The quantities now used in characterizing magnetization
were defined and named by William Thomson (Lord Kelvin) in
1850. The symbol B denotes the magnitude of magnetic flux density
inside a magnetized body, and the symbol H denotes the magnitude of
magnetizing force, or magnetic field, producing it. The two are
represented by the equation B = H, in which the
Greek letter mu, ,
symbolizes the permeability of the material and is a measure of the
intensity of magnetization that can be produced in it by a given magnetic
field. The modern units of the International Standard (SI) system for B
(T) or webers per square metre (Wb/m2) and for H are
amperes per metre (A/m). The units were formerly called, respectively, gauss and oersted. The
units of are henrys per
All ferromagnetic materials exhibit the
phenomenon of hysteresis, a lag
in response to changing forces based on energy losses resulting from
internal friction. If B
is measured for various values of H and the results are plotted
in graphic form, the result is a loop of the type shown in the
accompanying figure, called a hysteresis loop.
The name describes the situation in which the path followed by the values
of B while H is increasing differs from that followed as
H is decreasing. With the aid of this diagram, the characteristics
needed to describe the performance of a material to be used as a magnet
can be defined. Bs is the saturation flux density
and is a measure of how strongly the material can be magnetized.
Br is the remanent flux density and is the
residual, permanent magnetization left after the magnetizing field is
removed; this latter is obviously a measure of quality for a permanent
magnet. It is usually measured in webers per square metre. In order to
demagnetize the specimen from its remanent state, it is necessary to apply
a reversed magnetizing field, opposing the magnetization in the specimen.
The magnitude of field necessary to reduce the magnetization to zero is
Hc, the coercive force,
measured in amperes per metre. For a permanent magnet to retain its
magnetization without loss over a long period of time,
Hc should be as large as possible. The
combination of large Br and large
Hc will generally be found in a material with a
large saturation flux density that requires a large field to magnetize it.
Thus, permanent-magnet materials are often characterized by quoting the
maximum value of the product of B and H,
(BH)max, which the material can achieve. This
product (BH)max is a measure of the minimum vol
ume of permanent-magnet material required to produce a required flux
density in a given gap and is sometimes referred to as the energy product.
It was suggested in 1907 that a ferromagnetic
material is composed of a large number of small volumes called domains,
each of which is magnetized to saturation. In 1931 the existence of such
domains was first demonstrated by direct experiment. The ferromagnetic
body as a whole appears unmagnetized when the directions of the individual
domain magnetizations are distributed at random. Each domain is separated
from its neighbours by a domain wall. In the wall region, the direction of
magnetization turns from that of one domain to that of its neighbour. The
process of magnetization, starting from a perfect unmagnetized state,
comprises three stages: (1) Low magnetizing field. Reversible
movements of the domain walls occur such that domains oriented in the
general direction of the magnetizing field grow at the expense of those
unfavourably oriented; the walls return to their original position on
removal of the magnetizing field, and there is no remanent magnetization.
(2) Medium magnetizing field. Larger movements of domain walls
occur, many of which are irreversible, and the volume of favourably
oriented domains is much increased. On removal of the field, all the walls
do not return to their original positions, and there is a remanent
magnetization. (3) High magnetizing field. Large movements of
domain walls occur such that many are swept out of the specimen
completely. The directions of magnetization in the remaining domains
gradually rotate, as the field is increased, until the magnetization is
everywhere parallel to the field and the material is magnetized to
saturation. On removal of the field, domain walls reappear and the domain
magnetizations may rotate away from the original field direction. The
remanent magnetization has its maximum value.
The values of Br, Hc,
and (BH)max will depend on the ease with which
domain walls can move through the material and domain magnetization can
rotate. Discontinuities or imperfections in the material provide obstacles
to domain wall movement. Thus, once the magnetizing field has driven the
wall past an obstacle, the wall will not be able to return to its original
position unless a reversed field is applied to drive it back again. The
effect of these obstacles is, therefore, to increase the remanence.
Conversely, in a pure, homogeneous material, in which there are few
imperfections, it will be easy to magnetize the material to saturation
with relatively low fields, and the remanent magnetization will be small.
and magnetic anisotropy.
As far as domain rotation is concerned, there are two important factors to
be considered, demagnetization and magnetic anisotropy (exhibition of
different magnetic properties when measured along axes in different
directions). The first of these concerns the shape of a magnetized
specimen. Any magnet generates a magnetic field in the space surrounding
it. The direction of the lines of force of this
field, defined by the direction of the force exerted by the field on a
(hypothetical) single magnetic north pole, is opposite to the direction of
field used to magnetize it originally. Thus, every magnet exists in a
self-generated field that has a direction such as to tend to demagnetize
the specimen. This phenomenon is described by the demagnetizing factor. If
the magnetic lines of force can be confined to the magnet and not allowed
to escape into the surrounding medium, the demagnetizing effect will be
absent. Thus a toroidal (ring-shaped) magnet, magnetized around its
perimeter so that all the lines of force are closed loops within the
material, will not try to demagnetize itself. For bar magnets,
demagnetization can be minimized by keeping them in pairs, laid parallel
with north and south poles adjacent and with a soft-iron keeper laid
across each end.
The relevance of demagnetization to domain rotation arises from the
fact that the demagnetizing field may be looked upon as a store of
magnetic energy. Like all natural systems, the magnet, in the absence of
constraints, will try to maintain its magnetization in a direction such as
to minimize stored energy; i.e., to make the demagnetizing field as
small as possible. To rotate the magnetization away from this
minimum-energy position requires work to be done to provide the increase
in energy stored in the increased demagnetizing field. Thus, if an attempt
is made to rotate the magnetization of a domain away from its natural
minimum-energy position, the rotation can be said to be hindered in the
sense that work must be done by an applied field to promote the rotation
against the demagnetizing forces. This phenomenon is often called shape
anisotropy because it arises from the domain's geometry which may, in
turn, be determined by the overall shape of the specimen.
Similar minimum-energy considerations are involved in the second
mechanism hindering domain rotation, namely magnetocrystalline anisotropy.
It was first observed in 1847 that in crystals of magnetic material there
appeared to exist preferred directions for the magnetization. This
phenomenon has to do with the symmetry of the atomic arrangements in the
crystal. For example, in iron, which has a cubic crystalline form, it is
easier to magnetize the crystal along the directions of the edges of the
cube than in any other direction. Thus the six cube-edge directions are
easy directions of magnetization, and the magnetization of the crystal is
Magnetic anisotropy can also be induced by strain in a
material. The magnetization tends to align itself in accordance with or
perpendicular to the direction of the in-built strain. Some magnetic
alloys also exhibit the phenomenon of induced magnetic anisotropy. If an
external magnetic field is applied to the material while it is annealed at
a high temperature, an easy direction for magnetization is found to be
induced in a direction coinciding with that of the applied field.
The above description explains why steel makes a
better permanent magnet than does soft iron. The carbon in steel causes
the precipitation of tiny crystallites of iron carbide in the iron that
form what is called a second phase. The phase boundaries between the
precipitate particles and the host iron form obstacles to domain wall
movement, and thus the coercive force and remanence are raised compared
with pure iron.
The best permanent magnet, however, would be one in which the domain walls were all locked permanently in position and the magnetizations of all the domains were aligned parallel to each other. This situation can be visualized as the result of assembling the magnet from a large number of particles having a high value of saturation magnetization, each of which is a single domain, each having a uniaxial anisotropy in the desired direction, and each aligned with its magnetization parallel to all the others.
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