Table 8.1 Magnetic quantities and their units.
Magnetic quantity Symbol Definition
Magnetic field;
magnetic induction
Magnetic flux
B
F = qv ! B
"#
$" = Bnormal $A
Magnetic dipole
moment
Bohr magneton
% m#
%m = I A
&#
& = e!/2me.
Magnetization
vector
Magnetizing field;
Magnetic field
intensity
Magnetic
susceptibility
Absolute
permeability
Relative
permeability
Magnetic
permeability
Inductance
Magnetostatic
energy density
M
Units
Comment
T = tesla =
webers m-2
Wb =
weber
Produced by moving charges or currents
and acts on moving charges or currents.
$" is flux through $A and Bnormal is normal
to $A. Total flux through any closed
surface is zero.
Experiences a torque in B and a net force in
a nonuniform B.
Magnetic moment due to the spin of the
electron. & = 9.27!10-24 A m2
Net magnetic moment in a material per unit
volume
H is due to external conduction currents
only and is the cause of B in a material.
A m2
H
A m2 or
J T-1
Magnetic moment A m-1
per unit volume
A m-1
H = B/%o – M
'm
M = 'm H
None
%o
c = [(o%o]-1/2
%r
%r = B / (%oH).
H m-1 =
Wb m-1 A-1
None
%#
% = %o %r
H m-1
Not to be confused with magnetic moment.
L
Evol
L = ")otal / I
dEvol = H dB
H (henries)
J m-3
Total flux threaded per unit current.
dEvol is the energy required per unit volume
in changing B by dB.
Relates the magnetization of a material to
the magnetizing field H.
A fundamental constant in magnetism. In
free space %o = B/H.
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
Table 8.2 Classification of magnetic materials.
Type
'm
'm vs. T
(typical
values)
T independent
Negative and
small
Diamagnetic
(–10-6)
Paramagnetic
Negative and
large (–1)
Positive and
small,
*10-5 – 10-4)
Positive and
small
(10-5)
Ferromagnetic
Positive and
very large
Antiferromagnetic
Positive and
small
Ferrimagnetic
Positive and
very large
Below a critical
temperature
Independent of T
Comment and examples
Atoms of the material have closed shells. Organic
materials, e.g. many polymers; covalent solids,
e.g. Si, Ge, diamond; some ionic solids, e.g.
alkalihalides, some metals e.g. Cu, Ag, Au.
Superconductors
Due to the alignment of spins of conduction
electrons.
Alkali and transition metals.
Curie or Curie-Weiss Materials in which the constituent atoms have a
law
permanent magnetic moment, e.g. gaseous and
liquid oxygen, ferromagnets (Fe),
'm = C / (T–TC)
antiferromagnets (Cr) and ferrimagnets (Fe3O4) at
high temperatures.
Ferromagnetic below May possess a large permanent magnetization
and paramagnetic
even in the absence of an applied field.
above the Curie
Some transition and rare earth metals, Fe, Co, Ni,
temperature
Gd, Dy
Antiferromagnetic
Mainly salts and oxides of transition metals e.g.
below and
MnO, NiO, MnF2, and some transition metals, +–
paramagnetic above Cr, Mn.
the Neel temperature
Ferrimagnetic below May possess a large permanent magnetization
and paramagnetic
even in the absence of an applied field.
above the Curie
Ferrites.
temperature
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
Table 8.3 Properties of the ferromagnets Fe, Co, Ni and Gd.
Fe
Co
Ni
Gd
Crystal structure
BCC
HCP
FCC
HCP
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, 2002)
http://Materials.Usask.Ca
Table 8.4 Selected soft materials and some typical values and applications (Wh is the hysteresis loss, energy
dissipated per unit volume per cycle in hysteresis losses, J m-3 cycle-1, typically at Bm = 1 T).
Magnetic
Material
%oHc
(T)
Bsat
(T)
Br
(T)
%ri
%rmax
Wh
Typical applications
IDEAL
SOFT
0
Large
0
Large
Large
0
2.2
<0.1
150
104
250
2.0
0.5-1
103
104 –
4!105
30-100
2!10-7
0.7-0.8
<0.1
105
106
<0.5
5!10-6
0.86
<0.1
8!103
105
<0.1
Transformer cores, inductors, electrical
machines, electromagnet cores, relays,
magnetic recording heads etc.
