Editing Paramagnetism (section)

==Examples of paramagnets==
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. 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.

===Systems with minimal interactions===
The narrowest definition would be: a system with unpaired spins that ''do not interact'' with each other. In this narrowest sense, the only pure paramagnet is a dilute gas of [[monatomic hydrogen]] atoms. Each atom has one non-interacting unpaired electron.

A gas of lithium atoms already possess two paired core electrons that produce a diamagnetic response of opposite sign. Strictly speaking Li is a mixed system therefore, although admittedly the diamagnetic component is weak and often neglected. In the case of heavier elements the diamagnetic contribution becomes more important and in the case of metallic gold it dominates the properties. 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<sub>2</sub> and in so doing, the magnetic moments are lost (''quenched''), because of the spins pair. Hydrogen is therefore ''diamagnetic'' and the same holds true for many other elements. 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. 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.  Consequently, the lanthanide elements with incompletely filled 4f-orbitals are paramagnetic or magnetically ordered.<ref>{{Cite book|url=http://www2.nbi.ku.dk/page40667.htm|title=Rare Earth Magnetism|author1=Jensen, J.|author2=MacKintosh, A. R.|name-list-style=amp|publisher=Clarendon Press|place=Oxford|year=1991|access-date=2009-07-12|archive-url=https://web.archive.org/web/20101212232011/http://www2.nbi.ku.dk/page40667.htm|archive-date=2010-12-12|url-status=dead}}</ref>

{|class="wikitable sortable" style="float:right; margin:20px" width="200px"
|+μ<sub>eff</sub> values for typical d<sup>3</sup> and d<sup>5</sup> transition metal complexes.<ref>Orchard, A. F. (2003) ''Magnetochemistry''. Oxford University Press.</ref>
!Material!!μ<sub>eff</sub>/μ<sub>B</sub>
|-
|[Cr(NH<sub>3</sub>)<sub>6</sub>]Br<sub>3</sub>||3.77
|-
|K<sub>3</sub>[Cr(CN)<sub>6</sub>]||3.87
|-
|K<sub>3</sub>[MoCl<sub>6</sub>]||3.79
|-
|K<sub>4</sub>[V(CN)<sub>6</sub>]||3.78
|-
|[Mn(NH<sub>3</sub>)<sub>6</sub>]Cl<sub>2</sub>||5.92
|-
|(NH<sub>4</sub>)<sub>2</sub>[Mn(SO<sub>4</sub>)<sub>2</sub>]·6H<sub>2</sub>O||5.92
|-
|NH<sub>4</sub>[Fe(SO<sub>4</sub>)<sub>2</sub>]·12H<sub>2</sub>O||5.89
|-
|}
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. There are two classes of materials for which this holds:
*Molecular materials with a (isolated) paramagnetic center.
** Good examples are [[coordination complex]]es of d- or f-metals or proteins with such centers, e.g. [[myoglobin]]. In such materials the organic part of the molecule acts as an envelope shielding the spins from their neighbors.
** Small molecules can be stable in radical form, [[oxygen]] O<sub>2</sub> is a good example. Such systems are quite rare because they tend to be rather reactive.
* Dilute systems.
** Dissolving a  paramagnetic species in a diamagnetic lattice at small concentrations, e.g. Nd<sup>3+</sup> in CaCl<sub>2</sub> will separate the neodymium ions at large enough distances that they do not interact. Such systems are of prime importance for what can be considered the most sensitive method to study paramagnetic systems: [[Electron paramagnetic resonance|EPR]].

===Systems with interactions===
[[File:Para-ferro-anti.jpg|thumb|300px|Idealized Curie–Weiss behavior; N.B. T<sub>C</sub>=θ, but ''T''<sub>N</sub> is not θ. Paramagnetic regimes are denoted by solid lines. Close to ''T''<sub>N</sub> or ''T''<sub>C</sub> the behavior usually deviates from ideal.]]

As stated above, many materials that contain d- or f-elements do retain unquenched spins. Salts of such elements often show paramagnetic behavior but at low enough temperatures the magnetic moments may order. It is not uncommon to call such materials 'paramagnets', when referring to their paramagnetic behavior above their Curie or Néel-points, particularly if such temperatures are very low or have never been properly measured.  Even for iron it is not uncommon to say that ''iron becomes a paramagnet'' above its relatively high Curie-point. In that case the Curie-point is seen as a [[phase transition]] between a ferromagnet and a 'paramagnet'. The word paramagnet now merely refers to the linear response of the system to an applied field, the temperature dependence of which requires an amended version of Curie's law, known as the [[Curie–Weiss law]]:

:<math>\mathbf{M} = \frac{C}{T- \theta}\mathbf{H}</math>

This amended law includes a term θ that describes the exchange interaction that is present albeit overcome by thermal motion. The sign of θ depends on whether ferro- or antiferromagnetic interactions dominate and it is seldom exactly zero, except in the dilute, isolated cases mentioned above.

Obviously, the paramagnetic Curie–Weiss description above ''T''<sub>N</sub> or ''T''<sub>C</sub> is a rather different interpretation of the word "paramagnet" as it 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. Even if ''θ'' is close to zero this does not mean that there are no interactions, just that the aligning ferro- and the anti-aligning antiferromagnetic ones cancel. An additional complication is that the interactions are often different in different directions of the crystalline lattice ([[anisotropy]]), leading to complicated [[magnetic structure]]s once ordered.

Randomness of the structure also applies to the many metals that show a net paramagnetic response over a broad temperature range. They do not follow a Curie type law as function of temperature however; often they are more or less temperature independent. 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.

===Superparamagnets===
Some materials show induced magnetic behavior that follows a Curie type law but with exceptionally large values for the Curie constants. These materials are known as [[superparamagnetism|superparamagnets]]. They are characterized by a strong ferromagnetic or ferrimagnetic type of coupling into domains of a limited size that behave independently from one another. The bulk properties of such a system resembles that of a paramagnet, but on a microscopic level they are ordered. The materials do show an ordering temperature above which the behavior reverts to ordinary paramagnetism (with interaction). [[Ferrofluid]]s are a good example, but the phenomenon can also occur inside solids, e.g., when dilute paramagnetic centers are introduced in a strong itinerant medium of ferromagnetic coupling such as when Fe is substituted in TlCu<sub>2</sub>Se<sub>2</sub> or the alloy AuFe. Such systems contain ferromagnetically coupled clusters that freeze out at lower temperatures. They are also called [[mictomagnetism|mictomagnets]].