Paramagnetism Totally Explained

Everything about Paramagnetism totally explained

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). The force of attraction generated by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect. Unlike ferromagnets, paramagnets don't retain any magnetization in the absence of an externally applied magnetic field, because thermal motion causes the spins to become randomly oriented without it. Thus the total magnetization will drop to zero when the applied field is removed. Even in the presence of the field there's only a small induced magnetization because only a small fraction of the spins will be oriented by the field. This fraction is proportional to the field strength and this explains the linear dependency. The attraction experienced by ferromagnets is non-linear and much stronger, so that it's easily observed on the door of one's refrigerator.

Curie's law

For low levels of magnetisation, the magnetisation of paramagnets follows Curie's law to good approximation:
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. This amended law includes a term θ that describes the exchange interaction that's present albeit overcome by thermal motion. The sign of θ depends on whether ferro- or antiferromagnetic interactions dominate and it's seldom exactly zero, except in the dilute, isolated cases mentioned above.
Obviously, the paramagnetic Curie-Weiss description above T_N or T_C 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 doesn't 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 structures once ordered.
Randomness of the structure also applies to the many metals that show a net paramagnetic response over a broad temperature range. They don't follow a Curie type law as function of temperature however, often they're more or less temperature independent. This type of behavior is of an itinerant nature and better called Pauli-paramagnetism, but it isn't 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

There are materials that show induced magnetic behavior that follows a Curie type law but with exceptionally large values for the Curie constants. These materials are known as superparamagnets. They are characterized by a strong ferro- 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 microsopic level they're ordered. The materials do show an ordering temperature above which the behavior reverts to ordinary paramagnetism (with interaction). Ferrofluids are a good example, but the phenomenon can also occur inside solids, for example when dilute paramagnetic centers are introduced in a strong itinerant medium of ferromagnetic coupling such as when Fe is substituted in TlCu₂Se₂ or the alloy AuFe. Such systems contain ferromagnetically coupled clusters that freeze out at lower temperatures. They are also called mictomagnetsFurther Information

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