MagnetismMagnetism, the phenomenon by which materials assert an
attractive or repulsive force or influence on other materials.
Basic ConceptsAn electrical current in a loop
generates a magnetic field.Magnetic fields are generated by
moving electrically charged particles.
Magnetic field strength - H
Earth North Pole is actually the South magnetic pole.
Field lines come out from the north towards the south
Magnetization, Permeability, and the Magnetic Field
(A/m) LnIH =
A current passing through a coil sets up a magnetic field (H).
Where n=number of turns; L=length of the coil and I=current. Units
for H (A/m) and oersted 31 104.11 = mAoersted
)(weber/m 2HB oo =
When H is applied in vacuum, lines of magnetic flux are
inducted. The number of lines of flux, called flux density or
inductance B, is related to the applied magnetic filed by the
o magnetic permeability of vacuum.
Units:H(oersted), B(gauss), o(gauss/oersted)H(A/m), B(weber/m2
tesla), o(4x10-7weber/A.m henry/m)
)(weber/m 2HB =When we place a material within the magnetic
field, B is determined by the manner in which induced and permanent
= permeability of the material in the field>o magnetic dipole
moments reinforce the field
Magnetization of a SolidB = oH + oM
o = permeability under vacuum
M = magnetization of the material
Review of TermsB Magnetic Induction (Tesla or kg/A-s2 or Wb/m2)H
Magnetic field (amp-turn/m or C/m-s)M Magnetization (same as
magnetic field)o Permeability (henry/m or kg-m/C2)
Magnetic susceptibility (m) 1=
17104 = mhenryO .
M is defined as the magnetic moment per unit volume. It is a
property of the material and depends on both the individual
magnetic moments of the constituent ions, atoms or molecules and
how these dipole moments interact with each other. )1( mo +=
17104 = mhenryO .
Magnetic MaterialsMagnetic behavior is determined primarily by
the electronic structure of a material, which provides magnetic
Magnetic Dipoles: (Analogous to electric dipoles) They are the
result of (a) electrons orbiting around the nucleus and (b) spin of
theelectron around its axis.
These two motions (i.e. orbital and spin) contribute to the
magnetic behavior of the material. The interaction between these
dipoles determine the type of magnetic behavior of the material.The
magnetic behavior can be controlled by composition, microstructure
and processing.The magnetic moment of an electron due to its spin
is known as the Bohr Magneton (MB Fundamental Constant)q=charge of
electron,h=Planck constantme=mass of the electronThen, we can view
electrons as small elementary magnets.However, the magnetic moments
due to electron do not all line up in the same direction.
Two mechanisms to cancel magnetic dipole moments:(1) Electron
pairs have opposite spins they cancel each other.(2) Orbital
moments of the electrons also cancel outThus:Atoms having
completely filled electron shells (He, Ne, Ar, etc) are not
capable of being permanently magnetized.Some elements, such as
transition elements (3d, 4d, 5d partially filled) have a net
magnetic moment since some of their levels have unpaired electrons.
Example (Sc to Cu) the electrons in the 3d level do not enter the
shells in pairs. Mn has five electrons with the same spin.
Transition metals have a permanent magnetic moment, which is
related to the number of unpaired electrons.
Types of magnetism: Ferromagnetism. Property of iron, nickel,
Strongest type of magnetism. Uncancelled electron spins as a
consequence of the electron structure.
Paramagnetism. Exhibited by materials containing transition,
rare earth or actinide elements
Diamagnetism Exhibited by all common materials but masked if
other two types of magnetism are present
Ferrimagnetism Source of magnetic moment different as
ferromagnetic. Incomplete cancellation of spin moments due to
atomic position and surrounding. Ceramics (insulators).
Antiferromagnetism Alignment of the spin moments of neighboring
atoms or ions in exactly opposite direction.
DiamagnetismCompletely filled shells or subshells.Total
cancellation of orbital and spin momentsCannot be permanently
magnetized. Very weakIt is induced by change in orbital motion due
to applied fieldThe dipoles induced by the field are aligned
opposite to the field direction.Only exists while a field is on. It
is found in all materialsVery hard to observe. It is of no
practical purposer < 1 (~0.99) H = 0
External magnetic field acting on the atoms slightly unbalances
their orbiting electrons and creates small magnetic dipoles within
the atoms, which oppose the applied field, and this action produces
a negative magnetic effect to the applied field.
