# Paramagnetism

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Image:Paramagnetic probe without magnetic field.svg
Simple Illustration of a paramagnetic probe made up from miniature magnets.

Paramagnetism is a form of magnetism which only occurs in the presence of an externally applied magnetic field. Paramagnetic materials are attracted to magnetic fields, hence have a relative magnetic permeability greater than unity (or, equivalently, a positive magnetic susceptibility). However, unlike ferromagnets which are also attracted to magnetic fields, paramagnets do not retain any magnetisation in the absence of an externally applied magnetic field.

##  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 true 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.

##  Curie's law

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

$\mathbf{M} = C \cdot \frac{\mathbf{B}}{T}$

where

M is the resulting magnetisation
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).

##  Paramagnetic materials

### Compounds

Many salts of the d and f transitional metal group show paramagnetic behaviour. Examples are:

##  Types of paramagnetism

Speromagnetism - Local moments in random orientation, no net magnetisation

Asperomagnetism - Frozen spins

Helimagnetism - Crystalline aspero

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

##  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).