Ferromagnetism is the property of some materials, called ferromagnetic materials, to magnetize very intensely under the action of an external magnetic field and to remain magnetized for a long time when the field is canceled, thus becoming magnets. This property is maintained only below a certain temperature, called Curie temperature, above which the material behaves like a paramagnetic material. For iron, for example, this temperature is around 770 °C.

The ferrometer is the instrument used to measure the instantaneous value of magnetic induction in a sample of ferromagnetic material and to detect the hysteresis cycle of the material itself.

The magnetization of a ferromagnetic material can occur naturally or artificially, subjecting the material to a magnetic field. Natural ferromagnetic materials are, for example, magnetite, iron, cobalt, nickel and some transition metals. In ferromagnetic materials, the relative magnetic permeability of the material is not constant with the variation of the field, as instead occurs in diamagnetic materials and paramagnetic materials: the relationship between the magnetic induction field and the magnetic field is therefore not linear, nor even unique.

Ferromagnetic properties have a quantum origin and depend on the electronic structure of the materials and their crystalline structure. Ferromagnetism arises due to two effects from quantum mechanics: spin and the Pauli exclusion principle. Only atoms with partially filled shells (i.e., unpaired spins) can have a net magnetic moment, so ferromagnetism occurs only in materials with partially filled shells. Because of Hund’s rules, the first few electrons in a shell tend to have the same spin, thereby increasing the total dipole moment. These unpaired dipoles (often called simply “spins“ even though they also generally include orbital angular momentum) tend to align in parallel to an external magnetic field, an effect called paramagnetism. Ferromagnetism involves an additional phenomenon, however: in a few substances, the dipoles tend to align spontaneously, giving rise to a spontaneous magnetization, even when there is no applied field.

Ferromagnetic substances are composed of microscopic regions of thickness between 0.1 and 10-6 cm, called Weiss domains, which are spontaneously, i.e. in the absence of external field, magnetized by the effect of a strong molecular magnetic field that tends to align within the domain the individual magnetic dipoles of the atoms that compose it. The domains are separated by a transition zone called the Bloch wall. Magnetization directions of domains in general are random, but an external magnetic field, even weak, tends to align them causing a strong magnetization that increases with the increase of the external field until you reach a saturation value corresponding to the complete orientation in the direction of the external field.

Decreasing the intensity of the magnetizing field, a hysteresis phenomenon is observed, consisting in a decrease of the magnetization lower than the previous increase; moreover, when the field is cancelled, the magnetization still keeps a residual value not null. To cancel it is necessary to apply an opposite field whose value is called coercive field. The diagram that represents the relationship between the intensity H of the magnetizing field and the magnetic induction B produced in the material considered is called the curve of first magnetization or virgin curve: it depends on the temperature at which it operates.

Note that, as found experimentally, both the curve of first magnetization and the hysteresis curve are not continuous curves because the domains are not oriented simultaneously, but one after the other (Barkhausen effect), so that while H varies continuously, B varies in jumps, discontinuously.

The value of the ratio μ = B/H (magnetic permeability), which varies, is deduced from the magnetization curve. Ferromagnetic substances are characterized by having a permeability relative to that of vacuum, μr = μ/μ0, much greater than 1; it reaches on average values of the order of 103÷104.

As previously stated, permeability decreases with increasing temperature; there is a specific temperature, characteristic of each substance, called Curie point, above which ferromagnetic substances lose their properties, becoming paramagnetic, that is substances in which the relative permeability decreases to values very close to unity. At this temperature, due to thermal agitation, the molecules previously grouped in Weiss domains regain their freedom and then the action of the magnetizing field is expressed on the magnetic moments of individual molecules that are much smaller than those of Weiss domains. For absolute temperatures T greater than the Curie temperature TC the μr is proportional to the field and inversely proportional to T – TC.