A weak, negative, repulsive reaction of a material to an applied
is around 10-6to 10-5 . Inert gases, many organic compounds,
some metals (Bi, Zn, Ag) and nonmetals (S, P, Si)
Magnetization is negative (
ParamagnetismIncomplete cancellation of electron spin/orbital
magnetic momentsPermanent Dipoles. Randomly oriented when no field
is presentParamagnetism. Permanent dipoles align with an external
field No interaction between adjacent dipoles. Exists only in a
magnetic fieldRandomly oriented permanent dipoles align with field.
when field is applied)r = 1.00 to 1.01 H = 0
Magnetization is positive (> 0)Applied field aligns the
individual magnetic dipoles of the atoms or molecules and slightly
increases magnetic induction, B. The magnetic susceptibility ranges
from 10-6 to 10-2Temperature reduces the paramagnetic
effectsDiamagnetism and paramagnetism are all induced by an applied
field, when the field is removed, the effect disappears. Rare earth
metals, Li, Na, K, RhA weak, positive, attractive reaction of a
material to an applied fieldVery limited engineering
DiamagneticBismuth -16.6Mercury -2.85Silver -2.38Carbon
(diamond) -2.1Gold -3.44Sodium chloride -1.4Copper
-1.8ParamagneticIron aluminum alum 66Uranium 40Platinum 26Aluminum
2.07Sodium 0.85Chromium 3.13
Material Susceptibility m(x 10-5)
FerromagnetismElectron Spins dont cancel outCoupling
interactions cause adjacent atoms to align with one
anotherFerromagnetism. Permanent magnetic moment in the absence of
an external field.
large magnetizationr = up to 106
Permanent dipoles are aligned even in the absence of a magnetic
H = 0
Magnetic susceptibility is positive and very large (101< <
106)Very large magnetization will be created by the
material.Relationship between magnetization (M) and applied field
(H) is nonlinear and complicated. Repeated magnetization leads to
hysteresis.Large magnetic field can be retained after the applied
field removed.Most important ferromagnetic elements are: Fe, Co, Ni
Great engineering importance.A rare-earth element gadolinium (Gd)
is also ferromagnetic below 16oC, but has little engineering
Fe atom has four unpaired 3d electrons; Co has three unpaired 3d
electrons; Ni has two unpaired 3d electrons.
Spins of the 3d electrons of adjacent atoms align in a parallel
direction by a phenomenon called spontaneous magnetization. This
parallel alignment of atomic magnetic dipoles occurs in microscopic
regions called magnetic domains. Most critical difference between
Ferromagnetism and Paramagnetisim: The former has Spontaneous
Magnetization. Randomly oriented domains No net
magnetizationDomains aligned in a magnetic field Very strong
As a whole the materials magnetic domains are oriented randomly
and effectively cancel each other out
If H is applied, domains align giving a strong net H field in
same direction as H
Net H field partially exists even when Hext is removed
Fe, Co and Ni ferromagnetic materials
Cr and Mnnot ferromagnetic materials, Why?
(they all have unpaired 3d electrons)
Magnetic exchange interaction energy Energy associated with the
coupling of individual magnetic dipoles into a single magnetic
domain. Only when this exchange energy is positive material be
ferromagnetic. Magnetic exchange energy is related to the ratio of
atomic spacing to 3d orbit, must be in the range of 1.4 to 2.7.
AntiferromagnetismAlignment of neighboring atomsSpin moments are
no net magnetic moment
Antiparallel alignmentCeramic oxides, Manganese (Mn), chromium
(Cr), MnO, CrO, and CoOexhibit this behavior M2+ O 2-
A type of magnetism in which the magnetic dipoles of atoms are
aligned themselves in opposite directions by an applied field so
that there is no net magnetic moment.
If we place ferromagnetic material (e.g. iron) inside a solenoid
with field B0 , increase the total B field inside coil to
BM is magnitude of B field contributed by iron coreBM result of
alignment of the domainsBM increases total B by large amount - iron
core inside solenoid increases B by typically about 5000 times For
the electromagnetic core we use soft iron where the magnetism is
not permanent (goes away when the external field isturned off).
The maximum possible magnetization, or saturation magnetization
Msrepresents the magnetization that results when all the magnetic
dipoles in a solid piece are mutually aligned with the external
field. There is also a corresponding saturation flux density Bs
MBBB += 0 HB 00 = MBM 0=
The magnetic moments change direction continuously for
B small: Domains with favorable orientation to applied field
grow at the expense of others.
