20s

The magnetism is produced by the electric charges moving. One distinguishes:

• the magnetism produced by currents developed in Magnetostatic
• magnetism in the matter or various kinds of magnetization developed Ci below.

Experiment of Ørsted

In 1820, Danish Hans Christian Ørsted watch that near a rectilinear wire traversed by an electric current, the needle of a compass deviates.

the displacement of electric charges creates a Magnetic field.

Characteristics of the magnetic field $\backslash \; vec\; B$

It reigns a magnetic field when a magnetized needle takes a given direction.

• direction : that of the magnetized needle which detects it.

• direction : chosen according to the direction south-north of the magnetized needle.
• standard : unit IF, the Tesla (T).

Magnetism in the matter

Faraday showed that any substance is aimantable but generally the effect is appreciable only in one intense magnetic field; let us place in a nonuniform magnetic field of the bars of different substances:

• some are attracted towards the areas of high field while being directed the lines of field parallel to as would do it a soft iron bar.

• of others is pushed back towards the areas where the magnetic field is weak and are directed perpendicular to the lines of field; such substances are known as ''' diamagnetic ''' (money, gold, copper, mercury, lead, almost all organic compounds…)

The substances which are comparable with iron are known as ''' ferromagnetic ''' (iron, cobalt, nickel and a great number of their alloys in particular steels) and certain their compounds like certain combinations of nonferromagnetic elements.

The substances which undergo actions of comparable nature that iron but much less intense are known as ''' paramagnetic ''' (aluminum, chromium, platinum… and some ferromagnetic compounds of elements for example the alloy 68% iron 32% of nickel).

Macroscopic description

A Solenoid (cylindrical rolling up) traversed by a current of intensity $I\; \backslash ,$ creates a magnetic field noted $\backslash \; vec\; B\_0\; \backslash ,$. If, inside this solenoid one places a material, one notes a modification of the module of the vector magnetic field which one will note now $\backslash \; vec\; B\; \backslash ,$.

Remark : In certain old works or certain technical books $\backslash \; vec\; B\; \backslash ,$ is called magnetic vector induction

Magnetic excitation

One poses: $\backslash \; vec\; H\; =\; \backslash \; frac\; \{\backslash \; vec\; B\_0\}\; \{\backslash \; mu\_0\}\; -\; \backslash \; vec\; M$, with $\backslash \; mu\_0\; \backslash ,$: permeability of the vacuum, and $\backslash \; vec\; M$, magnetization

Magnetic permeability and susceptibility

The presence of material modifies the magnetic field. One poses:

• $\backslash \; vec\; B\; =\; \backslash \; driven.\; \backslash \; vec\; H$ with $\backslash \; driven\; \backslash ,$: magnetic Permeability of the material
  

One defines by $\backslash \; vec\; M\; \backslash ,$ the vector magnetization acquired by the matter

• $\backslash \; vec\; M\; =\; \backslash \; chi.\; \backslash \; vec\; H$ with $\backslash \; chi\; \backslash ,$: magnetic Susceptibility of the matériau
  
• from where: $\backslash \; vec\; B\; =\; \backslash \; mu\_0\; (\backslash \; vec\; H\; +\; \backslash \; vec\; M)\; =\; (1\; +\; \backslash \; chi)\; \backslash \; vec\; B\_0$

One also poses:

• $\backslash \; mu\_r\; =\; \backslash \; frac\; \{\backslash \; driven\}\; \{\backslash \; mu\_0\}\; =\; (1\; +\; \backslash \; chi)$ with $\backslash \; mu\_r\; \backslash ,$: relative Permeability of material.

Classification of the magnetic effects

• Diamagnetism : materials for which $\backslash \; chi\; \backslash ,$ is negative but always extremely weak : about 10^{- 5}
• Paramagnetism : materials for which $\backslash \; chi\; \backslash ,$ is positive but always very weak : about 10^{- 3}
• Ferromagnetism and Ferrimagnetism : materials for which $\backslash \; chi\; \backslash ,$ is positive and very large : it can reach 10 ⁵! In electrotechnical only these materials are important because they are the only ones to produce increases in the magnetic field which are significant (see below).

