The generation of magnetic fields can be divided into two main aspects: one is based on moving electric current (electromagnetic induction), and the other is based on the spin of the fundamental particles that make up matter. The first is the magnetic effect of electric current, which we are more familiar with; when an electric current flows through a conductor, the directional movement of free electrons generates a magnetic field. The second is the magnetic field generated by matter itself, which is the main topic we will discuss today.
Everything in the world possesses magnetism. From the small tables and chairs around us to the planets and the sun in the universe, everything has magnetism, regardless of its state (crystalline, amorphous, liquid, or gaseous), temperature, or pressure. The difference lies in the strength of the magnetism; some substances have strong magnetism, while others have weak magnetism. It can be said that there is no substance without magnetism.
Matter can be classified into five categories based on its properties in an external magnetic field: paramagnetic, diamagnetic, ferromagnetic, ferrimagnetic, and antiferromagnetic. What causes matter to possess magnetism? And what causes different substances to have these different properties? This requires starting with the foundation of matter—the atom.
Matter is composed of atoms, and atoms are composed of a nucleus and electrons. In an atom, electrons possess an orbital magnetic moment due to their orbital motion around the nucleus; electrons also possess a spin magnetic moment due to their spin. The magnetic moment of an atom primarily originates from the orbital and spin magnetic moments of electrons, which are the source of magnetism in all matter. (The magnetic moment of the atomic nucleus is only 1/1836.5 of the electron’s magnetic moment, therefore the nuclear magnetic moment is generally ignored.)
Magnetic Moment of a Single Isolated Atom
A magnetic moment is a directional vector. Electrons in an atom have two spin orientations: up and down. In most substances, the number of electrons with up spin and down spin is equal, and their magnetic moments cancel each other out, resulting in no external magnetism for the atom. Only in a few substances are the number of electrons in different spin directions within the atom. In this case, after the magnetic moments of electrons with opposite spins cancel each other out, the remaining spin magnetic moments of some electrons are also canceled out, resulting in a total magnetic moment for the entire atom. The magnetic moment of a single atom depends on its atomic structure, specifically the arrangement and number of electrons. Atoms of all elements in the periodic table have their own magnetic moments.
Magnetic Moment of Atoms in Crystals
The above discussion concerns the magnetic moment of a single atom. However, in solid crystals or amorphous solids, atoms are located at crystal nodes. These atoms are influenced by the nuclear electric field and electrostatic field of neighboring atoms. Therefore, the magnetic moment of atoms in crystals differs from that of a single isolated atom. For example, iron, cobalt, and nickel are called 3d transition metals. In crystals, some electrons of certain atoms become shared electrons of neighboring atoms, changing the electronic structure of the atoms. Some orbital magnetic moments are frozen, leaving only the spin magnetic moment to contribute to the atomic magnetic moment in the crystal. This results in a difference between the actual magnetic moment of the atoms in the crystal and the theoretical value.
Magnetic Moment of Macroscopic Matter
As we know from the preceding content, everything in the universe possesses magnetism, primarily originating from atomic magnetism. Because different atoms have different magnetic moments, interactions occur between atomic magnetic moments in macroscopic matter. The arrangement of atomic magnetic moments at room temperature differs. Based on the magnetic properties of macroscopic matter, we classify it into paramagnetic, diamagnetic, ferromagnetic, ferrimagnetic, and antiferromagnetic materials. These characteristics include the following three:
1. Magnetization M
The macroscopic magnetism of a substance is contributed by the magnetic moments of its constituent atoms or molecules. The total magnetic moment per unit volume of a material is called its magnetization, denoted by M, with units of A/m.
1. Let the volume of a substance be V, and it have n atoms. The magnetic moment of each atom is μJ. Then M = μJ1 + μJ2 + … + μJn, or M = ΣμJ/v.
2. Magnetization Curve (M~H Curve)
When the external magnetic field is zero, the atomic magnetic moments may be randomly arranged. However, when a non-zero external magnetic field is applied, under the influence of the field, each atomic magnetic moment will align with the direction of the magnetic field. At this time, the magnetization M of the substance changes. The curve showing the relationship between magnetization M and the external magnetic field H is called the magnetization curve, abbreviated as M~H magnetization curve. Different substances have different magnetization curves.
3. Magnetic Susceptibility χ
On the M~H magnetization curve, the ratio of M to H at any point is called the magnetic susceptibility, denoted by χ. χ = M/H, where the unit of M is A/m, and the unit of H is also A/m. Therefore, it is a relative magnetic susceptibility and has no unit.
We use the magnitude and arrangement of atomic magnetic moments, the shape of the M~H magnetization curve, and parameters such as magnetic susceptibility to describe the magnetism of substances and classify them.