B large: Rotation of the domain orientation towards the applied
MS: Saturation Magnetization
1) Fast stage: The domains with moments parallel to the applied
field grow at the expense of those with less favorable
orientations. The domain growth takes place by domain wall
movement. The magnetization increases rapidly as the applied field
increases2) Second stage: When domain wall growth has finished, if
the applied field is continuously increased, domain rotation
occurs. The magnetization increases slowly with the applied
Domain movement during magnetizationWhen an external magnetic
field is applied, the magnetic domains will follow two-stage
B small: Domains with favorable orientation to applied field
grow at expense of others .B large: rotation of the magnetization,
B M || BRemanence Mr: remaining magnetization at B = 0 due to
irreversible Bloch wall displacements.Coercitivity BC : required
field to remove remaining magnetization.Ms: saturation
magnetization lim M(B) B
The maximum magnetization, called saturation magnetization MSAT,
in iron is about 1.75x106 Am-1. This corresponds to all possible
net spins aligning parallel to each other. Calculate the effective
number of Bohr magnetons per atom that would give MSAT, given that
the density and relative atomic mass of iron are 7.86g.cm-3 and
Number of iron atoms per unit volume( )( )
The magnetic saturation is given by the expression:
Where is the number of net spins that contribute to
magnetization per iron atom
Fe Co Ni Gd
Bohr magnetons per atom 2.22 1.72 0.60 7.1
Msat(0) (MA m-1) 1.75 1.45 0.50 2.0
Bsat = o Msat (T) 2.2 1.82 0.64 2.5
TC 770 C 1043 K
1127 C 1400 K
358 C 631 K
16 C 289 K
From Principles of Electronic Materials and Devices, Second
Edition, S.O. Kasap ( McGraw-Hill,
Table 8.3 Properties of the ferromagnets Fe, Co, Ni and Gd.
Calculate the maximum, or saturation magnetization and the
saturation flux density that we expect in iron. The lattice
parameter of BCC iron is 2.866Angstroms. Data Fe (Z=26)
Based on the unpaired electronic spins (see table), we expect
each iron atom to have 2.22 electrons that act as magnetic
The maximum volume magnetization (MSAT) is the total magnetic
moment per unit volume
( )( )( )16
In ferromagnetic materials OM >> OH and therefore B~OM
19219210751104 267 ==
Calculate (a) the saturation magnetization and (b) the
saturation flux density for nickel, which has a density of
8.90g.cm-3. Data ANi = 58.69g.mol-1
(a) Based on the table, we expect each nickel atom to have 0.6
electrons that act as magnetic dipoles. The number of nickel atoms
per cubic meter is related to the density of the nickel 32810139
A __. ==
The saturation magnetization is151015600 == mANMagnetonBohrMSAT
(b) Flux density : TeslaMB SATOSAT _.640==
FerrimagnetismIn some ceramic compounds, different ions have
different magnitude of magnetic moments. When these magnetic
moments are aligned in an antiparallel manner, there is a net
magnetic moment in one direction.
100< < 104These ceramic magnetic materials are called
ferrites and have very useful electronic applications.
FerrimagnetismCeramics. Permanent magnetism(Source of net
magnetic moment is
different)Cubic ferrites MFe2O4 (M = Ni, Mn,
Co, Cu)Can adjust composition to get
different propertiesFerrites are usually good electronic
Cubic ferrites having other compositions may be produced by
adding metallic ions that substitute for some of the iron in the
crystal structure. Again, from the ferrite chemical formula,
M2+O2(Fe3+)2(O2-)3 , in addition to Fe2+, M2+ may represent
divalent ions such as Ni2+, Mn2+, Co2+, and Cu2+, each of which
possesses a net spin magnetic moment different from 4; several are
listed in Table 18.4.Thus, by adjustment of composition, ferrite
compounds having a range of magnetic properties may be produced.
For example, nickel ferrite has the formula NiFe2O4 .Other
compounds may also be produced containing mixtures of two divalent
metal ions such as (Mn,Mg)Fe2O4 , in which the Mn2+:Mg2+ ratio may
be varied; these are called mixed ferrites.
Calculate the saturation magnetization for Fe3O4 given that each
cubic unit cell contains 8 Fe2+ and 16 Fe3+ ions and that the
lattice parameter is 0.839nm.
The net magnetization results from the Fe2+ ions only. Since
there are 8 Fe2+ ions per unit cell and 4 Bohr magneton per Fe2+
ion, then the number of electron contributing to the dipole
magnetization per unit cell is 32 (nB).
