v.2016.APR
D. Magnetic Properties of Materials
• Introduction (8.1)
– magnetic moments (), torque (), magnetization (M), magnetic field (B)
• classification (8.2)
– dia, para, ferro, anti-ferro, ferri
• ferromagnetism
– origin: exchange interaction (8.3)
– magnetic domains (8.5.1), domain walls (8.5.3), wall motion (8.5.5),
anisotropy (8.5.2), M-H curves (8.5.6), demag (8.5.7)
• soft & hard magnets (8.6)
• superconductivity
+Text: D.R. Askeland and P.P. Phulé, The Science and Engineering of Materials (4th ed.) (2004)
Magnetic Properties
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Magnetic field B
How it can be generated:
1. wire
3. ferromagnet
Biot–Savart law (1820)
2. solenoid B = μ0NI = μ0(n / L)I
How it affects charges:
(สภาพซาบซึมได้)
magnetic permeability of free space
Lorentz force:
 0  4 10 7 H / m
Magnetic Properties
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2
8.1.1 Magnetic Moment
m
• dielectric properties () of materials are based on (electric) dipole moments
• magnetic properties () of materials are based on magnetic (dipole) moments


+Q
po = aQ 
F=QE
E
F
m
un
area
B
A
current
loop I
A
I

B
Definition of a magnetic dipole moment.
torque tries to rotate m to align with B
magnetic moments originate from the flow of electrons
m
Magnetic Properties
m

m  IAu
n
o magnetic permeability (H/m)
magnetic moments (A-m2)
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8.1.2 Atomic Magnetic Moments
atom
Origins of m in atoms
orb
1. Orbiting electrons

2. Spinning electrons
z
B
A
r
z
I
µspin
-e
L
dq
e
e
I
 
dt
T
2
er 2
e
2
L
 orb  I r  

2
2me
spin
 
z  
L  mvr  mr 
• overall magnetic moments of the electron:
μ electron  μ spin  μ orb
• overall magnetic moments of the atom:

all electrons
L : Orbital angular momentum
Magnetic Properties
e
e
e

S z   ms   
2me
me
me
  B  9.274 10  24 A  m 2
2
μ atom 
Sz
e
S

me
μ electron
Bohr
magneton
Quantum numbers:
n = 1,2,3...
l = 0,1,...(n-1)
ml = -l,...-1,0,1...l
ms =  ½
electrons in closed subshells  atom = 0
S : Spin (intrinsic) angular momentum
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m : magnetic quantum number
4
8.1.3 Magnetization (M), magnetic flux density (B)
Magnetization (M)  magnetic dipole moment / volume [unit: (A·m2)/m3 = A/m]
• torque  each atom develops a net
magnetic moment along the applied field
I

• material is said to be magnetized
Bo
(a)
Surface currents
I
I
A
B
(b)
M
no net
bulk
current
I
B
M
Im
I
Magnetic Properties



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Surface currents
(magnetization current Im)
the surface of the medium
now behaves like a solenoid !
5
magnetic field
magnetic flux density B (Wb/m2)
field amplification
susceptability  m
permeability  r
(a) vacuum:
Magnetizing field (magnetic field strength)
H
nI
l
[A/m]
Magnetic field (magnetic flux density)
Bo   o H
[Tesla, Wb/m2]
(b) medium:
B  o H  o M
 
  o H  M 
field
amplification
  o H   m H 
  o 1   m H
Current I (A)
magnetizing field H (A/m)
susceptability
 o  r H
 H
The field B in the material inside the solenoid is due to the conduction
current I through the wires and the magnetization current Im on the
surface of the magnetized medium, or B = Bo + oM.
polarizability:   P / 
relative permittivity :  r  1 N e /  o


m 
M
H
relative permeability
r 

 1 m
o
Permittivity สภาพยอม (ยอมสนามไฟฟ้ า)
Susceptibility สภาพรับไว้ได้ (รับสนามแม่เหล็ก)
Permeability สภาพให้ซึมได้ (ให้สนามแม่เหล็กซึ มผ่านได้)
Magnetic Properties
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T = Wb/m2
= HA = Vs
H = Wb/A
Magnetic Properties
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Magnetic Properties
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Magnetic Properties of Materials
• Introduction (8.1)
– magnetic moments (), torque (), magnetization (M), magnetic field (B)
• classification (8.2)
– dia, para, ferro, anti-ferro, ferri
• ferromagnetism
– origin: exchange interaction (8.3)
– magnetic domains (8.5.1), domain walls (8.5.3), wall motion (8.5.5),
anisotropy (8.5.2), M-H curves (8.5.6), demag (8.5.7)
• soft & hard magnets (8.6)
• superconductivity
Magnetic Properties
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8.2 Magnetic Material Classifications





