The magnetic moment of an atom is the main physical vector quantity characterizing the magnetic properties of any substances. The source of the formation of magnetism, according to the classical electromagnetic theory, is the microcurrents arising from the motion of an electron in its orbit. The magnetic moment is an indispensable property of all elementary particles, nuclei, atomic electron shells and molecules, without exception.
Magnetism, which is inherent in all elementary particles, according to quantum mechanics, is due to the presence of a mechanical moment called spin (their own mechanical momentum of a quantum nature). The magnetic properties of an atomic nucleus are composed of spin momenta of the constituent parts of the nucleus - protons and neutrons. Electron shells (intra-atomic orbits) also have a magnetic moment, which is the sum of the magnetic moments of the electrons on it.
In other words, the magnetic moments of elementary particles and atomic orbitals are due to the intra-atomic quantum-mechanical effect, known as the spin momentum. This effect is similar to the angular momentum of rotation around its own central axis. The spin momentum is measured in the Planck constant - the main constant of quantum theory.
All neutrons, electrons and protons, of which, in fact, is the atom, according to Planck, have a spin equal to ½. In the structure of an atom, electrons rotating around a nucleus, in addition to a spin momentum, also have an orbital angular momentum. The nucleus, although it occupies a static position, also has an angular momentum created by the nuclear spin effect.
The magnetic field that generates an atomic magnetic moment is determined by various forms of this angular momentum. The most noticeable contribution to the creation of a magnetic field is precisely the spin effect. According to the Pauli principle, according to which two identical electrons cannot stay simultaneously in the same quantum state, the bound electrons merge, while their spin momenta acquire diametrically opposite projections. In this case, the magnetic moment of the electron is reduced, which reduces the magnetic properties of the entire structure. In some elements having an even number of electrons, this moment decreases to zero, and substances cease to have magnetic properties. Thus, the magnetic moment of individual elementary particles directly affects the magnetic properties of the entire nuclear-atomic system.
Ferromagnetic elements with an odd number of electrons will always have nonzero magnetism due to an unpaired electron. In such elements, adjacent orbitals overlap, and all spin moments of unpaired electrons take the same orientation in space, which leads to the achievement of the lowest energy state. This process is called exchange interaction.
With this alignment of the magnetic moments of ferromagnetic atoms, a magnetic field arises. And paramagnetic elements consisting of atoms with disoriented magnetic moments do not have their own magnetic field. But if you act on them with an external source of magnetism, then the magnetic moments of the atoms will equalize, and these elements will also acquire magnetic properties.