PARAMAGNETISM PHENOMENON (copy from http://en.wikipedia.org/wiki/ )
Paramagnetism is a form of magnetism that occurs only in the presence of an externally applied magnetic field. Paramagnetic materials are attracted to magnetic fields and hence have a relative magnetic permeability of ≥1 (a positive magnetic susceptibility). The magnetic moment induced by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect and modern measurements on paramagnetic materials are often conducted with a SQUID magnetometer. 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, for instance, in magnets on one's refrigerator.
Simple Illustration of a paramagnetic probe made up from miniature magnets.
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 spin of unpaired electrons in the atomic/molecular electron orbitals (see Magnetic moment). 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 behavior can also be observed in ferromagnetic materials that are above their Curie temperature, and in antiferromagnets above their Néel temperature. At these temperatures the available thermal energy simply overcomes the interaction energy between the spins.
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.
Selected Pauli-paramagnetic metals[1] |
|
6.8 |
|
5.1 |
|
2.2 |
|
1.4 |
|
1.2 |
|
0.72 |
In many metallic
materials the electrons are itinerant, i.e. they travel through the solid more
or less as an electron gas. This is the result of very strong
interactions (overlap) between the wave functions of neighboring atoms in the
extended lattice structure. The wave functions of the valence electrons thus
form a band with equal numbers of spins up and down. When exposed to an
external field only those electrons close to the Fermi level
will respond and a small surplus of one type of spins will result. This effect
is a weak form of paramagnetism known as Pauli-paramagnetism. The effect always competes with a diamagnetic
response of opposite sign due to all the core electrons of the atoms. Stronger
forms of magnetism usually require localized rather than itinerant electrons.
However in some cases a bandstructure can result in
which there are two delocalized subbands with states
of opposite spins that have different energies. If one subband
is preferentially filled over the other, one can have itinerant ferromagnetic
order. This usually only happens in relatively narrow (d-)bands,
which are poorly delocalized.
In general one can say
that strong delocalization in a solid due to large overlap with neighboring
wave functions tends to lead to pairing of spins (quenching) and thus
weak magnetism. This is why s- and p-type metals are typically either
Pauli-paramagnetic or as in the case of gold even diamagnetic.
In the latter case the diamagnetic contribution from the closed shell inner
electrons simply wins from the weak paramagnetic term of the almost free
electrons.
Stronger magnetic effects
are typically only observed when d- or f-electrons are involved. Particularly
the latter are usually strongly localized. Moreover the size of the magnetic
moment on a lanthanide atom can be quite large as it can carry up to 7 unpaired
electrons. This is one reason why superstrong magnets are typically based on lanthanide
elements like neodymium
or samarium.
Of course the above
picture is a generalization as it pertains to materials with an extended
lattice rather than a molecular structure. Molecular structure can also lead to
localization of electrons. Although there are usually energetic reasons why a
molecular structure results such that it does not exhibit partly filled orbitals (i.e. unpaired spins), some non-closed shell
moieties do occur in nature. Molecular oxygen is a good example. Even in the
frozen solid it contains di-radical molecules
resulting in paramagnetic behavior. The unpaired spins reside in orbitals derived from oxygen p wave functions, but the
overlap is limited to the one neighbor in the O2 molecules. The
distances to other oxygen atoms in the lattice remain too large to lead to
delocalization and the magnetic moments remain unpaired.
For low levels of magnetization, the magnetization of paramagnets follows Curie's law to good approximation:
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
This law indicates that
the susceptibility χ of paramagnetic materials is inversely proportional
to their temperature. Curie's law is valid under the commonly encountered
conditions of low magnetization (μBH ≲ kBT), but does not apply in the high-field/low-temperature regime where
saturation of magnetization occurs (μBH
≳ kBT) and magnetic dipoles are all aligned with the applied field. When the
dipoles are aligned, increasing the external field will not increase the total
magnetization since there can be no further alignment.
For a paramagnetic ion with noninteracting magnetic moments with angular momentum J, the Curie constant is related the individual ions' magnetic moments,
.
The parameter μeff is interpreted as the effective magnetic moment per paramagnetic ion. If one uses a classical treatment with molecular magnetic moments represented as discrete magnetic dipoles, μ, a Curie Law expression of the same form will emerge with μ appearing in place of μeff.
When orbital angular momentum contributions to the magnetic moment are small, as occurs for most organic radicals or for octahedral transition metal complexes with d3 or high-spin d5 configurations, the effective magnetic moment takes the form (ge = 2.0023... ≈ 2),
, where n is the number of unpaired electrons. In other transition metal complexes this yields a useful, if somewhat cruder, estimate.
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.
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. Of course, 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 H2 and in so
doing, the magnetic moments are lost (quenched), because the spins pair.
Hydrogen is therefore diamagnetic and the same holds true for most
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 ambient temperature quenching is very much
the rule rather than the exception. However, the quenching tendency is weakest
for f-electrons because f (especially 4f) 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.[2]
μeff values for typical d3 and d5 transition metal complexes.[3] |
|
[Cr(NH3)6]Br3 |
3.77 |
K3[Cr(CN)6] |
3.87 |
K3[MoCl6] |
3.79 |
K4[V(CN)6] |
3.78 |
[Mn(NH3)6]Cl2 |
5.92 |
(NH4)2[Mn(SO4)2]•6H2O |
5.92 |
NH4[Fe(SO4)2]•12H2O |
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:
1. Molecular materials with a (isolated) paramagnetic center.
1. Good examples are coordination complexes 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.
2. 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.
2. Dilute systems.
1. 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.
Idealized Curie–Weiss behavior; N.B. TC=θ,
but TN is not θ. Paramagnetic regimes are denoted by solid
lines. Close to TN or TC 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:
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.
Further information: Superparamagnetism
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 microscopic
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).
1. ^ Nave, Carl L. "Magnetic Properties of Solids". HyperPhysics. http://hyperphysics.phy-astr.gsu.edu/Hbase/tables/magprop.html. Retrieved 2008-11-09.
2. ^ J. Jensen and A. R. MacKintosh, "Rare Earth Magnetism". http://www2.nbi.ku.dk/page40667.htm. Retrieved 2009-07-12., (Clarendon Press, Oxford: 1991).
3. ^ A. F. Orchard, Magnetochemistry, (Oxford University Press: 2003).
4. Wikipedia