Magnetic Properties
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
Diamagnetism
Greek
dia – 1. across, through (diameter)
2. apart, opposite
• atoms of diamagnets have closed electronics shells
and subshells: group IB (Cu, Ag, Au), Si, NaCl
S
N
M
Origin:
F
• orbiting electrons try to resist B 
• dipole moments try to expel the applied field from the
materials
• diamagnets experience force toward smaller fields
•
M  0  m  0
 r  0.99995
 m  (0.4  3.4) 10 5
no practical
importance
• superconductors: perfect diamagnets
 m  1
Magnetic Properties
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
Paramagnetism
Greek
para – alongside, beyond
(microscopic) each atom/molecule has net magnetic
dipole moment
(macroscopic) no net magnetic moments due to
thermal agitation
• atoms have unpaired electrons.
• Incomplete cancellation of spin and/or orb
• Al, Ti, Cu alloys, Mo, Na, Zr, Mg
Origin:
oH
• alignment of majority of spins of conduction
electrons with B
M
• small +ve magnetization
 m  10 4  10 5
µav = 0 and M = 0
(a)
µav  0 and M = mH
•dipoles do not interact
• ferro-magnets and ferri-magnets above Tcurie
exhibit paramagnetism
(b)
(a) In a paramagnetic material each individual atom possesses a
permanent magnetic moment but due to thermal agitation there is no
average moment per atom and M = 0. (b) In the presence of an
applied field, individual magnetic moments take alignments along the
applied field and M is finite and along B.
Magnetic Properties
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
Ferromagnetism
Latin
Ferr(um) – iron
TCurie
Ferro  |  Para
• atoms of ferromagnets have many unpaired electrons: Fe, Ni, Co, (Gd, Dy)
RT
< RT
• Contribution: mainly  , partly 
spin
orb
Origin: magnetic ordering (constructive), dipoles reinforced (exchange interaction) 
magnetic domain
6
 m  10
, non-linear with H, can be 
Fe
i/o relationship (H,M)
highly nonlinear
(see later...)
M 0
H = 0 but M  0  (m  )
M   m H 
B0
In a magnetized region of a ferromagnetic material such as iron all
the magnetic moments are spontaneously aligned in the same
direction There is a strong magnetization vector M even in the
absence of an applied field.
Magnetic Properties
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
Anti-Ferromagnetism
• small, positive susceptability
TNeel
Anti-Ferro  |  Para
Cr, Mn, MnO, NiO
• no H  no M
Origin: magnetic ordering (destructive)
equal amplitudes
opposite directions
MnO
Cr
M=0
opposing
spins
none
B0
In this antiferromagnetic BCC crystal (Cr) the magnetic moment of
the center atom is cancelled by the magnetic moments of the corner
atoms (an eighth of the corner atom belongs to the unit cell).
Magnetic Properties
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
Ferrimagnetism
TCurie
Ferri  |  Para
cubic ferrite:
Fe3O4
hexagonal ferrites:
AB12O19
* [A = Ba, Pb, St] * [B = Al, Ga, Cr, Fe]
garnets:
M3Fe5O12
Origin: magnetic ordering (partially destructive)
usually non-conducting (oxides) 
do not suffer from eddy losses 
used in HF electronics
different amplitudes
opposite directions
Fe3O4
M 0
A
B
B0
Illustration of magnetic ordering in a ferrimagnetic crystal. All
A-atoms have their spins aligned in one direction and all B-atoms
have their spins aligned in the opposite direction. As the magnetic
moment of an A-atom is greater than that of a B-atom, there is net
magnetization, M, in the crystal.
Magnetic Properties
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Magnetic-classification flowchart
…
N
atom has
unpaired electron(s)?

