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Magnetism and magnetic moment

The generation of magnetic field can be divided into two aspects: one is based on the moving current (electromagnetic induction), the other is based on the spin of the basic particles of matter. The first is the familiar magnetic effect of electric current, which is caused by the directional movement of free electrons after the wire is electrified. The second is the magnetic field produced by matter itself, which we will mainly introduce today.
All things in the world have magnetism, ranging from the tables and chairs around us to the planets and the sun in the universe. No matter what state they are in (crystalline, amorphous, liquid and gaseous), high or low temperature, high or low pressure, they all have magnetism. The difference is that some substances have strong magnetism, some have weak magnetism, but they can be said to have no magnetism Matter doesn’t exist.
According to their characteristics in the external magnetic field, substances can be divided into five categories: paramagnetic substances, diamagnetic substances, ferromagnetic substances, ferromagnetic substances and antiferromagnetic substances. So what’s the reason that makes matter magnetic? What causes different substances to have the above different characteristics? It starts with the atom, the basis of matter.

Matter is made up of atoms, which are made up of nuclei and electrons. In the atom, the electron has orbital magnetic moment because of its motion around the nucleus; the electron has spin magnetic moment because of its spin, and the magnetic moment of the atom mainly comes from the orbital magnetic moment and spin magnetic moment of the electron, which is the source of magnetism of all substances. (the magnetic moment of the nucleus is only 1/1836.5 of that of the electron, so the magnetic moment of the nucleus is generally ignored.)

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Magnetic moment of a single isolated atom

The magnetic moment is a directional vector. They have the same number of spins up and down in the whole matter as the electrons do, and most of them have the same number of spins up and down. Only a few matter atoms have different numbers of electrons in different spin directions. In this way, after the magnetic moments of electrons with opposite spin cancel each other, the spin magnetic moments of the remaining electrons are cancelled, and the whole atom has the total magnetic moment. The magnetic moment of a single atom depends on the atomic structure, that is, the arrangement and number of electrons.

Magnetic moment of atom in crystal

We discussed the magnetic moment of a single atom above, but in solid crystal or non crystal, the atoms are at the crystal node, and these atoms will be affected by the nuclear electric field and electronic electrostatic field near the atoms, so the magnetic moment of the atoms in crystal is different from that of a single isolated atom. For example, iron, cobalt, nickel, they are called 3d transition metals. In the crystal, the electrons of some atoms will become the public electrons of adjacent atoms. The electronic structure of atoms will change, and part of the orbital magnetic moment will be frozen. At this time, the only contribution to the magnetic moment of atoms in the crystal is the spin magnetic moment, so the magnetic moment of atoms in the crystal is different from the theoretical value.

Magnetic moment of macroscopic matter

Through the previous content, we have known that everything in the universe is magnetic, and magnetism mainly originates from atomic magnetism. Due to the different magnetic moments of different atoms, the interaction between the atomic magnetic moments of macro materials is caused, and the arrangement of the atomic magnetic moments at room temperature is different. According to the magnetic properties of macro materials, we divide them into paramagnetic materials, diamagnetic materials, ferromagnetic materials, ferromagnetic materials and antiferromagnetic materials, which include the following three characteristics.

Magnetization M

The macroscopic magnetism of a material is contributed by the magnetic moment of its atoms or molecules. We call the total magnetic moment of the material in unit volume as the magnetization of the material, which is expressed by m, and the unit is A/m.
Let the volume of a substance be V, it has N atoms, and the magnetic moment of each atom is μJ, then M=μJ1 + μJ2 + +μjn, that is M=∑μJ/v.

Magnetization curve of magnetization (M ~ H curve)

When the external magnetic field is zero, the atomic magnetic moment may be disorderly arranged, but when we apply a non-zero external magnetic field, under the action of the external magnetic field, each atomic magnetic moment can turn to the direction of the external magnetic field, and the magnetization m of the material changes. The curve of magnetization m changing with the change of external magnetic field H is called magnetization curve, which is abbreviated as m ~ H magnetization curve. The magnetization curves of different materials are also different.

Magnetic susceptibility χ

On the M ~ H magnetization curve, the ratio of m to h at any point is called susceptibility, which is expressed by χ. χ= M/H, where the unit of M is A/m, and the unit of H is also A/m, so it is relative susceptibility, and there is no unit.
We use the above parameters to describe the magnetic properties of materials and classify them.

