MAGNETISM

Magnetism, in physics, is a general term that refers to the
effects originating from the electromagnetic interactions of
particles.  Magnetic phenomena have been recognized since
ancient times, but understanding of magnetism began only with
developments in physics in the 19th century.
 
Basic Concepts
 
The magnetic field is the central concept used in describing
magnetic phenomena.  If a moving, charged particle experiences
a force always at right angles to its direction of motion (with 
the exception that the forces is zero when moving along one
particular line), then it is moving in a magnetic field.  The
field lies along the particular line.  This force is called the 
Lorentz force, after the Dutch physicist Hendrik LORENTZ.  A
magnetic field originates from moving charges or electric
currents, according to the law discovered by Andre AMPERE (see
ELECTRICITY).  The Biot-Savart law, named for French physicist
J.B.  BIOT and Felix Savart, permits the calculation of the
magnetic field from any arbitrarily shaped current paths.  The
laws of electricity and magnetism are summarized in elegant but 
simple fashion by Maxwell's equations, named for the
19th-century physicist James Clerk MAXWELL.
 
Many important magnetic effects originate from the flow of
charge in a circular loop.  This flow gives rise to a
characteristic distribution of magnetic lines of force, called
a dipole.  A dipole can be thought of as looking and behaving
like a small bar MAGNET.  One end, or pole, is called north,
the other end south.  Lines of magnetic force flow around the
dipole from north to south, just as in a bar magnet.  The
so-called magnetic moment is the measure of the strength of the 
dipole.  Thus far, all experimental evidence indicates that
magnetic poles come in pairs that can never be separated, even
though quantum theory predicts the existence of a unit magnetic 
charge called a MONOPOLE.  At the atomic level, a magnetic
dipole moment arises from the orbital motions of the electrons
around the nucleus and from the intrinsic spin of the electron. 
The magnetic moments of atoms are expressed as multiples of
BOHR MAGNETONS.  A Bohr magneton has a value of 9.27 times 10
to the minus 24 joules/tesla.
 
The effects that are more specifically associated with the
terms magnetism and magnets and that will be treated in the
following sections are those displayed by material objects when 
subjected to magnetic fields.  The attraction between the
unlike poles of two iron bar magnets is a consequence of the
interaction of the magnetic moments of the atoms in each magnet  
with the field produced by atoms in the other magnet.  The bar
magnet, or horseshoe magnet, has the property of permanent
magnetism and is an example of ferromagnetism.  Other types of
magnetism exist, called ferrimagentism, antiferromagnetism,
paramagnetism, and diamagnetism.
 
For ferromagnetism and ferrimagnetism, three important physical 
quantities can be defined:  the magnetic induction, or B-field, 
which is the magnetic flux density within the magnetized
material;  the magnetization, which is the sum of moments over
all the atoms in a unit volume;  and the permeability, which is 
the ratio of the B-field to the applied field.  For
paramagnetism, antiferromagnetism, and diamagnetism, the
important quantities are the magnetization and the magnetic
susceptibility;  the susceptibility, represented by the Greek
lower case letter chi, is the ratio of magnetization to applied 
field.
 
History
 
The lodestone was the first permanent magnetic material to be
identified and studied.  The Greeks were aware of the power of
this mineral, now called MAGNETITE, to attract pieces of iron.
The name magnet is thought to be derived from Magnesia, a
district in Thessaly where the lodestone was mined in ancient
times.
 
Credit for inventing the magnetic compass is variously given to 
the Chinese, the Arabs, and the Italians during the first ten
centuries AD (see COMPASS, NAVIGATIONAL).  By the 12th century
mariners were using the instrument for navigation.  In the 13th 
century Peter Perigrinus of France determined that the two
poles of a spherical lodestone were the regions of strongest
force, and he found that like poles repel whereas unlike poles
attract.  In 1600 the English scientist William Gilbert
confirmed these discoveries and concluded, correctly, that the
Earth itself is a magnet (see EARTH, GEOMAGNETIC FIELD OF).
Another English scientist, John Michell (1724-93), discovered
in 1750 that the attractive and repulsive forces between the
poles of a magnet vary inversely as the square of the distance
of separation (see INVERSE SQUARE LAW).  Charles COULOMB of
France verified Michell's experiments in 1785 and also showed
that the same law is applicable to the forces between
electrical charges.  Coulomb concluded that regardless of how
small the pieces into which a magnet might be subdivided, each
piece would always retain a north and south pole.
In 1820, Hans Christian OERSTED of Denmark discovered a direct
relationship between electricity and magnetism by showing that
an electric current flowing in a wire causes a nearby compass
needle to be deflected.  Two French physicists, Andre Ampere
and Dominique ARAGO, demonstrated later that same year that an
electric current flowing in a solenoid (a coil of wire carrying 
direct current) increases the permanent magnetism of an iron
needle within the solenoid.  In 1825, Ampere generalized that a 
current-carrying loop is equivalent to a magnet and he proposed 
that the origin of permanent magnetism resides in the many
molecular-sized current whorls within the magnet.
 
