Paramagnetism

Paramagnetism
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Simple Illustration of a paramagnetic probe made up from miniature magnets.Paramagnetism is a form of magnetism which occurs only in the presence of an externally applied magnetic field. Paramagnetic materials are attracted to magnetic fields, hence have a relative magnetic permeability greater than one (or, equivalently, a positive magnetic susceptibility). However, unlike ferromagnets which are also attracted to magnetic fields, paramagnets do not retain any magnetization in the absence of an externally applied magnetic field.

Contents [hide]
1 Introduction
2 Curie's law
3 Paramagnetic materials
3.1 Elements
3.2 Compounds
4 See also
5 References
6 External links



[edit] Introduction
Constituent atoms or molecules of paramagnetic materials have permanent magnetic moments (dipoles), even in the absence of an applied field. This generally occurs due to the presence of unpaired electrons in the atomic/molecular electron orbitals. 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 truer origins of the alignment can only be understood via the quantum-mechanical properties of spin and angular momentum.

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 behaviour can also be observed in ferromagnetic materials that are above their Curie temperature, and in antiferromagnets above their Néel temperature.

In general paramagnetic effects are quite small: the magnetic susceptibility is of the order of 10−3 to 10−5 for most paramagnets, but may be as high as 10-1 for synthetic paramagnets such as ferrofluids.


[edit] Curie's law
For low levels of magnetisation, the magnetisation of paramagnets is approximated by Curie's law:


where

M is the resulting magnetization
B is the magnetic flux density of the applied field, measured in teslas
T is absolute temperature, measured in kelvins
C is a material-specific Curie constant
This law indicates that the susceptibiliy of paramagnetic materials is inversely proportional to their temperature. However, Curie's law is only valid under conditions of low magnetisation, since it does not consider the saturation of magnetisation that occurs when the atomic dipoles are all aligned in parallel (after everything is aligned, increasing the external field will not increase the total magnetisation since there can be no further alignment).


[edit] Paramagnetic materials

[edit] Elements
Elements can be paramagnetic if they have unpaired electrons.

The following are some examples of paramagnetic elements:

Aluminium Al [13] (metal) — Al is the preferred paramagnetic material in theoretical designs of lunar mass driver applications using regolith as an ore.
Barium Ba [56] (metal)
Calcium Ca [20] (metal) [Ar]4s2 — diamagnetic
Oxygen. O [8] (non-metal)
Platinum Pt [78] (metal)
Sodium Na [11] (metal)
Strontium Sr [38] (metal)
Uranium U [92] (metal)
Magnesium Mg [12] (metal) 1s2 2s2 2p6 3s2 — diamagnetic
Technetium Tc [43] (artificial)
Dysprosium Dy [66] (metal) — ferromagnetic

[edit] Compounds
Many salts of the d and f transitional metal group show paramagnetic behaviour.

Examples are:

Copper sulphate
Dysprosium oxide
Ferric chloride
Ferric oxide
Holmium oxide
Manganese chloride
Some simple molecules contain unpaired electrons and are thus paramagnetic. The most common is the diatomic oxygen molecule.


[edit] See also
Pierre Curie
Ferromagnetism



Magnetic states
diamagnetism – superdiamagnetism – paramagnetism – superparamagnetism – ferromagnetism – antiferromagnetism – ferrimagnetism – metamagnetism – spin glass


[edit] References
Charles Kittel, Introduction to Solid State Physics (Wiley: New York, 1996).
Neil W. Ashcroft and N. David Mermin, Solid State Physics (Harcourt: Orlando, 1976).
John David Jackson, Classical Electrodynamics (Wiley: New York, 1999).

[edit] External links
Classification of Magnetic Materials by Applied Alloy Chemistry Group at University of Birmingham.
Retrieved from "http://en.wikipedia.org/wiki/Paramagnetism"
Categories: Electric and magnetic fields in matter | Magnetism | Fundamental physics concepts