# Magnetism and magnetization

## Atomic magnetic moment

Automatic translation Updated January 03, 2015

An electric current that flows through a wire creates a magnetic field, the Danish Hans Christian Oersted (1777-1851) who discovers that interaction between electricity and magnetism. Thus, any electrical charge that moves generates a magnetic field in the plane perpendicular to the movement and we can see it.
In an experiment with his students, Oersted demonstrated that a current in a wire, moves the needle of a compass. He published in 1820 in Journal für Chemie und Physik "Experiments on the effect of the electric conflict on the magnetic needle", translation « Experimenta circa effectum conflictus electrici in acum magneticam ».
But it is the French André-Marie Ampère (1775-1836) who builds the theoretical foundations of electromagnetism. Ampere defines the direction of the magnetic field that moves the needle of a compass in a rule called "the rule of Ampere man." The man is lying on the wire, the electric current flows from the feet to the head, the needle is facing his eyes, the north pole of the needle is on the left.
Electrons that move is magnetism, but at the beginning of the 19th century, we do not know the electron and can not explain the magnetism of the matter. Will have to wait Niels Bohr (1885-1962) and quantum mechanics (Bohr-van Leeuwen theorem in 1919) for the first explanation.

It is the rotation of the electrons around the nucleus, which creates the magnetic field in the material, known orbital magnetic field. In the matter, the global source of the magnetic field comes of the multiple microscopic currents associated with the electron cloud. The electron cloud is created by the permanent movement of all the electrons around the nucleus, it is about 10 000 times larger than its nucleus and filled all the spatial extent of the atom.
In addition to the orbital magnetic moment (concept of quantum mechanics), each electron, pictorially "turns on itself", and all electrons carry with them an angular momentum and thus a spin magnetic moment.
The spin of the core, when it is not zero, also creates a nuclear magnetic field that will interact with the magnetic moment of the electron.
In summary, the magnetic moment of the matter is the combination of all these microscopic atomic magnetic moments.
The unit of measurement of the magnetic field is the tesla (T). Earth's magnetic field in France is ≈47 µT. That of a decorative fridge magnet is ≈1000 µT.

NB: the magnetic moment of a current loop as the orbit of the electron, which surrounds an area as the surface of the atom, is μ = i S.
μ = magnetic moment
S = vector orthogonal to the surface
i = electric current amplitude equal to its area

## magnetic order

All the atoms the matter carry magnetic properties (permanent magnetic moments more or less ordered), but in the matter, little elements are magnetic because the electrons, which move around the nucleus of the atom, each create a small disordered magnetic field, which at the global level, that of the element, is canceled.
This concerns the atoms have electronic orbits "full" where the magnetic moments are compensated globally. In some cases linked to the existence of incomplete sub-layers, the compensation of the moments is not complete and the atom is magnetic.
Most magnetic elements are chromium (Cr), manganese (Mn), iron (Fe), cobalt (Co), nickel (Ni) and the rare earth elements Rare earth metals are a group of neighboring properties comprising scandium (Sc), yttrium (Y) and the fifteen elements of the lanthanides series in the table of Mendeleev, lanthanum (La), cerium (Ce), praseodymium (Pr), neodymium (Nd), Promethium (Pm), samarium (Sm), europium (Eu), gadolinium (Gd), terbium (Tb), dysprosium (Dy), holmium (Ho), erbium (Er), Thulium (Tm), ytterbium (Yb), and lutetium (Lu). these metals are paradoxically, quite common on Earth and they are malleable and ductile. (series of the lanthanides in the periodic table). These elements wear strongly coupled magnetic moments together (parallel). Furthermore, iron, cobalt and nickel are magnetic at room temperature. The temperature destroys the magnetization in a ferromagnetic material, the Curie temperature is the temperature at which the material loses its magnetization, 354 ° C for nickel, 769 ° C for iron, 1126 ° C for the Cobalt (see table attached).
Above this temperature, the material is in a disordered state, said paramagnetic, in other words, it no longer possesses spontaneous magnetization but if the temperature falls below the Curie temperature, it can recover a magnetization under the influence of an external magnetic field.
This is the French physicist Pierre Curie (1859-1906), who discovered in 1895, this property of the elements related to the Curie temperature.
Why these elements carry strongly coupled magnetic moments between them?
For an element to be strongly magnetic it is necessary that all microscopic magnetic moments interact with each other, in other words, that they are ordered and parallel between them.
This magnetic order or this coupling of the magnetic moments is called the molecular field (see note below) that gives this property to ferromagnetic materials.