During the 1830s the English scientist Michael FARADAY
introduced the idea of representing the magnetic field by lines  
of flux that extend through the space surrounding a magnet,
running from the north pole to south.  This pictorial model was 
to prove extremely useful in understanding ELECTROMAGNETIC
INDUCTION--the generation of an ELECTROMOTIVE FORCE in a closed 
circuit when lines of flux passing through the circuit change.
In the 1870s, James Clerk Maxwell of Scotland unified all
electromagnetic phenomena under a single theory.
 
In addition to the ferromagnetism of permanent magnets, other
types of magnetism became known after the middle of the 19th
century.  In 1845 Michael Faraday found that bismuth and glass
are repelled from magnetic fields.  He classified this behavior 
as diamagnetism.  Faraday also discovered that some substances
clearly not permanent magnets are nevertheless attracted by
magnetic fields, a behavior he called paramagnetism.  These
opposite characteristics stem from fundamental differences at
the atomic level and require separate theoretical explanations. 
In the 1930s two other forms of magnetism were recognized and
described:  ferrimagnetism and antiferromagnetism.  Theoretical 
explanations of the behavior of magnetic materials began with
the formulation of the quantitative theories of paramagnetism
and diamagnetism by Paul Langevin (1872-1946) and of
ferromagnetism by another French scientist, Pierre-Ernest Weiss 
(1865-1940), in 1907.  The subsequent application of quantum
theory after 1925 has provided a more exact understanding of
these phenomena of magnetic behavior.
 
Diamagnetism
 
A substance is diamagnetic if its magnetic susceptibility is
negative.  This property is displayed by a repulsion of the
sample from a magnetic field.  The theory of diamagnetism
explains it as a consequence of an induced magnetization set up 
when lines of magnetic flux penetrate the electron loops around 
atoms.  The direction of this induced magnetization is opposite 
to that of the external field, in accordance with LENZ's LAW.
This makes the susceptibility negative.  The magnetization
persists only as long as the external field is present.
Diamagnetism is very weak, compared to ferromagnetism, and it
is virtually independent of temperature.  Some metals are
diamagnetic such as bismuth, copper, gold, silver and lead,
with bismuth being the strongest.  Water and most organic
compounds are also diamagnetic, as are many nonmetals.  All
substances possess an inherent diamagnetism, so susceptibility
measurements on other magnetic materials must always be
corrected for the diamagnetic contributions of their
constituent atoms.  If a magnetic field is applied to a
superconductor while it is being cooled through its
superconducting transition temperature, the magnetic field is
expelled from the sample and it behaves like a perfect
diamagnet.  This is called the Meissner effect for its
co-discoverer, German physicist Walther Meissner.
 
Paramagnetism
 
A paramagnetic substance is characterized by a positive
susceptibility.  Like a diamagnet, it can acquire a
magnetization only from induction by an external magnetic
field.  The magnetization, however, is in the same direction as 
the inducing field, and a sample will be attracted toward the
strongest part of a field.  In 1895, Pierre CURIE first
determined experimentally that the paramagnetic susceptibility
obeys the law Greek lower case letter chi = C/T, where C is a
constant and T is the absolute temperature.  Langevin's theory
explained the phenomenon by assuming that the paramagnet
consists of a large number of noninteracting atomic dipoles in
thermal equilibrium.  In zero field the magnetization of the
system is zero, because the dipoles are randomly oriented.  A
magnetic field forces the dipoles to partially align along the
field direction, like little magnetic compasses, against the
randomizing effects of the thermal agitation of the atoms.  The 
amount of alignment and hence the magnetization depend directly 
on the strength of the field and inversely on the absolute
temperature.  This accounts for the Curie-law behavior.  A much 
closer description of the real behavior of paramagnetic
materials is given by the Weiss-Curie law, as follows:  Greek
lower case letter chi = C/T plus or minus Greek letter theta.
 
