From Wikipedia, the free encyclopedia

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, because thermal motion causes the spins to become randomly oriented without it. Thus the total magnetization will drop to zero.

Contents 1 Introduction 1.1 Delocalization 1.1.1 s and p electrons 1.1.2 d and f electrons 1.1.3 Molecular localization 2 Curie's law 3 Paramagnetic materials 3.1 Elements 3.2 Compounds 4 See also 5 References 6 External links

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 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.

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 diamagentic 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 that 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 and thus weak magnetism. This is why s- and p-type metals are typically either Pauli-paramagnetic or as in the case 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 Nd or Sm.

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 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 delocalisation and the magnetic moments remain unpaired.

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 susceptibility 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).

Elements can be paramagnetic if they have unpaired electrons.

The following are some examples of paramagnetic elements:

• Aluminum 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

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.

• Pierre Curie
• Ferromagnetism

v • d • e Magnetic states
diamagnetism – superdiamagnetism – paramagnetism – superparamagnetism – ferromagnetism – antiferromagnetism – ferrimagnetism – metamagnetism – spin glass

• 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).

• Electromagnetism - a chapter from an online textbook
• Classification of Magnetic Materials by Applied Alloy Chemistry Group at University of Birmingham.