Dia-
Y
dipoles interact?
magnetic ordering?
N
Para-
Y
destructive
constructive
completely
partially
Anti-Ferro-
Ferri-
Ferro-



Magnetic Properties
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@ T > TCurie
for ferro, ferri
@ T > TNeel
for anti-ferro
16
random
aligned
c
c
aligned
aligned
none
c
   o  r   o 1   m 
Pair up:
ferromagnetism
diamagnetism
paramagnetism
Magnetic Properties
opposing
H0
H=0
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8.4 Saturation Magnetization and Curie Temperature
Msat = condition at which all atomic moments have been aligned
Msat(T)
Msat(0)
1
Iron
0.8
0.6
0.4
lattice vibration
0.2
0
0
0.2
0.4
0.6
T / TC
0.8
1
TCurie is the temperature at which
thermal energy = potential energy
(from vibration) (from exchange interaction)
Magnetic Properties
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Magnetic Properties of Materials
• Introduction (8.1)
– magnetic moments (), torque (), magnetization (M), magnetic field (B)
• classification (8.2)
– dia, para, ferro, anti-ferro, ferri
• ferromagnetism
– origin: exchange interaction (8.3)
– magnetic domains (8.5.1), domain walls (8.5.3), wall motion (8.5.5),
anisotropy (8.5.2), M-H curves (8.5.6), demag (8.5.7)
• soft & hard magnets (8.6)
• superconductivity
Magnetic Properties
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8.3 The Origin of Ferromagnetism
1925: Pauli exclusion principle
1927: Hund’s rule
No two electrons may occupy the same quantum state
simultaneously. For example, if n, l, and ml are the same,
ms must be different (electrons have opposite spins).
Electrons in the same n, l orbitals prefer their spins
to be parallel (same ms)
-1
L
(n=2)
0
C
1 = m
p
p
L
s
s
H
K
(n=1)
He
Li
s
K
s
F
L
(n=2)
K
(n=1)
O
N
p
Ne
p
L
s
Be
B
K
s
Fig 3.38
Electronic configurations for the first five elements. Each box represents
an orbital  (n, , m ).
Electronic configurations for C, N, O, F and Ne atoms. Notice that Hund's
rule forces electrons to align their spins in C, N and O. The Ne atom has
all the K and L orbitals full.
Exchange Interaction (Pauli exclusion principle & Hund’s rule) forces 2 electrons to take ms/ml values that
result in minimum electrostatic energy.
Magnetic Properties
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The 3d elements
Fe atom
3d 6
Fe = [Ar]3d64s2
4s2
4 unpaired electrons
 intrinsic moments = 4B
n = 3, l = 2
ml = -2,-1, 0,1,2
26
Fe crystal
- 3d electrons spontaneously parallel their spins to minimize overall potential energy
- some conduction electrons [1.8]
- number of unpaired electrons reduced to 2.2 per atom [41.8 = 2.2]
O
5g
5f
N
6p
5d
Energy
4f
4d
M
6s
5p
5s
para
4p
4s
3d
anti-ferro
3p
3s
L
ferro
2p
2s
K
1s
1
2
3
4
n
5
dia
6
Energy of
various one-electron states. The energy depends on both n and 
Magnetic
Properties
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Ex. 19.1 Calculate saturation magnetization of Fe, given that Fe has a BCC lattice structure with a =
2.866 Angstrom. Compare with measured value of 2.1 T.
Magnetic Properties
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8.5.1 Magnetic Domains
Q) Fe can be non-magnetic at room temperature, why?
A) magnetic domains (external field lines cancel each other)
Domain wall (180¡)
N
N
S
Closure domain
Closure domains
90¡ domain wall
S
N
N
S
N
S
S
M
S
S
Magnetostatic energy:
potential energy stored
in magnetic fields
N
N
demagnetized (M = 0)
domain walls formed.
energetically more favorable closure domains 
(magnetostatic energy  ),
(magnetostatic energy ),
no external field lines
some external field lines
Potential energy: external (magnetostatic) + internal (walls)
*** magnetic domains creation continues until
reduction in external (B) potential energy = increase in internal (domain wall) potential energy
Magnetic Properties
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size, shape, orientation of domain walls depend on many factors, including size, shape of
specimens (small particles of <10nm are always magnetized)


magnetized
[100]
A
A
B
B
H
magnetization
results from
movements of
Bloch walls
spins (in walls and B)
gradually rotated by H
(they experience a torque)
A
B