Design a cubic mixed-ferrite magnetic material that has a
saturation magnetization of 5.25x105A.m-1
From the previous example the, if all were Fe2+, the saturation
magnetization should be 5.0x105A.m-1. Then, some of the iron Fe2+
ions must be replaced by other ions with more than 4 Bohr Magnetons
per ions, such as Mn.
aMn SATB _____._4533
If x represents the fraction of Mn2+ that have substitute for
Fe2+, then the remaining unsusbstituted Fe2+ fraction is (1-x)
xx Or 18.1%Mn
a) Soft magnetic materials: 0.001 < Hc < 1 A/cmb) Hard
magnetic materials: 100 < Hc < 30000 A/cm
Area of hysteresis loop: losses due to reversal of magnetization
(dissipated as heat).
Ms: material property.Hc: depends strongly on
Domain structureFerromagnetic sample generally has no net
magnetic moment!Reason: domain structure tends to the reduction of
magnetostatic energy.Reduction of magnetostatic energy, stored in
the magnetic field, by formation of domains of uniform spin
orientation. The domains are generated by so-called Bloch walls,
where the spin orientation changes gradually within a distance of
the order of 40nm (for Fe). Typical domain sizes are 1 - 10 m.
There is a competition between reduction in magnetostatic energy
and the energy required to form Bloch walls.
Closure domains eliminate the magnetostatic energy but introduce
magnetostrictiveenergy.Bloch wall energy limits density of Bloch
Magnetic AnisotropyA material is called magnetically anisotropic
if the magnetization curve of the material depends on the direction
to which the material is magnetized. Some directions need only a
little energy to be magnetized, while others need more. The
direction that is easy to magnetize is called the easy
magnetization direction (ED). The direction that needs most energy
to be magnetized is called the hard magnetization direction
When a magnetic field is applied in a certain direction, the
magnetic moments align along the easy axes that are closest to the
direction of the applied magnetic field. The other directions along
which the magnetic moments do not become aligned as easily are
known as the hard axes. The magnetization reaches its saturation
value in a comparatively lower applied field along an easy axis as
compared to the hard axis.
Polycrystalline material -different grains approach MSaturation
differently. Easy-orientation grains saturate at lower applied
Grains with hard orientations rotate their moment into the field
direction at higher fields.
The energy required during the magnetization to rotate the
magnetic domains because of crystalline anisotropy
magnetocrystalline energyormagnetocrystalline anisotropic
Magnetocrystallineanisotropy is the energy necessary to deflect
the magnetic moment in a single crystal from the easy to the hard
direction. The easy and hard directions arise from the interaction
of the spin magnetic moment with the crystal lattice (spin-orbit
In cubic crystals, like magnetite, the magnetocrystalline
anisotropy energy is given by a series expansion in terms of the
angles between the direction of magnetization and the cube axes. It
is sufficient to represent the anisotropy energy in an arbitrary
direction by just the first two terms in the series expansion.
These two terms each have an empirical constant associated with
them called the first- and second order anisotropy constants, or K1
and K2, respectively. At 300 K, K1 = -1.35x105 ergs/cm3 K2 = -0.44
The simplest form of crystal anistropy is uniaxial anisotropy.
For cubic crystals the anisotropy energy can be expressed in terms
of the direction cosines (cos1, cos2, cos3) of the internal
magnetisation with respect to the three cube edges. Due to the high
symmetry of the cubic crystal this can be expressed in a simple
manner as a polynomial series in the direction cosines.
( ) ( ) ......32221221232322222121 ++++=
In hexagonal crystals the anisotropy energy is a function of
only one parameter, that is the angle between the magnetization and
the c-axis. Experiments show, that it is symmetric with respect to
the base plane, and so odd powers of Coscan be omitted in a power
series expansion for the anisotropy energy density . The typical
values of the anisotropy for cobalt K1=4.1x106erg/cm3 and
1 coscos KKwani +=
Summary:The dependence of magnetic properties on a preferred
direction is called magnetic anisotropy. There are several
different types ofanisotropy:Type depends on1. magnetocrystalline-
crystal structure2. shape- grain shape3. stress- applied or
residual stressesMagnetic anisotropy strongly affects the shape of
hysteresis loops and controls the coercivity and remanence.
