Editing Paramagnetism (section)

==Relation to electron spins==
[[File:Paramagnetism, ferromagnetism and spin waves.webm|thumb|Paramagnetism, ferromagnetism and spin waves]]

Constituent atoms or molecules of paramagnetic materials have permanent magnetic moments ([[dipole]]s), even in the absence of an applied field. The permanent moment generally is due to the spin of unpaired electrons in [[Atomic orbital|atomic]] or [[Molecular orbital|molecular electron orbitals]] (see [[Magnetic moment]]).  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. 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 the classical description, this alignment can be understood to occur due to a [[torque]] being provided on the magnetic moments by an applied field, which tries to align the dipoles parallel to the applied field. However, the true origins of the alignment can only be understood via the [[quantum mechanics|quantum-mechanical]] properties of [[Spin (physics)|spin]] and [[angular momentum]].<ref>{{Cite web |last=Feynman |last2=Leighton |last3=Sands |title=The Feynman Lectures on Physics. |url=https://www.feynmanlectures.caltech.edu/II_34.html}}</ref>

If there is sufficient energy exchange between neighbouring dipoles, they will interact, and may spontaneously align or anti-align and form magnetic domains, resulting in [[ferromagnetism]] (permanent magnets) or [[antiferromagnetism]], respectively. Paramagnetic behavior can also be observed in ferromagnetic materials that are above their [[Curie temperature]], and in antiferromagnets above their [[Néel temperature]]. At these temperatures, the available thermal energy simply overcomes the interaction energy between the spins.

In general, paramagnetic effects are quite small: the [[magnetic susceptibility]] is of the order of 10<sup>−3</sup> to 10<sup>−5</sup> for most paramagnets, but may be as high as 10<sup>−1</sup> for synthetic paramagnets such as [[ferrofluid]]s.<ref>{{Cite book |last=Griffiths |first=David J. |title=Introduction to electrodynamics |date=2013 |publisher=Pearson |isbn=978-0-321-85656-2 |edition=4th |series=Always learning |location=Boston |chapter=Magnetostatic Fields in Matter}}</ref>

===Delocalization===
{|class="wikitable sortable" style="float:right; margin:20px" width="200px"
|+ Selected Pauli-paramagnetic metals<ref name="magneticValues">{{Cite web|url=http://hyperphysics.phy-astr.gsu.edu/Hbase/tables/magprop.html|title=Magnetic Properties of Solids|last=Nave|first=Carl L|work=HyperPhysics|access-date=2008-11-09}}</ref>
!Material!!Magnetic susceptibility, <math>\chi_v</math> [10<sup>−5</sup>]

(SI units)
|-
|[[Tungsten]]||6.8
|-
|[[Caesium]]||5.1
|-
|[[Aluminium]]||2.2
|-
|[[Lithium]]||1.4
|-
|[[Magnesium]]||1.2
|-
|[[Sodium]]||0.72
|}

In conductive materials, the electrons are [[delocalized]], that is, they travel through the solid more or less as [[Free particle|free electrons]]. Conductivity can be understood in a [[band structure]] picture as arising from the incomplete filling of energy bands.
In an ordinary nonmagnetic conductor the conduction band is identical for both spin-up and spin-down electrons. 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 potential energy]] for spin-up and spin-down electrons.
Since the [[Fermi level]] must be identical for both bands, this means that there will be a small surplus of the type of spin in the band that moved downwards. This effect is a weak form of paramagnetism known as ''Pauli paramagnetism''.

The effect always competes with a [[diamagnetic]] response of opposite sign due to all the core electrons of the atoms. Stronger forms of magnetism usually require localized rather than itinerant electrons. 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. If one subband is preferentially filled over the other, one can have itinerant ferromagnetic order. This situation usually only occurs in relatively narrow (d-)bands, which are poorly delocalized.

====s and p electrons====
Generally, strong delocalization in a solid due to large overlap with neighboring wave functions means that there will be a large [[Fermi velocity]]; this means that the number of electrons in a band is less sensitive to shifts in that band's energy, implying a weak magnetism. This is why s- and p-type metals are typically either Pauli-paramagnetic or as in the case of gold even diamagnetic. 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.

====d and f electrons====
Stronger magnetic effects are typically only observed when d or f electrons are involved. Particularly the latter are usually strongly localized. 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 high magnetic moments associated with lanthanides is one reason why [[rare-earth magnet|superstrong magnets]] are typically based on elements like [[neodymium]] or [[samarium]].

====Molecular localization====
The above picture is a ''generalization'' as it pertains to materials with an extended lattice rather than a molecular structure. Molecular structure can also lead to localization of electrons. Although there are usually energetic reasons why a molecular structure results such that it does not exhibit partly filled orbitals (i.e. unpaired spins), some non-closed shell moieties do occur in nature. Molecular oxygen is a good example. Even in the frozen solid it contains [[diradical|di-radical molecules]] resulting in paramagnetic behavior. The unpaired spins reside in orbitals derived from oxygen p wave functions, but the overlap is limited to the one neighbor in the O<sub>2</sub> molecules. The distances to other oxygen atoms in the lattice remain too large to lead to delocalization and the magnetic moments remain unpaired.