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Paramagnetism is the property of some materials in which, when subjected to a magnetic field, a force is generated, which disappears when the field is removed. Before explaining paramagnetism, let’s first look at some ideas about magnetism and magnetic fields.
Magnetism and magnetic fields
Magnetism is one of the three interactions of matter that classical physics contemplated, that is, Newtonian physics, along with gravitational attraction and electrical interactions. In past times it had already been observed that certain materials attracted iron, and it is in ancient Greece where the term “magnetic” originates, associated with an iron mineral with ferromagnetic properties. Then a fundamental application of magnetism was discovered in China, the compass, which aligns a magnetized needle in the earth’s magnetic field allowing orientation in any geographical environment. Magnetism and electricity are related, as Hans Christian Oersted first demonstrated in 1820 when he observed that an electric current produced a magnetic force. A moving electric charge generates a magnetic field, while a moving magnetic field generates an electric current. This last statement is the principle of operation of electric generators, which by rotating a magnetic field with a motor generate an electric current. This association between electric charges in motion and magnetic fields is essential to understand the behavior of magnetic materials and paramagnetism.
An electron is a negative electric charge, and moving in an atom generates a magnetic field; this is the origin of the magnetic properties of materials. It is the electrons and their movement that generate the magnetism of materials. The magnetic field is understood as the distribution of forces at each point around the source of the field , which will have a magnitude , a direction and a direction .; The presentation figure of the article shows the magnetic field of a magnetic bar, with its two poles of attraction. Electrons and their movement generate magnetic fields in two ways, associated with the types of movement they develop in the atom: orbital movement around the nucleus and rotation on itself, its spin. The latter, the spin magnetic moment, is the most important due to its magnitude. The magnetic moment of the atom is the sum of the magnetic moments of the electrons. Electrons occupy atomic orbitals in pairs, with spins in opposite directions; the spin magnetic moment of pairs of electrons in the same orbital will be zero. since they cancel when they have opposite directions. Therefore, only atoms with orbitals that are not complete, that have only one electron, they will have a net magnetic moment, and the intensity will depend on the number of orbitals with only one electron. Iron, for example, has 26 electrons and 4 3 orbitals.d are occupied by a single electron; Cobalt, with 27 electrons, has 3 3d orbitals occupied by a single electron.
Ferromagnetic and ferrimagnetic materials
In a material, the atomic magnetic moments are disordered, following different directions. When all the atomic magnetic moments of a material are ordered in the same direction and in the same sense, they add up and generate the magnetization of the material. In this case we have a ferromagnetic material, which has a permanent magnetic field. This ordering of atomic magnetic moments is generated spontaneously in some materials, but it does not only depend on the element, but also on how it is organized microscopically, and in particular on the crystalline structure. A material that generates spontaneous permanent magnetization can be composed of microscopic sectors with different magnetization directions, as shown in the following figure. In this case,
Iron (Fe), cobalt and nickel are some elements that, either forming crystalline structures as elements or as part of molecules, constitute ferromagnetic materials. A ferromagnetic compound made up of iron is diferric ferrous oxide, Fe 3 O 4 , the so-called magnetite, which gave rise to the term magnetic.
Another way of orientation of the atomic magnetic moments in a material can be in the same direction but in the opposite direction in alternating lines, as shown in the following figure. Since the magnitude of the magnetic moment is different for each direction, the assembly has a net magnetization. These materials are called ferrimagnetic and, like ferromagnetics, are permanently magnetized. Ferrites are the most widespread ferrimagnetic material. Ferrites are a group of iron compounds alloyed with barium, zinc, cobalt, strontium, manganese, molybdenum or nickel, which form centered cubic crystalline structures. Their importance lies in the fact that they are materials with permanent magnetization but they are not conductors of electricity, and they have very good mechanical properties. Its applications range from magnets in refrigerators to ink in laser printers. They formed the memory core of early computers, and in powdered form they are used in data recording tapes and bands, in paints, and in many other applications.
paramagnetic materials
A paramagnetic material is one whose atomic magnetic moments are ordered in a magnetic field, and which will therefore be subject to a force when placed in a magnetic field, but when the external magnetic field ceases, its atomic magnetic moments return to become disordered and does not retain magnetization. Some examples of paramagnetic materials are iron oxide (FeO) and transition metal complexes: chromium, copper, manganese, scandium, titanium and vanadium. But all ferromagnetic and ferrimagnetic materials become paramagnetic when heated above a certain temperature, called the Curie temperature (T c ) . For example, the Curie temperature of iron is 770 o C, that of cobalt is 1127 oC and that of magnetite 585 o C.
In paramagnetic materials, temperature affects the magnetic force that is generated in the material when an external magnetic field is applied, since as temperature increases, the ordering of atomic magnetic moments decreases. This is expressed in Curie’s law. by the following expression:
χ = C/T
where χ is the magnetic susceptibility, T is the absolute temperature (in Kelvin) and C is a material-dependent parameter, the Curie constant.
The magnetization M of a paramagnetic material also depends on the intensity of the external magnetic field H. The expression for the magnetization is:
M = χH = (C/T)H
This expression is valid for high temperatures and for weak external magnetic fields; however, it loses its validity when all the atomic magnetic moments are close to being completely aligned. At that point, even if the external magnetic field is increased or the temperature is decreased, there will be no effect on the magnetization of the material, since there will be no change in the ordering of the atomic magnetic moments. This is a magnetic saturation point .
The idea of saturation is clearly observed in the extension of Curie’s law to ferromagnetic materials in the so-called Curie-Weiss law, introducing the Curie temperature T c that we saw before:
χ = C/(TT c )
This expression makes sense only for temperature values greater than the Curie temperature, a situation in which the material behaves as paramagnetic; for temperature values less than or equal to the Curie temperature, the material is ferromagnetic and its magnetization takes the maximum possible value.
Sources
Amikam Aharoni. Introduction to the theory of ferromagnetism . Second edition. Oxford University Press, 2000.
Rolf E. Hummel. Electronic Properties of Materials . Springer, 2011.
WKH Panofski and M. Philips. Classical electricity and magnetism . New York: Dover, 2005.
Fundamentals of materials course, UPV. https://www.upv.es/materiales/Fcm/Fcm10/trb10_2.html