Anisotropy is also of considerable practical importance because it
is exploited in the design of most magnetic materials of commercial
Shape AnisotropyThe second type of anisotropy is due to the
shape of a mineral grain. A magnetized body will produce magnetic
charges or poles at the surface. This surface charge distribution,
acting in isolation, is itself another source of a magnetic field,
called the demagnetizing field. It is called the demagnetizing
field because it acts in opposition to the magnetization that
For example, take a long thin needle shaped grain. The
demagnetizing field will be less if the magnetization is along the
long axis than if is along one of the short axes. This produces an
easy axis of magnetization along the long axis. A sphere, on the
other hand, has no shape anisotropy. The magnitude of shape
anisotropy is dependent on the saturation magnetization.For
magnetite smaller than about 20 microns, shape anisotropy is the
dominant form of anisotropy. In larger sized particles, shape
anisotropy is less important than magnetocrystalline anisotropy.
For hematite, because the saturation magnetization is so low, shape
anisotropy is usually never important.
Stress AnisotropyIn addition to magnetocrystalline anisotropy
and shape anisotropy, there is another effect related to spin-orbit
coupling called magnetostriction. Magnetostriction arises from the
strain dependence of the anisotropy constants. Upon magnetization,
a previously demagnetized crystal experiences a strain that can be
measured as a function of applied field along the principal
crystallographic axes. A magnetic material will therefore change
its dimension when magnetized (Joule Magnetostriction). The inverse
affect, or the change of magnetization with stress also occurs
(Villary Effect). A uniaxial stress can produce a unique easy axis
of magnetization if the stress is sufficient to overcome all other
anisotropies. The magnitude of the stress anisotropy is described
by two more empirical constants known as the magnetostriction
constants (111 and 100) and the level of stress.
Magnetostrictive MaterialsMagnetostriction is a property of
ferromagnetic materials that causes them to change their shape when
subjected to a magnetic field. The effect was first identified in
1842 by James Joule when observing a sample of nickel. This effect
can cause losses due to frictional heating in susceptible
ferromagnetic cores. Magnetostriction is a phenomenon observed in
all ferromagnetic materials. In normal ferromagnets, such as Fe or
Ni, the strain associated with magnetostriction are of the order of
10-4%, while in materials with exceptionally large
magnetostriction, such as Tb-Dy-Fe alloys (Terfenol-D) shos strains
of the order on 0.1%.
Magnetostriction is a transduction process in which electrical
energy is converted to mechanical energy. It couples elastic,
electric, magnetic and in some situations also thermal fields and
is of great industrial interest for use in sensors, actuators,
adaptive or functional structures, robotics, transducers and
Magnetostriction:Reversible strain along the magnetization
Magnetization curve is anisotropic for different
orientationsElastic deformation is anisotropic
Magnetostriction and magnetization saturate at the same
A magnetostrictive material develops large mechanical
deformations when subjected to an external magnetic field. This
phenomenon is attributed to the rotations of small magnetic domains
in the material, which are randomly oriented when the material is
not exposed to a magnetic field.
The orientation of these small domains by the imposition of the
magnetic field creates a strain field. As the intensity of the
magnetic field is increased, more and more magnetic domains
orientate themselves so that their principal axes of anisotropy are
collinear with the magnetic field in each region and finally
saturation is achieved.
Magnetostriction or Joule magnetostriction is a consequence of
the magnetoelastic coupling. It pertains to the strain produced
along the field direction and is the most commonly used
magnetostrictive effect.Joule magnetostriction is the coupling
between the magnetic and elastic regimes in a magnetostrictive
material. Magnetostriction is an intrinsic property of magnetic
Magnetostriction refers to magnetically induced shape change in
ferromagnetic materials (Joule Effect)Villari effect is a change in
magnetization state due to a mechanical stress
Transfers magnetic energy into mechanical energy Experiences a
change in strain due to a magnetic field The internal strain causes
a change in length which can be controlled by the magnetic
First application: First used during WWII in sonar and
If a helical magnetic field is applied to a material, then a
twisting in the material is observed. This is the Wiedemann effect.
The inverse of this is the Matteucci effect, which refers to the
creation of a magnetic field when a material is subjected to a
Magnetostrictive materials' ability to convert magnetic energy
into mechanical energy and vice versa makes them suitable for
building both actuation and sensing devices.