A
B
(a) An unmagnetized crystal of iron in the absence of an applied magnetic
field. Domains A and B are the same size and have opposite
magnetizations. (b) When an external magnetic field is applied he domain
wall migrates into domain B which enlarges A and B. The result is that the
specimen now aqcuires net magnetization.
enlarges A and shrinks B
Magnetic Properties
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8.5.2 Magnetocrystalline Anisotropy
magnetization along some
planes are easier than others
(easy directions)
2
Analogy: optical anisotropy
Magnetizing field H (104 A m-1)
1
2
3
4
0
Fe (BCC)
Msat
[100]
[110]
1.5
notes:
rotate to OD
(difficult)
[111]
M  m H
B  o H  o M
Hard
[111]
D
Medium
[110]
P
1
C
0.5
Easy
[100]
0
magnetizations along
OA, OB, OC  (easy)
0
A
O
0.01 0.02 0.03 0.04 0.05
Applied magnetic field oH (T)
B
0.06
Magnetocrystalline anisotrpy in a single iron crystal. M vs. H
depends on the crystal direction and is easiest along [100] and
hardest along [111]
Magnetic Properties
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K: energy required to magnetize a unit volume in a
particular direction w.r.t. the easy directions
(also determine Hc – see later)
Table 8.4 Exchange interaction, magnetocrystalline anisotropy energy K, and saturation
magnetostriction coefficient λsat
Material
Crystal
Eex ≈ kTC
(meV)
Easy
Hard
K
(mJ cm−3)
λsat
(× 10−6 )
(hard vs easy)
Fe
BCC
90
<100>
<111>
48
20 [100]
−20 [111]
Co
HCP
120
// to c axis
 to c axis
450
Ni
FCC
50
<111>
<100>
5
−46 [100]
−24 [111]
Magnetic Properties
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8.5.4 Magnetostriction
(analogy: piezoelectric)
• magnetic energy  mechanical energy
 stress ferro crystal  a   exchange interactions between atomic spins   M 
 H   M   strain (a )  l    

H
Original Fe crystal
y [010]

x [100]
l
l
Strain:
magnetostrictive constant (sign
dependent on direction and
magnitude of H)
Magnetostriction is responsible
for hum noise near transformers
(l/l vibrate the surroundings)
 + 
Magnetostriction means that the iron crystal in a magnetic field
along x, an easy direction, elongates along x and but contracts in
the transverse dirtections
Ni (FCC) -46ppm
Fe (BCC) +20ppm
(see Table 8.4)
(the opposite is true for Ni)
for the curious mind
Keywords: ferrofluid, magnetic fluid
Applications: speakers, disk drives….. spin, silence
Magnetic Properties
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8.5.3 Domain Walls

In a Bloch wall the neighboring spin magnetic moments rotate
gradually and it takes several hunbdred atomic spacings to rotate the
magnetic moment by 180°.
N = /a
(-z)
(+z)
Potential energy
Domain wall
energy, Uwall
 exchange interation (Hund’s rule) prefers
c.f. easy
direction

Anisotropy energy, Uanisotropy
Magnetic Properties
 anisotropy energy (K) prefers thin walls
1/
(ideal = 0) i.e. z  –z in one atomic
spacing in the easy directions (see 8.5.2)
Domain wall thickness, 
 compromise: minimize total potential
Exchange energy, Uexchange

parallel spins ( or ). Hence, thick
walls (ideal = )  adjacent magnetic
dipoles tend to minimise 
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energy ~ 0.1m for Fe
28
8.5.5 Domain wall motion
Walls interact with dislocations.
Magnetization involves movements of domain walls ( domains growth / shrink).
Motion of domain walls (not smooth) affected by crystal imperfection / impurities.
Stress distribution around domain walls is complicated due to magnetostriction (8.5.4)
Domain
BLOCH WALL

