FERROMAGNETISM: MATERIALS, APPLICATIONS AND EXAMPLES - PHYSICAL - 2025

The ferromagnetism is the property that gives some substances intense and permanent magnetic response. In nature there are five elements with this property: iron, cobalt, nickel, gadolinium and dysprosium, the latter rare earths.

In the presence of an external magnetic field, such as that produced by a natural magnet or an electromagnet, a substance responds in a characteristic way, according to its internal configuration. The magnitude that quantifies this response is the magnetic permeability.

Magnets forming a bridge. Source: Pixabay

Magnetic permeability is a dimensionless quantity given by the quotient between the intensity of the magnetic field generated inside the material and that of the magnetic field applied externally.

When this answer is much greater than 1, the material is classified as ferromagnetic. On the other hand, if the permeability is not much greater than 1, the magnetic response is considered to be weaker, they are paramagnetic materials.

In iron the magnetic permeability is of the order of 10 ⁴. This means that the field inside the iron is about 10,000 times greater than the field applied externally. Which gives an idea of ​​how powerful the magnetic response of this mineral is.

How does the magnetic response originate inside substances?

Magnetism is known to be an effect associated with the movement of electric charges. That is exactly what the electric current consists of. Where then do the magnetic properties of the bar magnet with which a note has been stuck on the refrigerator come from?

The material of the magnet, and also any other substance contains inside protons and electrons, which have their own motion and generate electrical currents in various ways.

A very simplified model assumes the electron in a circular orbit around the nucleus made up of protons and neutrons, thus forming a tiny loop of current. Each loop is associated with a vector magnitude called "orbital magnetic moment", whose intensity is given by the product of the current and the area determined by the loop: the Bohr magneton.

Of course, in this small loop the current depends on the charge of the electron. Since all substances contain electrons in their interior, all have in principle, the possibility of expressing magnetic properties. However, not all of them do.

This is because its magnetic moments are not aligned, but randomly arranged inside, such that its macroscopic magnetic effects cancel out.

The story does not end here. The magnetic moment product of the electron motion around the nucleus is not the only possible source of magnetism on this scale.

The electron has a kind of rotational motion around its axis. It is an effect that translates into an intrinsic angular momentum. This property is called the electron spin.

Naturally it also has an associated magnetic moment and it is much stronger than the orbital moment. In fact, the greatest contribution to the net magnetic moment of the atom is through the spin, however both magnetic moments: the translation moment plus the intrinsic angular momentum, contribute to the total magnetic moment of the atom.

These magnetic moments are the ones that tend to align in the presence of an external magnetic field. And they also do it with the fields created by neighboring moments in the material.

Now, electrons usually pair up in atoms with many electrons. Pairs are formed between electrons with opposite spin, resulting in the spin magnetic moment canceling out.

The only way that the spin contributes to the total magnetic moment is if one of them is unpaired, that is, the atom has an odd number of electrons.

What about the magnetic moment of protons in the nucleus? Well, they also have spin moment, but it is not considered to contribute significantly to the magnetism of an atom. This is because the spin moment is inversely dependent on mass and the mass of the proton is much greater than that of the electron.

The magnetic domains

In iron, cobalt and nickel, the triad of elements with great magnetic response, the net spin moment produced by the electrons is not zero. In these metals, the electrons in the 3d orbital, the outermost ones, are the that contribute to the net magnetic moment. That is why such materials are considered ferromagnetic.

However, this individual magnetic moment of each atom is not enough to explain the behavior of ferromagnetic materials.

Inside strongly magnetic materials there are regions called magnetic domains, whose extension can vary between 10 ^-4 and 10 ^-1 cm and that contain billions of atoms. In these regions, the net spin moments of neighboring atoms become tightly coupled.

When a material with magnetic domains approaches a magnet, the domains align with each other, intensifying the magnetic effect.

It is because domains, like bar magnets, have magnetic poles, equally denoted North and South, such that like poles repel and opposite poles attract.

As the domains align with the external field, the material emits cracking sounds that can be heard by appropriate amplification.