Quantum theory explains the individual atomic dipole moments as 
resulting from the adding together of the electron spin and
orbital moments in unfilled interior electron shells.  The
unfilled 3d shells are the source of paramagnetism in the iron
group, the so-called transition metals.  Similar effects occur
in the rare earth, palladium, platinum, and actinide groups in
the periodic table.  Almost all compounds and alloys containing 
elements from the above groups exhibit paramagnetic behavior at 
high temperatures but undergo phase transitions to the
magnetically ordered states of ferromagnetism and
antiferromagnetism at sufficiently low temperatures.
 
Ferromagnetism
 
Ferromagnetism is characterized by a spontaneous magnetism that 
exists in the absence of a magnetic field.  The retention of
magnetism distinguishes ferromagnetism from the induced
magnetisms of diamagnetism and paramagnetism.  When
ferromagnets are heated above a critical temperature, the
ability to possess permanent magnetism disappears.  Curie first 
identified this effect in iron as occurring at 770 deg C, and
his name is now attached to this characteristic temperature.
Other ferromagnetic elements and their Curie temperatures
include nickel (358 deg.  C), cobalt (1,130 deg C), gadolinium
(16 deg C), and dysprosium (- 188 deg C).
 
Theories to explain ferromagnetism started with the
molecular-field approach formulated by Weiss in 1907.  His
theory assumes that each atomic dipole is subject to a local
field proportional to the net magnetization produced by all the 
other dipoles.  Above a critical temperature identified with
the Curie temperature, the susceptibility is given by Greek
lower case letter chi = C/T minus Greek letter theta, where
theta is a constant, as in a paramagnet, since the atomic
moments are free to orient in any direction.  Below the Curie
temperature the local "molecular" field is sufficiently strong
to cause a spontaneous parallel alignment of the moments, which 
overcomes the randomizing effects of the thermal motion.  This
represents a phase transition to the ordered ferromagnetic
state.  The theory predicts that with further decrease in
temperature below the Curie temperature, an increase in
magnetization will occur as the moments approach complete
alignment at absolute zero.  The application of quantum
mechanics has led to considerable refinement of the molecular
field theory, but the theoretical problems in calculating
exactly the properties of ferromagnets from quantum principles
are formidable.
 
Ferromagnetism has been found in many compounds, including
several europium compounds that are insulators, such as the
oxide (- 196 deg C) and the hydride (- 244 deg C).
Ferromagnetic glasses can also be prepared.  One way is to
cool, rapidly, a molten mixture of carbon (a ferromagnetic
element) and a glass-former such as silicon or phosphorus.
Evidence exists that the organic transfer salt composed of
decamethyl ferrocene cations and tetracyanoethylene (TCNE)
anions is ferromagnetic below - 286 deg C, and it is possible
that plastic ferromagnetic materials will eventually become
available.
 
A distinctinve characteristic of a real ferromagnet is its
HYSTERESIS CURVE.  That is, the ferromagnet in its virgin state 
has zero magnetization.  It will acquire a magnetization
represented by the magnetic induction B only when an external
field H is applied.  The leveling off of the B-field as H
continues to increase is called saturation.  When the H-field
is reduced to zero, however, the ferromagnet remains
magnetized.  The amount of induction remaining is called the
remanence or retentivity.  In order to eliminate the remanent
induction completely, a field must be applied in the opposite
direction;  this is called the coercive field.  The shape of
the hysteresis loops can be explained by the domain theory
first proposed by Weiss.  A real ferromagnet, such as iron,
contains many small regions called domains.  Initially the
magnetizations point in random directions and cancel each other 
out in these domains.  The application of an external field
first increases the size of those domains with components along 
the field direction through movement of domain walls, and then
causes the domains to rotate toward the field direction.  When
the H-field is reduced to zero, the domains retain much of
their high-field configuration and orientation, so the specimen 
remains magnetized.  The response of domains to external fields  
is strongly influenced by the tendency of the magnetization to
lie along particular crystalline axes.

