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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Langevin theory of paramagnetism

They are also called mictomagnets. 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. Ferrofluids are a good example, but the phenomenon can also occur inside solids, e. 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 quenching is very much the rule rather than the exception.

Molecular oxygen is a good example. In that case the Curie-point is seen as a phase transition between a ferromagnet and a ‘paramagnet’. Stronger magnetic effects are typically only observed when d or f electrons are involved.

For these materials one contribution to the magnetic response comes from the interaction with the electron spins and the magnetic field known as Pauli paramagnetism. Strictly speaking Li is a mixed system therefore, although admittedly the diamagnetic component is weak and often neglected.

The magnetic moment induced by the applied field is linear in the field strength and rather weak. For some alkali metals and noble metals, conductions electrons are weakly interacting and delocalized in space forming a Fermi gas.

Even in the frozen solid it contains di-radical molecules resulting in paramagnetic behavior. Constituent atoms or molecules of paramagnetic materials have permanent magnetic moments dipoleseven in the absence of an applied field.

Paramagnetic materials include aluminiumoxygentitaniumand iron oxide FeO. In pure paramagnetism, the dipoles do not interact with one another and are randomly oriented in the absence of an external field due to thermal agitation, resulting in zero net magnetic moment.

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Moreover, the size of the magnetic moment on a lanthanide atom can be quite large as it can carry up to 7 unpaired electrons in the case of gadolinium III hence its use in MRI.

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.


For low levels of magnetization, the magnetization of paramagnets follows what is known as Curie’s lawat least approximately. The attraction experienced by ferromagnetic materials is non-linear and much stronger, so that it is easily observed, for instance, in the attraction between a refrigerator magnet and the iron of the refrigerator itself.

Although there are usually energetic reasons why a molecular structure results such that it does not exhibit partly filled orbitals i.

Langevin's Theory of Paramagnetism

If one subband is preferentially filled over the other, one can have itinerant ferromagnetic order. Some paramagnetic materials retain spin disorder even at absolute zeromeaning they are paramagnetic in the ground statei.

This type of behavior is of an itinerant nature and better called Pauli-paramagnetism, but it is not unusual to see, for example, the metal aluminium called a “paramagnet”, even though interactions are strong enough to give this element very good electrical conductivity. The high magnetic moments associated with lanthanides is one reason why superstrong magnets are typically based on elements like neodymium or samarium.

Paramagnetism is due to the presence of unpaired electrons in the material, so all atoms with incompletely filled atomic orbitals are paramagnetic. Each atom has one non-interacting unpaired electron. When the dipoles are aligned, increasing the external field will not increase the total magnetization since there can be no further alignment.

As stated above, many materials that contain d- or f-elements do retain unquenched spins. At these temperatures, the available thermal energy simply overcomes the interaction energy between the spins.

Pauli paramagnetism is named after the physicist Wolfgang Pauli. Theor we apply a magnetic field along what we choose to call the z-axis, the energy levels of each paramagnetic center will experience Zeeman splitting of its paramagntism levels, each with a z -component labeled by M J or just M S for the spin-only magnetic case. The unpaired spins reside in orbitals derived from oxygen p wave functions, but the overlap is limited to the one neighbor in the O 2 molecules.

In conductive materials, the electrons are delocalizedthat is, they travel through the solid more or less as free tneory. For a paramagnetic ion with noninteracting magnetic moments with angular momentum Jthe Curie constant is related the individual ions’ magnetic moments.

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.

In other transition metal complexes this yields a useful, if somewhat cruder, estimate. The distances to other oxygen atoms in the lattice remain too large to lead to delocalization and the magnetic moments remain unpaired.


In the latter case the diamagnetic contribution from the closed shell inner electrons simply wins over the weak paramagnetic term of the almost free electrons.

However, the true paramavnetism of the alignment can only be understood via the quantum-mechanical properties of spin and angular momentum. The quenching tendency is weakest for f-electrons because f especially 4 f orbitals are radially contracted and they overlap only weakly with orbitals on adjacent atoms.

Wikipedia articles with NDL identifiers. These materials are known as superparamagnets.

Some materials show induced magnetic behavior that follows a Curie type law but with exceptionally large values for the Curie constants. Before Pauli’s theory, the lack of a strong Curie paramagnetism in metals was an open problem as the leading model could not account for this contribution without the use of quantum statistics.

The element hydrogen is virtually never called ‘paramagnetic’ because the monatomic gas is stable only at extremely high temperature; H atoms combine to form molecular H 2 and in so doing, the magnetic moments are lost quenchedbecause of the spins pair. Obviously, the paramagnetic Curie—Weiss description above T N or T C is a rather different interpretation of the word “paramagnet” as paramavnetism does not imply the absence of interactions, but rather that the magnetic structure is random in the absence of an external field at these sufficiently high temperatures.

The Pauli paramagnetic susceptibility is a macroscopic effect and has to be contrasted with Landau diamagnetic susceptibility which is equal to minus one third of Pauli’s and also comes from delocalized electrons. Conductivity can theort understood in a band structure picture as arising from the incomplete filling of energy bands. Both description are given below.

Materials that are called “paramagnets” are most often those that exhibit, at least over an appreciable temperature range, magnetic susceptibilities that adhere to the Curie or Curie—Weiss laws. This effect is a weak form of paramagnetism known as Pauli paramagnetism. When a magnetic field is applied, the conduction band splits apart into a spin-up and a spin-down band due to the difference in magnetic lanegvin energy for spin-up and spin-down electrons.