Tension
if wall gets close to dislocation 
Domain
 cancels 
 Compression
 lowers strain energy
Dislocation
** Walls usually formed at dislocations
Tension
Stress and strain distributions around a dislocation and near a
domain wall.
Magnetic Properties
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29
Walls interact with (non-magnetic) inclusions / impurities.
H  [(a)(b)]  [Pinned @ (b)]  snapped [(b)...]  lattice vibration  heat loss
Movements of domain walls are jerky.
Bloch wall
Bloch wall
Domain
Domain
Impurity
S
S
N
N
Domain walls are pinned at
impurity. (can snap away if
large energy is applied)
low magnetostatic energy
(a)
(b)
Interaction of a Bloch wall with a non-magnetic (no permanent
magnetization) inclousion. (a) The inclusion becomes magnetized
and thereis magnetostatic energy. (b) This arrangement has lower
potneital energy and is thus favorable.
Magnetic Properties
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8.5.6 Polycrystalline materials and M-H curves
Oabcd: Initial magnetization curve
new domains
generated (nucleated
at impurity sites)
Hc: coercivity, coercive field
H
d
Msat
c
e
Mr
Msat: saturation magnetization
M in each grain rotates to
align parallel to the nearest
easy direction
M
remnant
magnetization
Mr: remanant/residual magnetization
H
e
a
Reversible
boundary
motion
b
Irreversible
boundary
motion
c
Rotation
of M
d
Saturation
of M
discrete jumps due to sudden
jerks in wall motions
H
f
-H
-Hc
coercive field -x
represents resistance to
demagnetization
a
Barkhausen
effect
b
H
M
H
O
H
+x
M
M vs. H behavior of a previously unmagnetized polycrystalline iron specimen. An example grain in the unmagnetized specimen is that at O.
(a) Under very small fields the domain boundary motion is reversible. (b) The boundary motions are irreversible and occur in sudden jerks.
(c) Nearly all the grains are single domains with saturation magnetizations in the easy directions. (d) Magnetizations in individual grains
have to be rotated to align with the field, H. (e) When the field is removed the specimen returns along d to e. (f) To demagnetize the
specimen we have to apply a magnetizing field of Hc in the reverse direction.
Magnetic Properties
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31
Magnetization curves
B  o H  o M
Ferro- and ferriM
M-H
Mr
-H
-Hc
-Hsat
d
Msat
Br
i
h
Hc
-M
Hsat
H -H
H
-Mr
-Msat
g
d
Bsat
e
f
O
B
B-H
energy dissipated per
unit volume per cycle
of field variation
-Br
-Bsat
g
-B
Hysteresis loss due to:
- Joules loss (Eddy)
- heat loss (Barkhausen)
Saturation (major) hysteresis loop (datasheet)
B
Bsat
Magnetized
to saturation
Bm
H
-H
Hm
Hsat
Small cyclic
applied field
The B vs. H hyterisis loop depends on the magntitude of the applied
field in addition to the material and sample shape and size.
Magnetic Properties
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-B
32
Permeability
r 
B
B
o H
not a constant!
B
Slope = rmaxo
P
Slope = rio
B = oH
H
O
(a)
H
O
B = oH
(b)
Many transformers are
designed to operate at P
 r  max
 ri
Definitions of (a) maximum permeability and (b) initial permeability
(usually quoted values in material datasheet)
Magnetic Properties
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33
8.5.7 Demagnetization
How to demagnetize magnets?

B
no
Br
-Hc f
e
e' B '
r
O
f'
f  e’
small domain walls
motions are
reversible (bounce
back)
f’  O
only possible if f’
is known precisely
Magnetic Properties
Deperming
B
maybe
-H

