Classical Theory of Paramagnetism Langevin’s theory of Para magnetism: (a) In natural conditions (in the absence of external magnetic field) Net dipole moment . diamagnets, that is the susceptibility, is according to the classical Langevin theory of describe than ferromagnetism and good theories of paramagnetism have. Langevin’s Theory of Diamagnetism, Langevin’s Theory of Paramagnetism, Langevin’s Function, Saturation value of Magnetization, Curie’s Law.

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This is why s- and p-type metals are typically either Pauli-paramagnetic or as in the case of gold even diamagnetic. Although the electronic configuration of the individual atoms and ions of most elements contain unpaired spins, they are not necessarily paramagnetic, because at ambient temperature theiry is very much the rule rather than the exception.

The permanent moment generally is due to the spin of unpaired electrons in atomic or paramagneetism electron orbitals see Magnetic moment.


If we apply a magnetic field along what we choose to call thdory z-axis, the energy levels of each paramagnetic center will experience Zeeman splitting of its energy levels, each with a z -component labeled by M J or just M S for the spin-only magnetic case. However, the true origins of the alignment can only be understood via the quantum-mechanical properties of spin and angular momentum. Each atom has one non-interacting unpaired electron. If there is sufficient energy exchange between neighbouring dipoles, they will paramagnteism, and may spontaneously align or anti-align and form magnetic domains, resulting in ferromagnetism permanent magnets or kangevinrespectively.

In this narrowest sense, paramagnetlsm only pure paramagnet is a dilute gas of monatomic hydrogen atoms. Thus, condensed phase paramagnets are only possible if the interactions of the spins that lead either to quenching or to ordering are kept at bay by structural isolation of the magnetic centers.


The paramagnetic response has then two possible quantum origins, either coming from permanents magnetic moments of the ions or from the spatial motion of the conduction electrons inside the material.

The bulk properties of such a system resembles that of a paramagnet, but on a microscopic level they are ordered. By using this site, you agree to the Terms of Use and Lf Policy.

The mathematical expression is:. Although there are usually energetic reasons why a molecular structure results such that it does not exhibit partly filled orbitals i. If one subband is preferentially filled over the other, one can have itinerant ferromagnetic order.

Constituent atoms or molecules of paramagnetic materials have permanent magnetic moments dipoleseven in the absence of an applied field. Molecular oxygen is a good example. Even for iron it is not uncommon to say that iron becomes a paramagnet above its relatively high Curie-point. In principle any system that contains atoms, ions, or molecules with unpaired spins can be called a paramagnet, but the interactions between them need to be carefully considered.

Langevin theory of paramagnetism

In that case the Curie-point is seen as a phase transition theoty a ferromagnet and a ‘paramagnet’. Wikipedia articles with NDL identifiers. The distances to other oxygen atoms in the lattice remain too large to lead to delocalization and the magnetic moments remain unpaired.

In this approximation the magnetization is given as the magnetic moment of one electron times the difference in densities:. These materials are known as superparamagnets.

In an ordinary nonmagnetic conductor the conduction band is identical for both spin-up and spin-down electrons. In conductive materials, the electrons are delocalizedthat is, they travel through the solid more or less as free electrons. An external magnetic field causes the electrons’ spins to align parallel to the field, causing a net attraction.


Paramagnetism is a form of magnetism whereby certain materials are weakly attracted by an externally applied magnetic fieldand form internal, induced magnetic fields in the direction of the applied magnetic field. When a magnetic field is applied, the dipoles will tend to align with the applied field, resulting in a net magnetic moment in the direction of the applied field.

However, in some cases a band structure can result in which there are two delocalized sub-bands with states of opposite spins that have different energies. Particularly the latter are usually strongly localized.

Paramagnetism – Wikipedia

For a paramagnetic ion with noninteracting magnetic moments with angular momentum Jthe Curie constant is related the individual ions’ magnetic moments.

The latter could be said about a gas of lithium atoms but these already possess two paired core electrons that produce a diamagnetic response of opposite sign. The magnetic response calculated for a gas of electrons is not the full picture as the magnetic susceptibility coming from the ions has to be included.

The above picture is a generalization as it pertains to materials with an extended lattice rather than a molecular structure.

The effect always competes with a diamagnetic response of opposite sign due to all the core electrons of the atoms. Curie’s Law can be derived by thheory a substance with noninteracting magnetic moments with angular momentum J.

Hydrogen is therefore diamagnetic and the same holds true for many other elements. Randomness of the structure also applies to the many metals that show a net paramagnetic response over a broad temperature range.