Paramagnetic material

When they are moved close to the magnetic field, they can be magnetized according to the direction of the magnetic field, but they are very weak and can only be measured by precision instruments. If the external magnetic field is moved away, the internal magnetic field will return to zero, resulting in no magnetism. Such as aluminum, oxygen, etc.
Every atom of paramagnetic material has magnetic moment, which makes paramagnetic material have inherent atomic magnetic moment; there is no interaction between neighboring atoms of paramagnetic material, so the atomic magnetic moment is disorderly arranged at room temperature, and the projection value of atomic magnetic moment μJ in any direction is zero. When there is an external magnetic field H, the atomic magnetic moment of this kind of material can only turn a very small angle along the direction of the external magnetic field, and its magnetization increases slowly with the increase of the external magnetic field. Its magnetic susceptibility χ > 0, the value is generally 10-5~10-3.
In order to make the atomic magnetic moment of paramagnetic material completely arranged in the direction of external magnetic field, according to rough estimation, the intensity of external magnetic field is 109~1010 A / m, which is difficult to achieve by artificial magnetic field at present.

Diamagnetic material

It is a material with negative magnetic susceptibility, that is to say, the direction of magnetic field after magnetization is opposite to that of external magnetic field. All organic compounds have diamagnetism, graphite, lead, water are diamagnetic materials.
In other words, the diamagnetic material has no net atomic magnetic moment, but under the action of the external magnetic field, the electron orbit will produce an induced additional magnetic moment, and the induced magnetic moment is opposite to the direction of the external magnetic field, so negative magnetism appears. The magnetization direction of diamagnetic material is negative, opposite to the external magnetic field, and its absolute value increases linearly with the increase of the external magnetic field.

Ferromagnetic material

It is a kind of magnetic material that can keep its magnetized state even if the external magnetic field disappears after being magnetized under the action of external magnetic field. So far, 83 metal elements have been found, of which four are ferromagnetic elements above room temperature, they are iron, cobalt, nickel and gadolinium; at very low temperature, five elements can be transformed into ferromagnetic elements, They are terbium, dysprosium, holmium, erbium and thulium.
In ferromagnetic materials, atoms have inherent atomic magnetic moments, some electrons will be public, and the spin magnetic moments of adjacent atoms are parallel to each other in the same direction (also known as spontaneous magnetization). The M ~ H magnetization curve of ferromagnetic materials is nonlinear, and the magnetic susceptibility χ changes with the change of magnetic field. The magnetic susceptibility χ of ferromagnetic materials is very large, up to 105~107.

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Antiferromagnetic material

It doesn’t produce a magnetic field. This kind of material is relatively uncommon. New antiferromagnetic materials are still being discovered. Most antiferromagnetic materials only exist at low temperature. Assuming that the temperature exceeds a certain value, they usually become paramagnetic. For example, chromium and manganese all have antiferromagnetism.
The atoms in antiferromagnetic materials also have inherent atomic magnetic moments. Some electrons will be public, but the magnetic moments of adjacent atoms are arranged in reverse (also known as antiferromagnetic order). The M ~ H magnetization curve of ferromagnetic material is linear, the magnetic susceptibility is more than 0, and its value is about 10-4~10-5, which is a constant. That is to say, when the antiferromagnetic material is magnetized in the external magnetic field, its atomic magnetic moment changes little with the external magnetic field, which is the same as the paramagnetic material and belongs to weak magnetism. The susceptibility χ of antiferromagnetic material changes with the change of temperature. As shown in the figure below, Tn is called Neal temperature.

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Ferromagnetic material

Macromagnetism is the same as ferromagnetism, but the susceptibility is lower (χ =102~105). The most significant difference between typical ferromagnetic materials such as ferrite and ferromagnetic materials is the internal magnetic structure (magnetic moment arrangement).

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The atomic magnetic moment of ferromagnetic material is not zero. There is indirect exchange or RKKY exchange between adjacent atoms, which makes the atomic magnetic moment of adjacent sublattices arranged in reverse parallel. However, the atomic magnetic moment of their adjacent sublattices is different (see figure above). This phenomenon is also known as ferromagnetic ordering or ferromagnetic spontaneous magnetization. The M ~ H magnetization curve of ferromagnetic materials is nonlinear, similar to that of ferromagnetic materials, except that the susceptibility is slightly lower, but it still belongs to strong magnetism.
In the next issue, we will introduce the magnetic moment of magnetic materials from the macro level, including the relationship between magnetic moment and flux, remanence, and how to measure and calculate the magnetic moment
Note: some contents of this paper are quoted from “sintered NdFeB rare earth permanent magnet materials and technology” by Zhou Shouzeng, Dong Qingfei and Gao xuexu
Source: China Permanent Magnet Manufacturer – www.rizinia.com

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