NB: The molecular field was invented in 1907 by Pierre Weiss (1865-1940) to translate the interactions that should exist between the magnetic moments to produce the saturation magnetization in ferromagnetic materials.

 Material Symbol Curie temperature(K) Curie temperature(°C) Cobalt Co 1400 1126 Iron Fe 1043 769 Iron Boron Fe2B 1015 742 Samarium Cobalt SmCo5SmCo17 9951098 722825 Magnetite FeOFe2O3 858 585 Nickel Iron oxide NiOFe2O3 858 585 Copper Iron oxide CuOFe2O3 728 455 Magnesium Iron oxide MgOFe2O3 713 440 Manganese Bismuth MnBi 630 357 Copper Manganese Aluminium Cu2MnAl 630 357 Nickel Ni 627 354 Manganese Antimony MnSb 587 314 Neodymium Iron Boron Nd2Fe14B 585 312 Manganese Boron MnB 578 305 Manganese Iron oxide MnOFe2O3 573 300 Chromium dioxide CrO2 386 113 Gadolinium Gd 292 19 Dysprosium Dy 88 -185 Europium oxide EuO 69 -204

## Filling orbital boxes

The electrons have negative charges which repel and will use different orbital to avoid to meet. This feature was already true in classical mechanics. In quantum mechanics it is said that two electrons in the same atom can't be in the same quantum state, this is the famous principle of exclusion of the Austrian physicist Wolfgang Pauli (1900-1958).
They must differ by one of four quantum parameters: n, l, m, s (see nota opposite).
What are the parameters?
They are used to define a quantum box "Box and Arrow".
A quantum box can contain only two electrons to the maximum and the two electrons must not have the same parameter s, i.e. the same spin. The spin can take only two values +1/2 or -1/2. On the picture opposite the spin is represented by a red arrow that occupies a quantum box, without violating the Pauli exclusion principle, when there are two electrons, their spins are antiparallel.
When we completely fills the atomic layers, then the orbitals have as much spin electrons as +1/2 than spin electrons as -1/2 and there is no magnetism, the overall magnetic moments cancel each other.
When we not completely fill a layer, a magnetic moment is created because the outer layer has a magnetic imbalance, the number of spin electrons +1/2 is different from the number of spin electron -1/2 (see 3d layer on the image opposite). Magnetism is a property of incomplete electronic layers.

The spin is therefor a quantum "magnet" not only the electron is both a body and a quantum wave, but in addition, it carries a mini-magnet called spin. This spin, like all quantum property, can take only certain values.
To the origin of the magnetism, the spin also explains the chemical bonds between atoms in the material.

NB: The quantum state of an electron is defined by four parameters (n, ℓ, m, s), called the atomic quantum numbers:
- The principal quantum number n takes integer values (n = 1, 2, 3...) and corresponds to the energy level, to an electronic layer, n is the number of quantum layer which belongs to the electron.
- The secondary quantum number ℓ may take all values between 0 and n-1. It determines the relevant electronic sub-layer. The inner layers are designated by the letters s (sharp) for ℓ = 0, p (principal) for ℓ = 1, d (diffuse) for ℓ = 2, f (Fundamental) for ℓ = 3 then (for excited states ) g, h, i... for ℓ = 4,5,6...
- The magnetic quantum number m can take all values between -ℓ and +ℓ. It determines the orientation of the atomic orbital.
- The spin quantum number s can take the +1/2 or -1/2 values and determines the value of the moment of spin of the electron. It allows to quantify the intrinsic angular momentum of the electron, and defines the direction of the electron in a magnetic field.

### Image: example of filling quantum boxes associated with the different layers and sub-layers for electronic iron atom (Z = 26).Supporters of least effort, each electron begins to occupy the empty boxes quantum in lowest energy i.e. those of the layers of numbers n the smallest (closest orbitals of the nucleus, left on the picture). Then will put two and two in the lower energy boxes as a quantum box can only contain a maximum of two electrons over these electrons must have opposite spins to get in the box. Then within a layer n, they will occupy the sub-layers in the order of lowest energy is s, p, d, f... and will move to the next layer n until all electrons occupy a place.The orientation of the red arrows indicate the value of the spin quantum number.On the image an anomaly is observed, the 3d sub-layer is incomplete, so that the quantum box layer 4s is already filled. 4s layer has an energy level less than the 3d sub-layer, that is why the electrons fill the boxes in the order 1s2 2s2 2p6 3s2 3p6 4s2 3d6.

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