Dictionary Definition
paramagnetism n : materials like aluminum or
platinum become magnetized in a magnetic field but it disappears
when the field is removed
User Contributed Dictionary
English
Pronunciation
- /ˌpæ.rə.ˈmæg.nə.tɪ.zəm/
- /%p
Extensive Definition
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
do not 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 is 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 is 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:- \boldsymbol = \chi \cdot\boldsymbol=C\cdot \frac
where
- M is the resulting magnetization
- χ is the magnetic susceptibility
- H is the auxiliary magnetic field, measured in amperes/meter
- T is absolute temperature, measured in kelvins
- C is a material-specific Curie constant
- χ is the magnetic susceptibility
This law indicates that the
susceptibility χ of paramagnetic materials is inversely
proportional to their temperature. 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. However such saturation
typically requires very strong magnetic fields.
Examples of paramagnets
It is not easy to identify
which materials should be called 'paramagnets', because the term is
often used for rather different systems. In principle any system
that contains atoms, ions or molecules with unpaired spins can be
called a paramagnet, but the interactions between them do need
consideration.
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. Of course, the latter could be said about a gas of lithium atoms but these 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. However, even the element hydrogen is usually not called a 'paramagnet' because at lower temperatures the monatomic gas is not stable. Two atoms will combine to form molecular H2 and in that interaction the magnetic moments are lost (quenched), because the spins will pair. As a substance hydrogen is therefore usually considered a diamagnet. This holds true for many elements. Although the electronic configuration of the individual atoms (and ions) of most elements contain unpaired spins, it is not correct to call these elements 'paramagnets' because at lower temperatures quenching is the rule rather than the exception. As pointed out above the quenching tendency is weakest for f-electrons.Thus, condensed phase
paramagnets are only possible if the interactions of the spins that
lead either to quenching or to ordering are somehow kept at bay.
There are two classes of materials for which this holds:
- Molecular materials with a (isolated)
paramagnetic center.
- Good examples are organometallic compounds 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 O2 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. Nd3+ in CaCl2 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: EPR.
Systems with interactions
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. \boldsymbol = C \frac . 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 TN or TC 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
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 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 e.g. 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 are 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,
e.g. 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 mictomagnets
- 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).
External links
- Electromagnetism - a chapter from an online textbook
- Classification of Magnetic Materials by Applied Alloy Chemistry Group at University of Birmingham.
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