Large eddy current losses. Generally
not preferred in electrical machinery
except in some specific applications
(e.g., some electromagnets and relays)
Higher resistivity and hence lower eddy
current losses. Wide range of electrical
machinery (e.g., transformers etc.)
High permeability, low loss electrical
devices, e.g. specialty transformers,
magnetic amplifiers
Low-loss electrical devices, audio
transformers, HF transformers,
recording heads, filters etc.
2!10-6
1.6
<10-6
105
20
Low-loss transformer cores
10-5
0.4
<0.01
5!103
<0.01
HF low-loss applications. Low
conductivity ensures negligible eddy
current losses. HF transformers,
inductors (pot cores, E and U cores
etc.), recording heads.
Iron
<10-4
(commercial
grade, 0.2%
impurities)
Silicon iron <10-4
(Fe: 2-4%Si)
Supermalloy
(79Ni-15Fe5Mo-0.5Mn)
78
Permalloy
(78.5%Ni21.5%Fe)
Glassy
metals
Fe-Si-B
Ferrites
Mn-Zn
ferrite
2!103
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
Table 8.5 Hard magnetic materials and typical values.
Magnetic Material
%oHc
(T)
Br
(T)
(BH)max
-3
(kJ m )
Examples and Uses
IDEAL HARD
Large
Large
Large
Permanent magnets in various
applications
Alnico (Fe-Al-NiCo-Cu)
0.19
0.9
50
Wide range of permanent magnet
applications
Alnico (Columnar))
0.075
1.35
60
Strontium ferrite
(anisotropic)
0.3-0.4
0.36-0.43
24-34
dc motors, starter motors, loudspeakers,
telephone receivers, various toys
Rare earth cobalt
e.g. Sm2Co17
(sintered).
0.62-1.1
1.1
150-240
Servo motors, stepper motors,
couplings, clutches, quality audio
headphones etc.
NdFeB magnets
0.9-1.0
1.0-1.2
200-275
Wide range of applications, small
motors (e.g. in hand tools), walkman
equipment, CD motors, MRI body
scanners, computer applications
Hard particles
--Fe2O3
0.03
0.2
Audio and video tapes, floppy disks
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
Table 8.6 Selected examples of Type I and Type II superconductors. Critical fields are close to
absolute zero (obtained by extrapolation). Type I for pure and clean elements.
Type I
Sn
Hg
Ta
V
Pb
Nb
Tc (K)
3.72
4.15
4.47
5.40
7.19
9.2
Bc (T)
0.030
0.041
0.083
0.14
0.08
0.198
Type II
Nb3Sn Nb3Ge
Ba2–xBrxCuO4
Hg-Ba-Ca-Cu-O
Y-Ba-Cu-O Bi-Sr-Ca-Cu-O
YBa2Cu3O7 (Bi2Sr2Ca2Cu3O10)
Tc (K)
18.05
23.2
30 - 35
93 - 95
Bc2 (Tesla)
at 0 K
24.5
38
~150
~300
-2
Jc (A cm ) ~ 107
at 0 K
122
130 - 135
104 - 107
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
Table 8.7 Selected examples of flexible magnetic storage media based on coatings of particulate mat
Typical values.
Particulate
matter
Typical
application
%oMr
(T)
%oHc
(T)
Comment
--Fe2O3
Audio tapes
(Type I)
0.16
0.036
Widely used particles
--Fe2O3
Floppy disk
0.07
0.03
Co(--Fe2O3)
Video tape
0.13
0.07
CrO2
Audio tapes
(Type II)
0.16
0.05
CrO2
Video tape
0.14
0.06
Fe
Audio tape
(Type IV)
0.30
0.11
Cobalt impregnated --Fe2O3
particles
More expensive than --Fe2O3
High coercivity and
magnetization. To avoid
corrosion, the particles have to be
treated (expensive)
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
Table 8.8 Selected examples of thin films in magnetic storage media; typical values.
Thin Film
Deposition
%oMs
(T)
%oHc
(T)
Comment and typical or
potential application
Co-(Rare
earth)
Sputtering in
vacuum
0.7-0.8
0.05-0.07
Longitudinal magnetic
recording media. Hard disks.
Co-Cr alloys
Sputtering in
vacuum
0.4-0.7
0.03
Perpendicular magnetic
recording media .
Co(--Fe2O3)
Sputtering in
vacuum
0.3
0.07-0.08
Longitudinal magnetic
recording media.
Co-Ni-P
Electroplating
1
0.1
Longitudinal magnetic
recording media.
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca