be discussed in detail here.

The magnetisation of matter in an external field, i.e. the orientation of the elementary magnets in the material, can be opposite or in the same direction as the external magnetic field. If the magnetisation is in the opposite direction to the external field, it is called diamagnetism. In paramagnetic objects, the magnetisation is aligned with the external magnetic field. In ferromagnetic materials, the magnetisation is aligned with the external magnetic field and is particularly strong due to a special interaction of the electron spins, the so-called exchange interaction. The magnetisation of ferromagnetic materials is generally significantly greater than the magnetisation of paramagnetic materials within the same external magnetic field. At room temperature, only the elements iron, nickel and cobalt are ferromagnetic. There are also ferromagnetic alloys and compounds as well as elements that become ferromagnetic at low temperatures. At very high temperatures, all ferromagnetic materials become paramagnetic because the thermal energy of the electrons is greater than the exchange interaction and the parallel alignment of the electron spins is destroyed. There is a characteristic temperature for this transition, the so-called Curie temperature.

The magnetisation of ferromagnetic materials is partially retained when the external magnetic field is switched off. This remaining magnetisation is referred to as remanence.

Observing diamagnetism, paramagnetism and ferromagnetism

In contrast to diamagnetism and paramagnetism, ferromagnetism is easily observable in everyday life. Ferromagnetic materials are noticeably attracted to magnetic fields. For example, a magnet will adhere to an iron wall, which is ferromagnetic, but not to a plastic wall, which is usually diamagnetic.

The interaction between magnetic fields and paramagnetic or diamagnetic substances is very weak and cannot be directly observed in everyday life.

A paramagnet (e.g. oxygen) is attracted to a magnetic field in the same way as a ferromagnet (e.g. iron). However, the attractive force is several million times weaker. A diamagnet (e.g. water), on the other hand, is repelled when it is placed in the magnetic field, although this too is almost imperceptibly weak. The repulsive force between magnetic fields and diamagnetic materials is only strong in superconductors. Superconductors are therefore also known as "perfect diamagnets". They exhibit a magnetisation that completely displaces the magnetic flux density inside the superconductor. A superconductor even floats above a magnet due to the repulsive diamagnetic effect.

Magnetic permeability to describe the strength of magnetisation

Magnetic permeability μ is introduced to describe the strength of the magnetisation. In simplified terms, the permeability μ indicates the factor by which the magnetic flux density is increased or decreased by the influence of the material. So, the magnetic flux density B in the presence of a substance with the permeability μ is in contrast to the magnetic flux density of the vacuum B₀:

B = μ • B₀

The magnetic field, in turn, is the sum of the external incident magnetic field H₀ (which would also be present in a vacuum) and the magnetisation M: H = H₀ + M

This magnetic field in the presence of the substance is also obtained by multiplying the vacuum field by the permeability μ: H= μ • H₀

Therefore, the following applies to the magnetisation:

M = H - H₀ = μ • H₀ - H₀ = (μ - 1) • H₀

The magnetisation M of a substance with an incident (vacuum) magnetic field H₀ is therefore:

M = (μ - 1) • H₀

The factor (μ - 1) is also known as the magnetic susceptibility χ and follows: M = χ • H₀

The permeability of a vacuum is μ = 1, which means that the vacuum does not react to a magnetic field at all. The magnetisation M of the vacuum is zero. And so is its magnetic susceptibility χ. Paramagnetic substances have a permeability that is slightly greater than 1. The magnetic susceptibility of paramagnets is slightly greater than zero. The permeability of diamagnetic materials is slightly less than 1, and the susceptibility correspondingly less than zero. In a superconductor, the magnetic permeability is μ = 0 and the susceptibility χ = -1. This means that magnetic flux no longer penetrates the superconductor. You can also imagine that the magnetisation of superconductors is equal to the external incident field, only in the opposite direction. Therefore, the external field is compensated inside the superconductor. Ferromagnets can have very high permeability numbers. For iron, μ can reach values of up to 10 000; certain ferromagnetic metals with a specially created arrangement of atoms can reach values of up to μ = 150 000.

However, the assumption that permeability is simply a constant for each substance is only an approximation. This can be seen in the hysteresis curve. In reality, the magnetisation of the material does not linearly follow the incident magnetic field (or the incident flux density). The relationship is more complicated and also depends on the "past history" of the material. If the material is already magnetised, it behaves differently in the external field than the same non-magnetised material. The linear formula M = χ • H₀ is therefore an approximation.

Physics consideration

To understand the physical cause of diamagnetism, paramagnetism and ferromagnetism, one can visualise that every substance consists of atoms with atomic nuclei and electrons.

When an external magnetic field is applied, movements of the electrons, i.e. currents, are induced under the influence of this magnetic field. According to Lenz's law, these currents are directed in such a way that they counteract their cause. That is why the induced magnetic moments, also known as induced magnetic polarisation, are aligned in such a way that the substance as a whole is pushed out of the external magnetic field in a weak fashion, i.e. it exhibits diamagnetic properties.

Every substance is slightly diamagnetic. However, additional paramagnetic or even ferromagnetic properties may eclipse the diamagnetism of a substance. Para- or ferromagnetism occurs if and only if the electrons of the entire electron shell on each atom of the substance have a resulting total spin. Individual electrons always have a so-called "spin", which carries a magnetic moment. In many materials, however, the electron spins cancel each other out in pairs. These materials are then diamagnetic. But, if each atom has an odd number of electrons, then the electron spins in each individual atom cannot cancel each other out in pairs. As a result, each atom with its electrons has a resulting total spin of the last remaining "unpaired" electron. These materials are para- or ferromagnetic.

Due to the motion of the atoms, the atomic magnetic moments of the resulting spins are evenly distributed in all spatial directions, so the magnetic fields of all elementary magnets collectively offset each other, and the material appears outwardly non-magnetic.

However, in an external magnetic field, the resulting total spins of all atoms are aligned. The north pole of each elementary magnet points in the direction of the south pole of the external field and vice versa. In this case, the probe itself behaves like a magnet and is attracted to the external magnetic field. The simultaneously induced circular currents, which are directed in the opposite direction to their cause (the external magnetic field) due to Lenz's law, are weaker in paramagnetic and ferromagnetic materials than the effect of the aligned elementary magnets, so that the attractive force of the aligned elementary magnets exceeds the repulsive force of the induced circular currents. This is the cause of para- and ferromagnetism.

In a ferromagnet, the electron spins are stabilised by the exchange interaction. The exchange interaction is particularly strong in ferromagnets. Each elementary magnet is additionally stabilised in its orientation. This leads to an attractive force that is often millions of times stronger. As a result, the material remains noticeably magnetic as a whole even when the external magnetic field is switched off (remanence). In paramagnets, the exchange interaction is smaller than the thermal energy of the atomic spins.

Demagnetisation due to heat

If the magnetised ferromagnet is heated to a high temperature (above the Curie temperature), ferromagnetism disappears because the increase in temperature leads to greater motion of the atoms with the individual resulting total spins of the electron shell. This motion destroys the mutual coupling of the electron spins through the exchange interaction because the supplied thermal energy exceeds the coupling energy of the electron spins. Above the Curie temperature, the object becomes a paramagnet. Strong vibrations or an opposing external field can also negate the remanence of a ferromagnet, i.e. lead to demagnetisation. However, the material remains ferromagnetic and could be magnetised again. A heated material also becomes ferromagnetic again when it cools below the Curie temperature.