Microscopic origin of magnetism

Movement of the electrons

The movement of the electrons in the electronic cloud is responsible for the existence of a magnetism known as orbital , whereas rotation on themselves is responsible for the magnetism of Spin . It is not possible to be unaware of the quantum aspect of these phenomena: in 1919, in its thesis of Doctorate, J.H. van Leeuwen proved that it was impossible to explain magnetism only using the electrodynamics of Maxwell and traditional statistical mechanics.

Origin of diamagnetism

The effect of a magnetic field is to give to the whole of the electronic movement an angular velocity of rotation around the direction of the magnetic field applied: traditional phenomenon of induction. This magnetic moment induced is proportional to the field applied and is opposed to this last. It is the origin of the diamagnetism which is thus a completely general phenomenon but which can be masked by the other phenomena of which the effect is more important.

Remark : One employment the term of perfect diamagnetism to indicate the behavior of the superconductors which create in their center of the induced currents which are opposed to any variation of magnetic field. This property is used to produce the magnetic levitation of the superconductors.

Origin of paramagnetism

When the atoms have their clean magnetic Moment permanent, diamagnetism (always present) is masked by paramagnetism. Under the effect of an external magnetic field, these atoms, small permanent magnet, are directed according to the field applied and amplify it. This phenomenon is limited by thermal agitation and strongly depends on the temperature: (Law of Curie: $\backslash \; mathbf\; \{M\}\; =\; C\; \backslash \; cdot\; \backslash \; frac\; \{\backslash \; mathbf\; \{B\}\}\; \{T\}\; \backslash ,$)

This phenomenon is related to the existence of the spin of the electron.

• For the atoms: An atom whose electron shells are completely filled does not have magnetic moment. When the layers are incomplete, there is always an imbalance which produces one magnetic moment of spin.
• For the solids that can be very different: the external electrons take part in the chemical bonds. In the covalent bonds the paired electrons are of opposite spin. The ions of the ionic crystals have complete layers. One can thus have a disappearance of clean magnetism. The existence of paramagnetism remains for the solids made up of atoms having incomplete internal electron shells: metals of transitions and Lanthanides (rare earths) for example.

Ferromagnetism

See also: Ferromagnetism

It is the property which under the effect of an external magnetic field has certain bodies to very strongly magnetize, and for some of between-them, called Aimant S ( IE. hard magnetic materials), to keep an important magnetization even after the disappearance of the external field (residual magnetization).

Ferromagnetic bodies

For the industrial use, only the Iron, the Cobalt and the Nickel are the ferromagnetic interesting ones. Certain rare earths (the Lanthanide S in the periodic classifiation) are also ferromagnetic at low temperature.

With regard to the Alloy S, the situation is very complex: certain nickel and iron alloys are not ferromagnetic, whereas the alloy of Heussler, only made up of nonferromagnetic metals (61% Cu, 24% mn, 15% Al), is ferromagnetic.

Lastly, it is necessary to add the ferrites, whose composition is form (MO; Fe₂O₃) or M is a divalent metal and whose oldest representative is the Magnétite Fe₃O₄ (FeO; Fe₂O₃).

Curve of the first magnetization

Hysteresis loops

See also: Hysteresis

When one magnetized a material sample until saturation and that one decreases the excitation H , one notes that B also decrease, but while following a different curve which is located above the curve of the first magnetization. This is the fact of a delay with demagnetization. It is said that there is Hystérésis .

When H is brought back to 0, there remains a magnetic field B_r called remanent field (of Latin remanere , to remain). To cancel this remanent field, it is necessary to reverse the current in the solenoid, i.e. to impose on H a negative value. The magnetic field then cancels for a value of the excitation H_c called coercive excitation .