When an axial magnetic field is applied to a magnetostrictive
wire, and a current is passed through the wire, a twisting occurs
at the location of the axial magnetic field. The twisting is caused
by interaction of the axial magnetic field, usually from a
permanent magnet, with the magnetic field along the
magnetostrictive wire, which is present due to the current in the
wire.The current is applied as a short-duration pulse, 1 or 2 s;
the minimum current density is along the center of the wire and the
maximum at the wire surface. This is due to the skin effect.The
magnetic field intensity is also greatest at the wire surface. This
aids in developing the waveguide twist. Since the current is
applied as a pulse, the mechanical twisting travels in the wire as
an ultrasonic wave. Themagnetostrictive wire is therefore called
the waveguide. The wave travels at the speed of sound in the
waveguide material, ~ 3000m/s.
Contactless absolute linear displacement sensor
Magnetic Shape Memory EffectA shape memory effect occurs in
certain ferromagnetic materials. The parent austemitic phase
transforms into the martensitic phase.
The cubic austenitic crystal structure transform into a
tetragonal martensiticstructure. The resultant strain is
accomodated by the formation of a twin structure. The shape memory
effect is based on the motion of the twin boundaries..
When B=0, the magnetic moment of each twin variant points in the
direction of the easy magnetization axis.When an external field B
is applied, the magnetic moments are aligned with the field by
redistributing the twin variants
Basic Requirements for the Appearance of the MSM Effect.The
material should be (ferro)magnetic and exhibit a martensitic
transformation.The magnetic anisotropy energy must be higher than
the energy required to move a twin boundary.
1) Induce the martensitictransformation with the application of
a magnetic field
2) Rearrangement of the martensitic variants with the magnetic
Example: Ni-Mn-Ga (Heusler Alloy)
Maximum induced deformation ~ 10% with an applied field ~ 10 kOe
two orders of magnitude larger than in magnetosrictive Terfenol-D
Heusler alloys Ni-Mn-X (X=Ga, Al, In) ; Co-Ni-Al ; Ni-Fe-Ga
Others: Fe-Pd ; Fe-Pt ; Co-Ni ;
Heusler, L21 (Fm3m)
Ferromagnetic order (Tc~ 370 K)Total magnetic moment: total 4.1
per unit cell
( ) BNitotal 3.5x12 +=Non-stoichiometric Ni2Mn1+xGa1-x(Ni 0.3 B
per unit cell) Weak magnetic anisotropy
Compare Superelasticity andShape-memory Effect
With Magnetic superelasticity and magnetic shape memory
Magnetically Induced MartensiteThe magnetic field favors the
J is the magnetization polarization difference between
martensite and austenite.
Materials with high J are required.
Materials must have a narrow temperature regime.
High magnetic fields are required for the transformation.
Magnetically Induced AusteniteInverse transformation.The
magnetic field favors the austenite because its ferromagnetism is
stronger than that of martensite.Large and negative J.
Magnetically Induced Reorientation (MIR)There is no phase
transition. Twinned martensite of many variants transforms into one
variant martensite due to the magnetic field.Only twin boundary
The material must have a high magnetocrystalline anisotropy and
easily movable twin boundaries.
The material is biased to a single-variant state by either (a)
applying a stress or by applying a static magnetic field.
B is applied along the hard axis (orthogonal to the biasing
The magnetization vector rotates until the SME takes place. It
requires B>0.2 or 0.3T.
Twin boundaries will travel in the opposite direction when the
direction of B is reversed == reversible process.
Strength of the MSM devices:
Solenoid: Faster response. Better proportional position
Servomotor: faster stroke. Simplier; Less moving parts
Piezoactuators: Larger stroke; lower operating voltage
Applications:Magnetostrictive Torque SensorA magnetostrictive
material coating is rigidly attached to the shaft. An easy axis of
magnetization is created in the tangential direction by mechanical
stresses. The coating is then magnetized by passing a pulsed
current through the shaft. Transducer operation is based on the
reorientation of the circumferentially directed remanent
magnetization in the coating.
The remanent magnetization, the amount of magnetization that
remains in a material after an externally applied field has been
removed, is initially oriented in the tangential direction, and the
magnetic field created by the shaft is zero. When torque is applied
to the shaft, the remanent magnetization reorients and becomes
increasingly helical as the torque value increases. This
reorientation produces a magnetic field, proportional to the
torque, to be detected by a nearby magnetic-field sensing device.
The output signal from this device is conditioned in associated
electronic circuitry to provide a signal that can be used in a
control unit. The drawback is that the generated magnetic fields
are weak and the orientation of the magnetization in the coating
can be affected by an external axial magnetic field-Earth's, for