Paramagnetism

paramagnetism is one of the behaviors of the matter when it is subjected to a magnetic field. -->

The paramagnetism is the tendency of the magnetic dipoles atomic to align itself with a external Magnetic field, because of their magnetic moments. Within the framework of paramagnetism, the magnetic dipole moments are without interaction between them.

Principle

The magnetic Moment of an atom $\backslash \; vec\; \backslash \; mu$ is connected to its kinetic moment $\backslash \; vec\; J$ by:

$\backslash \; vec\; \backslash \; mu=-g\; \backslash \; mu\_\; \backslash \; mathrm\; \{B\}\; \backslash \; vec\; J\; \{\backslash \; hbar\}$

with $G$ the Factor of Moor and $\backslash \; mu\_\; \backslash \; mathrm\; \{B\}$ the magneton of Bohr

The total kinetic moment results from 3 components:

• Spin
• orbital kinetic Moment of the electrons
• nuclear Spin of the nucleons.

The nuclear spin being very weak, it does not contribute a sufficient share to susceptibility to be taken into account. It is however possible to measure it, and it is used in medicine by the Imagerie by magnetic resonance

In the external absence of magnetic field , the magnetic moment of each atom is directed randomly, and summons it these magnetic moments (micromagnets) is thus null on the scale Macroscopique, the body is not magnetized.

In presence of an external magnetic field , each moment magnetic of atom $\backslash \; vec\; \backslash \; mu$ tends to be aligned in the same direction and the same direction that the external magnetic field, and one observes a Précession of this magnetic moment.

In paramagnetic materials, the magnetic moments of spin dominate over those produced by the orbital movements of the electrons. By convention, the paramagnetic materials are described by a magnetic Susceptibilité positive:

$\backslash \; vec\; M\; =\; \backslash \; chi\_m\; *\; \backslash \; vec\; B\_0$ with $\backslash \; chi\_m\; >\; 0$

Paramagmetism of Langevin

See also: Law of Curie

Paul Langevin introduced the idea according to which the magnetic moment of a body can be the sum of the magnetic moments of each atom. However, an increase in the temperature brings thermal Agitation which involves the confusion of the magnetic moments of the atoms, in spite of the influence of the external magnetic field. Paul Langevin then explains the reduction in paramagnetism like a function inversely proportional to the temperature. This phenomenon is described by the Loi of Curie:

$\backslash \; mathbf\; \{M\}\; =\; C\; \backslash \; cdot\; \backslash \; frac\; \{\backslash \; mathbf\; \{B\}\}\; \{T\}$

$\backslash \; mathbf\; \{M\}$ is magnetizing

$\backslash \; mathbf\; \{B\}$ is the flow of the magnetic field applied, measured in Teslas

$T$ is the absolute temperature, in Kelvin S

$C$ is the Constante of Curie material. It is defined by:

$C\; =\; \backslash \; frac\; \{NR\; \backslash \; mu^2\}\; \{k\_B\}$

where $N$ is the number of magnetic moments to consider, $\backslash \; mu$ is one individual magnetic moment and $k\_B$ is the Boltzmann constant.

Magnetic moment of the electrons of conduction: paramagnetism of Pauli

In a metal the electrons of conduction can move almost freely, they are very slightly related to the atoms of metal (for example Modèle of Drude). As the electrons have one magnetic moment of spin, one then awaits a contribution with the susceptibility, which is similar to the law of Curie. Let us électons being Fermions, they must then check the Principe of Pauli, and the following law is observed:

$\backslash \; chi\_\; \backslash \; mathrm\; \{Pauli\}\; \backslash \; sim\; \backslash \; frac\; \{C\}\; \{T\}\; \backslash \; cdot\; \backslash \; frac\; \{T\}\; \{T\_\; \backslash \; mathrm\; \{F\}\}\; =\; \backslash \; frac\; \{C\}\; \{T\_\; \backslash \; mathrm\; \{F\}\}$,

where $T\_\; \backslash \; mathrm\; \{F\}$ is a constant of materials.

To be more precise, one can show that there exists a dependence of the force of the magnetic fields.

Paramagnetic materials

• Aluminum Al (metal)
• Barium Ba (metal Alkaline-earth)
• Calcium Ca (metal Alkaline-earth)
• liquid Oxygen O₂ (nonmetal)
• Platinum Pt (Metal of transition)
• Sodium Na (Alkaline metal )
• Strontium Sr (metal Alkaline-earth)
• Uranium U (metal (Actinide))
• Magnesium Mg (metal Alkaline-earth)

• Technetium Tc (artificial Metal of transition)

• Lithium Li (Alkaline metal )

See too

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