Magnetization

When matter is placed in an external magnetic field, one observes either a weakening or a strengthening of the field depending on the material. This is usually described by the relation

$$
B = \mu_r B_0
$$

where $B_0$ is the flux density of the magnetic field in vacuum. The material constant $\mu_r$ is called the relative permeability and, for vacuum, has exactly the value 1, analogous to the dielectric constant $\varepsilon_r$. Just like in the case of the electric field, the constants $\mu_0$ and $\mu_r$ are often combined into the permeability constant $\mu$:

$$
\mu = \mu_0 \mu_r
$$

Sometimes the magnetic field strength $H$ is defined as the product of the permeability constant and the magnetic flux density:

$$
\boxed{H = \mu B}
$$

The field strength therefore incorporates the permeability constant and thus also the material properties.

Diamagnetism

Magnetic fields are always associated with magnetic currents. The magnetic properties of matter are therefore linked to the orbital and spin motions of electrons in atoms or molecules. These processes can only be described exactly using quantum mechanics, but they can be understood qualitatively as follows:

When matter that does not have intrinsic magnetic dipoles is placed in a magnetic field, the atoms or molecules are magnetically polarized by induced currents. According to Lenz’s law, the induced magnetic moments are oriented in such a way that they oppose the applied field, reducing the internal field. This phenomenon is called diamagnetism. For diamagnetic materials, the relative permeability satisfies $\mu_r < 1$. Almost all substances are at least weakly diamagnetic, though in some cases other magnetic effects dominate.

Paramagnetism

In addition to diamagnetism, there is paramagnetism. A paramagnetic material has permanent magnetic dipoles, but due to thermal motion they are normally randomly oriented. When an external field is applied, these dipoles align along the field lines.

The overlap of the dipole fields with the external field strengthens the overall field, so that $\mu_r > 1$. However, the higher the temperature, the weaker the magnetization, since thermal agitation counteracts the alignment. After switching off the field, the magnetization returns to zero.

Ferromagnetism

When substances exhibit a very strong magnetization, they are called ferromagnetic. In this case, $\mu_r \gg 1$, and the values can be extremely large depending on the material.

The enormous amplification of the field arises because the dipoles not only align with the external field (as in paramagnetism), but also interact with one another. They stabilize in regions known as Weiss domains. A ferromagnetic material thus retains part of its polarization even after the external field is switched off.

The degree of magnetization depends on the material’s history. This can be studied by placing a ferromagnetic sample in the magnetic field of a current-carrying wire. The magnetization initially increases linearly with the magnetic flux density, then saturates when all dipoles are aligned. As the external field decreases, the magnetization decreases but does not vanish at zero field. The remaining magnetization is called remanence. It can only be eliminated if the field is reversed and reaches a certain magnitude.

The resulting curve, called a hysteresis loop, characterizes the behavior of ferromagnetic materials. Above a certain temperature, known as the Curie temperature, ferromagnetism disappears, but the material remains paramagnetic. For most materials, the Curie temperature lies in the range of several hundred degrees Celsius.

Relative permeabilities of selected materials