Ferromagnetism

Ferromagnetic materials

Main article:

There are a number of crystalline materials that exhibit ferromagnetism (or ferrimagnetism). The table on the right lists a representative selection of them here, along with their Curie temperatures, the temperature above which they cease to exhibit spontaneous magnetization (see below).

Ferromagnetic metal alloys whose constituents are not themselves ferromagnetic in their pure forms are called Heusler alloys, named after Fritz Heusler.

One can also make amorphous (non-crystalline) ferromagnetic metallic alloys by very rapid P, or Al) that lowers the melting point.

A relatively new class of exceptionally strong ferromagnetic materials are the rare-earth magnets. They contain lanthanide elements that are known for their ability to carry large magnetic moments in well-localized f-orbitals.

Physical origin

The property of ferromagnetism is due to the direct influence of two effects from quantum mechanics: spin and the Pauli exclusion principle.

The spin of an electron shell), however, the total dipole moment of all the electrons is zero (i.e., the spins are in up/down pairs). Only atoms with partially filled shells (i.e., unpaired spins) can experience a net magnetic moment in the absence of an external field. A ferromagnetic material has many such electrons, and if they are aligned they create a measurable macroscopic field.

These permanent dipoles (often called simply "spins" even though they also generally include orbital angular momentum) tend to align in parallel to an external magnetic field, an effect called diamagnetism, due to the orbital motion induced by an external field, resulting in a dipole moment opposite to the applied field.) Ferromagnetism involves an additional phenomenon, however: the dipoles tend to align spontaneously, without any applied field. This is a purely quantum-mechanical effect.

According to classical electromagnetism, two nearby magnetic dipoles will tend to align in opposite directions (which would create an Hartree-Fock approximation to lead to a reduction in the electrostatic potential energy.) This difference in energy is called the exchange energy.

At long distances (after many thousands of Bloch/Néel wall, depending upon whether the magnetization rotates parallel/perpendicular to the domain interface) and is a gradual transition on the atomic scale (covering a distance of about 300 ions for iron).

Thus, an ordinary piece of iron generally has little or no net magnetic moment. However, if it is placed in a strong enough external magnetic field, the domains will re-orient in parallel with that field, and will remain re-oriented when the field is turned off, thus creating a "permanent" magnet. This magnetization as a function of the external field is described by a hysteresis curve. Although this state of aligned domains is not a minimal-energy configuration, it is extremely stable and has been observed to persist for millions of years in seafloor magnetite aligned by the Earth's magnetic field (whose poles can thereby be seen to flip at long intervals). The net magnetization can be destroyed by heating and then cooling (annealing) the material without an external field, however.

As the temperature increases,h thermal oscillation, or entropy, competes with the ferromagnetic tendency for dipoles to align. When the temperature rises beyond a certain point, called the Curie temperature, there is a second-order magnetic susceptibility is theoretically infinite and, although there is no net magnetization, domain-like spin correlations fluctuate at all lengthscales.

The study of ferromagnetic phase transitions, especially via the simplified mean field theory approaches failed to predict the correct behavior at the critical point (which was found to fall under a universality class that includes many other systems, such as liquid-gas transitions), and had to be replaced by renormalization group theory.

Unusual ferromagnetism

In 2004, it was reported that a certain boron and nitrogen, may also be ferromagnetic. The alloy Zr₂ is also ferromagnetic below 28.5 K.

See also

• Paramagnetic

Sources

• 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).
• E. P. Wohlfarth, ed., Ferromagnetic Materials (North-Holland, 1980).
• "Nanofoam makes magnetic debut," Physics World 17 (5), 3 (May 2004).
• "Heusler alloy," Encyclopedia Britannica Online, retrieved Jan. 23, 2005.
• F. Heusler, W. Stark, and E. Haupt, Verh. der Phys. Ges. 5, 219 (1903).
• S. Vonsovsky Magnetism of elementary particles (Mir Publishers, Moscow, 1975).

References

1. ^ Richard M. Bozorth, Ferromagnetism, first published 1951, reprinted 1993 by IEEE Press, New York as a "Classic Reissue." ISBN 0-7803-1032-2.