Paramagnetic Substances
These are substances that can be magnetized along the direction of a magnetic field when brought near it, but the magnetization is very weak and can only be measured with precise instruments. If the external magnetic field is removed, the internal magnetic field also returns to zero, resulting in no magnetism. Examples include aluminum and oxygen.
Each atom in a paramagnetic substance has a magnetic moment, giving it an intrinsic atomic magnetic moment. There is no interaction between adjacent atoms in paramagnetic substances; therefore, at room temperature, the atomic magnetic moments are randomly arranged, and the projection value of the atomic magnetic moment μJ in any direction is zero. When an external magnetic field H is applied, the atomic magnetic moments of these substances can only rotate a very small angle along the direction of the external magnetic field, and their magnetization increases slowly with the increase of the external magnetic field. Its magnetic susceptibility χ>0, and its value is generally 10⁻⁵ to 10⁻³.
To ensure that the atomic magnetic moments of a paramagnetic material align perfectly with the direction of an external magnetic field, a rough estimate suggests that an external magnetic field strength of 10⁹ to 10¹⁰ A/m is required, which is currently difficult to achieve with artificial magnetic fields.
Diamagnetic materials
are materials with negative magnetic susceptibility, meaning that after magnetization, the direction of the magnetic field is opposite to that of the external magnetic field. All organic compounds exhibit diamagnetism; graphite, lead, and water are examples of diamagnetic materials.
In diamagnetic materials, the projections of both the atomic orbital magnetic moments and spin magnetic moments onto the magnetic field are zero, meaning that diamagnetic materials have no net atomic magnetic moment. However, under the influence of an external magnetic field, electron orbitals generate an induced additional magnetic moment, and this induced magnetic moment is opposite to the direction of the external magnetic field, thus exhibiting negative magnetism. The magnetization intensity of diamagnetic materials is negative, opposite to the external magnetic field, and its absolute value increases linearly with the increase of the external magnetic field.
Ferromagnetic materials
These are materials that, once magnetized by an external magnetic field, retain their magnetization even after the field disappears. To date, 83 metallic elements have been discovered, four of which are ferromagnetic above room temperature: iron, cobalt, nickel, and gadolinium. At extremely low temperatures, five more elements can transform into ferromagnetic elements: terbium, dysprosium, holmium, erbium, and thulium.
In ferromagnetic materials, atoms possess inherent atomic magnetic moments. Some electrons are shared, and the spin magnetic moments of adjacent atoms are aligned parallel to each other (also known as spontaneous magnetization). The M-H magnetization curve of ferromagnetic materials is non-linear, and the magnetic susceptibility χ varies with the magnetic field. The magnetic susceptibility χ of ferromagnetic materials is very high, reaching 10⁵ to 10⁷.
Antiferromagnetic materials
These do not produce a magnetic field. They are relatively uncommon, and new antiferromagnetic materials are constantly being discovered. Most antiferromagnetic materials exist only at low temperatures; above a certain temperature, they typically become paramagnetic. For example, chromium and manganese are antiferromagnetic.
In antiferromagnetic materials, atoms also possess inherent atomic magnetic moments. Some electrons are shared, but adjacent atomic magnetic moments are aligned in opposite directions (also known as antiferromagnetic order). The M~H magnetization curve of ferromagnetic materials is linear, with a magnetic susceptibility χ>0, and its value is approximately 10⁻⁴ to 10⁻⁵, which is very small and a constant. This means that when an antiferromagnetic material is magnetized in an external magnetic field, its atomic magnetic moments change very little with the external magnetic field, similar to paramagnetic materials, belonging to weak magnetism. The magnetic susceptibility χ of antiferromagnetic materials varies with temperature, as shown in the figure below; Tn is called the Niehr temperature.
Ferriferromagnetic Materials
The macroscopic magnetism is the same as ferromagnetism, only the magnetic susceptibility is lower (magnetic susceptibility χ is 10²~10⁵). Typical ferrimagnetic materials include ferrites. Their most significant difference from ferromagnetic materials lies in their internal magnetic structure (magnetic moment arrangement).
Image The atomic magnetic moments of subferromagnetic materials are not zero. There is an indirect exchange interaction, or RKKY exchange interaction, between adjacent atomic magnetic moments, causing the atomic magnetic moments of adjacent sublattices to align in antiparallel order. However, the magnitudes of the atomic magnetic moments of adjacent sublattices differ. This phenomenon is also called subferromagnetic ordering or subferromagnetic spontaneous magnetization. The M~H magnetization curve of subferromagnetic materials is nonlinear, similar to that of ferromagnetic materials, only with a slightly lower magnetic susceptibility, but it still belongs to strong magnetism.