Consequences of hysteresis

The magnetization of the matter absorbs energy which only is partially restored during demagnetization. This energy is dissipated in calorific form: the material warms up. It is shown that the losses by hysteresis are proportional to the surface of the hysteresis loop.

If the ferromagnetic substance must describe a great number of cycles of hytérésis (revolving machines, transformers…), it is necessary to choose materials such as the surface of the cycle is as small as possible. These materials are known as magnetically “soft. ”

On the other hand, it is thanks to an important hysteresis that one can produce permanent magnets. One uses for their manufacture of magnetically hard materials: certain aluminum steels, with nickel or cobalt are appropriate perfectly. One produces also magnets with iron powder agglomerated in an insulator.

Soft magnetic materials

They are in general soft materials mechanically. These materials have very narrow cycles: the coercive excitation does not exceed 100 A.m^{- 1}. They have a great permeability.

Some examples:

• SuperMalloy (Iron, Nickel, Molybdenum,…) : H_c = 0,16 A.m^-1; B_r = 1,2 T (one of softest);
• Iron + Silicon 3%, directed grains: H_c = 8 A.m^-1; B_r = 1,0 T
  

The soft magnetic materials are used to carry out electromagnet S (their magnetization must be able easily to be cancelled) or magnetic circuits working at an alternative normal rate (electric machines, transformers).

Hard magnetic materials

right Contrary to the precedents, the cycles are extremely broad: several hundreds of kA.m^-1. It is impossible to draw them in the same reference mark as the precedents.

Some of these materials containing rare earths (alloys samarium-cobalt or neodymium-iron-boron) are not demagnetized, even when the internal magnetic field is cancelled (the excitation is worth H_cB then). To cancel (makes some reverse) magnetization, it is necessary to provide a magnetic excitation which one calls H_cM : irreversible excitation of demagnetization.

The application of these materials is the realization of Aimant S permanent of very strong power. The Ferrofluide S are suspensions of magnetized particles of micronic size in a liquid. These liquids react to an external magnetic field (for example, their surface roughcasts points).

Microscopic origin of the ferromagnetism

The theory of the integrals (or interactions) of exchange proposed by Heisenberg in 1928 constitutes the theoretical base of the explanations of this phenomenon. When a solid consists of paramagnetic atoms (each atom can be comparable with a small magnet), it occurs a coupling between the latter.

Ferromagnetism

See also: Ferromagnetism

When the atoms are distant from/to each other in the crystalline structure, the coupling supports an alignment of these elementary magnets. It is the case of Iron α (centered cubic structure), of nickel, the cobalt and, more slightly, certain metals of the family of rare earths like the Gadolinium. Some alloys whose meshs are large can have this property.

Antiferromagnetism

See also: Antiferromagnetism

When the atoms are closer from/to each other, as it is the case for Chromium, manganese or hematite, the most stable configuration corresponds to magnets in antiparallel. There is not then more apparent magnetization at long distance because each elementary magnet is compensated by its neighbor.

Ferrimagnetism

See also: Ferrimagnetism

It is observed in materials comprising two types of different atoms, producing each elementary magnet of different force and directed in head-digs.

Fields of Weiss

See also: Field of Weiss

When a material is ferro or ferrimagnetic, it is divided into fields, called fields of Weiss , inside whose the magnetic orientation is identical. This field behaves then like a magnet. These fields are separated by walls known as walls from Bloch .

• These fields do not exist when dimensions of material are very low (some Nm). These materials are known as nanocristallins.
• the displacement of these walls is responsible for the phenomena of hysteresis.

See too

• magnetic Magnetic field

• Susceptibility
• Magnetization
• Electromagnet

References

• L.P. Levy, Magnetism and Supraconductivité (EDP Sciences)
• Neil W. Ashcroft and NR. David Mermin, Solid State Physics (Harcourt: Orlando, 1976).

Simple: Magnetism

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