This effect can be seen when a magnet attracts the soft iron nails and these in turn behave like magnets attracting other nails.

Magnetic domains are not static boundaries established within the material. Its size can be modified by cooling or heating the material, and also subjecting it to the action of external magnetic fields.

However, the growth of the domain is not unlimited. At the moment in which it is no longer possible to align them, it is said that the saturation point of the material has been reached. This effect is reflected in the hysteresis curves below.

Heating of the material causes loss of alignment of the magnetic moments. The temperature at which magnetization is completely lost differs depending on the type of material, for a bar magnet it is usually lost at around 770ºC.

Once the magnet is removed, the magnetization of the nails is lost due to the thermal agitation present at all times. But there are other compounds that do have permanent magnetization, because they have spontaneously aligned domains.

Magnetic domains can be observed when a flat area of ​​non-magnetized ferromagnetic material, such as soft iron, is very well cut and polished. Once this is done, it is sprinkled with powder or fine iron filings.

Under the microscope it is observed that the chips are grouped on the mineral forming regions with a very well defined orientation, following the magnetic domains of the material.

The difference in behavior between different magnetic materials is due to the way the domains behave within them.

Magnetic hysteresis

Magnetic hysteresis is a characteristic that only materials with high magnetic permeability possess. It is not present in paramagnetic or diamagnetic materials.

It represents the effect of an applied external magnetic field, which is denoted as H, on the magnetic induction B of a ferromagnetic metal during a cycle of magnetization and demagnetization. The graph shown is called a hysteresis curve.

Ferromagnetic hysteresis cycle

Initially at point O there is no applied field H or magnetic response B, but as the intensity of H increases, the induction B increases progressively until reaching the saturation magnitude B _s at point A, which is expected.

Now the intensity of H is progressively decreased until it becomes 0, with that we reach point C, however the magnetic response of the material does not disappear, retaining a remanent magnetization indicated by the value B _r. It means that the process is not reversible.

From there the intensity of H increases but with the polarity reversed (negative sign), so that the remanent magnetization is canceled at point D. The necessary value of H is denoted as H _c and is called the coercive field.

The magnitude of H increases until it reaches the saturation value at E again and immediately the intensity of H decreases until it reaches 0, but there remains a remanent magnetization with polarity opposite to that previously described, at point F.

Now the polarity of H is reversed again and its magnitude is increased until the magnetic response of the material at point G is canceled. Following the path GA its saturation is obtained again. But the interesting thing is that you did not get there by the original path indicated by the red arrows.

Magnetically hard and soft materials: applications

Soft iron is easier to magnetize than steel, and tapping the material further facilitates the alignment of the domains.

When a material is easy to magnetize and demagnetize it is said to be magnetically soft, and of course if the opposite happens it is a magnetically hard material. In the latter the magnetic domains are small, while in the former they are large, so they can be seen through the microscope, as detailed above.

The area enclosed by the hysteresis curve is a measure of the energy required to magnetize - demagnetize the material. The figure shows two hysteresis curves for two different materials. The one on the left is magnetically soft, while the one on the right is hard.

A soft ferromagnetic material has a small coercive field H _c and a high, narrow hysteresis curve. It is an appropriate material to be placed in the core of an electrical transformer. Examples of them are soft iron and silicon-iron and iron-nickel alloys, useful for communications equipment.

On the other hand, magnetically hard materials are difficult to de-magnetize once magnetized, as is the case with alnico alloys (aluminum-nickel-cobalt) and rare earth alloys with which permanent magnets are made.

References

1. Eisberg, R. 1978. Quantum Physics. Limusa. 557 -577.
2. Young, Hugh. 2016. Sears-Zemansky's University Physics with Modern Physics. 14th Ed. Pearson. 943.
3. Zapata, F. (2003). Study of mineralogies associated with the Guafita 8x oil well belonging to the Guafita field (Apure State) using Mossbauer Magnetic Susceptibility and Spectroscopy measurements. Degree thesis. Central University of Venezuela.