Ferromagnetic materials are generally put in two categories:
those with high coercivities and retentivities, called hard;
and those with low coercivities and large initial
permeabilities, called soft.  Hard magnets are used in those
devices where a strong magnetic field is required for an
indefinite period of time.  This is what is popularly called a
permanent magnet.  Many commercial permanent magnets are of the 
Alnico group (composed of iron, nickel, cobalt, and aluminum).
In recent years cobalt-samarium and neodymium-iron-boron
magnets have also proved successful in permanent-magnet
applications.  Certain ferrites are also hard.  The use of fine  
powders that are sintered at high temperatures has been found
to enhance coercivity.  Magnetically soft materials find
application in such devices as lifting electromagnets and the
power transformers that convert standard 60-cycle commercial
electric power from one voltage to another.  The cores of such
transformers are usually made of iron-silicon alloys.  The low
coercivity keeps the hysteresis loop narrow and thus minimizes
power loses.  For high-frequency applications, where eddy
current losses in metal cores are significant, ferrite cores
are more effective because of their very much larger electrical 
resistance.  An extensive technology has evolved to synthesize
ferromagnetic and ferrimagnetic materials with specific
properties to meet a wide variety of needs.
 
Ferrimagnetism
 
Ferrites are similar to ferromagnets in that they undergo
transitions to ordered arrangements of magnetic moments below
Curie temperatures.  They form magnetic domains, have
hysteresis curves, and possess sizable permanent magnetism.
Above their Curie temperatures, they behave as paramagnets.
The important difference from ferromagnetism is that not all
the moments are aligned in the same direction in the ordered
state.  There are generally two sets of sites in the crystal
lattice on which the moments are located.  Even though some
moments are aligned oppositely, the sum of all the moments
still results in a net moment;  hence the specimen possesses a
net magnetization.  A simple example is magnetite.
Most ferrites are of two crystalline types:  spinels and
garnets.  The excellent electrical insulating properties of
ferrites have led to their use in components that operate in
high-frequency devices with low electrical losses, such as
transformers and phase shifters.

Antiferromagnetism
 
Antiferromagnetism is characterized by an antiparallel pattern
of magnetic moments below a critical temperature called the
Neel temperature, named for French physicist Louis Neel.  Above 
the Neel point, the susceptibility follows a Weiss-Curie law,
Greek lower case letter chi = C/T + Greek letter theta, as in
paramagnetism.  Below the Neel temperature, the susceptibility
depends on the particular pattern of ordering and whether the
specimen is single or polycrystalline.  In general the
susceptibility decreases with temperature after passing through a 
maximum at the Neel point.
 
The theory of antiferromagnetism was developed in the 1930s by
Neel and U.S.  physicist Francis Bitter (1902-67).  It followed 
the approach of the Weiss molecular-field theory.  In the
simplest case the magnetic atoms can be considered as lying on
two interpenetrating sublattices.  The molecular field acting
on an atom of one sublattice causes its moment to point
opposite to the moments on the other sublattice.  Below the
Neel temperature the two sublattices have oppositely directed
magnetizations, and the net magnetization is zero.  The
application of a magnetic field causes a partial alignment of
the moments;  the alignment depends on the direction of field
relative to crystalline axes and the crystalline anisotropy
energy.  Antiferromagnetism was first verified in 1939 in
manganous oxide.
 
Anitferromagnetic ordering patterns can be determined by
neutron diffraction experiments, because the magnetic moments
of the neutron interacts with the staggered array of moments in 
the antiferromagnet.  A large number of compounds--many of the
insulators--containing iron-group, rare earth, and actinide
metals are antiferromagnets.
 
Ferromagnetism, ferrimagnetism, and antiferromagnetism are all
representative of more general phenomena in solids, called
phase transitions.  A phase transition occurs when cooling
through a critical temperature is accompanied by a significant
change in a physical property.  Other examples of phase
transitions are ferroelectricity, in which a spontaneous
electrical polarization develops, and SUPERCONDUCTIVITY.

Bibliography:  Berkowitz, A.E., and Kneller, E., Magnetism and
Metallurgy, 2 vols.  (1969);  Bozorth, R.M., Ferromagnetism
(1951);  Chen, Chi-Wen, Magnetism and Metallurgy of Soft
Magnetic Materials (1986);  Lee, E.  W., Magnetism (1984);
Mattis, D.C., The Theory of Magnetism II (1985);  Morrish,
A.H., The Physical Properties of Magnetism (1965);  Sears,
F.W., Zemansky, M.W., and Young, H.D., University Physics, 7th
ed.  (1986).

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