-H
H
H
-B
-B
A magnetized specimen can be demagnetized by cycling the field
intensity with a decreasing magnitude, i.e. tracing out smaller and smaller
B-H loops until the origin is reached, H = 0.
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Magnetic Properties of Materials
• Introduction (8.1)
– magnetic moments (), torque (), magnetization (M), magnetic field (B)
• classification (8.2)
– dia, para, ferro, anti-ferro, ferri
• ferromagnetism
– origin: exchange interaction (8.3)
– magnetic domains (8.5.1), domain walls (8.5.3), wall motion (8.5.5),
anisotropy (8.5.2), M-H curves (8.5.6), demag (8.5.7)
• soft & hard magnets (8.6)
• superconductivity
Magnetic Properties
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35
8.6 Soft and Hard Magnetic Materials
Power loss / cycle is small, suitable for applications
where repeated mag/demag cycles are involved
(motors, transformers, inductors...)
Power loss / cycle is large,
suitable for permanent
magnets, data storage
Energy Product:
energy stored in
external magnetic field
(available to do work)
H c (hard )
 106
H c ( soft )
Magnetic Properties
(B·H) product:
T
A Wb A
J
 2   3
m m m m
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Magnetic Properties
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8.7 Soft Magnets
(J/m3 per cycle)
eddy
*
low-field app.
(Fe3O4)
(1 MHz)
Ni-Zn ferrite (200 MHz)
Garnets (Fe5O12)
YIG (microwave)
Y3- (- 300 GHz)
Y2.1Gd0.98 (8-12 GHz)
Magnetic Properties
high-freq app.
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Structural defects (particles of a non-magnetic phase or voids) tend to restrict the motion of
domain walls, and thus increase the coercivity. Consequently, a soft magnetic material must be
free of such structural defects. (Callister 6th Edition p 691)
Magnetic Properties
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8.8 Hard Magnets
Sm, Nd
4f metals
(Lanthanides)
Magnetic Properties
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Ex 19.6: calculate the force in kN for 1 m2 of a permanent
magnet whose saturation magnetization is 1.61 Tesla.
Lifting force:
F
Magnetic Properties
o M 2 A
2
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Magnetic Properties of Materials
• Introduction (8.1)
– magnetic moments (), torque (), magnetization (M), magnetic field (B)
• classification (8.2)
– dia, para, ferro, anti-ferro, ferri
• ferromagnetism
– origin: exchange interaction (8.3)
– magnetic domains (8.5.1), domain walls (8.5.3), wall motion (8.5.5),
anisotropy (8.5.2), M-H curves (8.5.6), demag (8.5.7)
• soft & hard magnets (8.6)
• superconductivity
Magnetic Properties
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Vanishing resistivity
Infinite conductivity
And.....
8.9 Superconductivity
8.9.1 Zero resistance and Meissner effect
Superconductor (e.g. Pb)
1911
residual
0
Tmp of Hg is 234 K (-38.8 degC)
Normal metal
(e.g. Ag)
0
Tc
Temperature, T
A superconductor such as lead evinces a transition to zero resisitivity
at a critical temperature Tc (7.2 K for Pb) whereas a normal
conductor such as silver does not, and exhibits residual resisitivity at
the lowest temperatures.
Residual resistivities of normal metals limited by scattering from impurities and lattice defects
Magnetic Properties
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...The Meissner effect
(complete expel of B)
Surface current I developed. Magnetization M and
external field lines cancel everywhere inside the material.
 = 0 and Meissner
Switching off field induces EMF (gives surface current)
that opposes the change (Lenz’s law)
 = 0 only
The Meissner effect. A superconductor cooled below its critical temperature expels all magnetic
field lines from the bulk by setting up a surface current. A perfect conductor (σ=∞) shows no
Meissner effect.
Magnetic Properties
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Magnet
N
S
Superconductor above Tc
N
Magnet
S
Surface currents
Superconductor below Tc
Left: A magnet over a superconductor becomes levitated. The superconductor is a perfect
diamagnet which means that there can be no magnetic field inside the superconductor.
Right: Photograph of a magnet levitating above a superconductor immersed in liquid nitrogen
(77 K). This is the Meissner effect. (SOURCE: Photo courtesy of Professor Paul C.W. Chu.)
Magnetic Properties
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External electric field does enter cladding even when i > c but with exponentially decreasing amplitude
External magnetic field does enter superconductor even below Tc but with exponentially decreasing amplitude:
B x   B0 exp x /  
Near 0 K:  ~ 10 – 100 nm
If B field too high,  > sample size.
At critical field Bc,   . Superconductivity is lost.
Bc (Tesla)
Bc (T)
0.08
Lead
0.06
0.1
Normal state
Lead
0.04
Superconducting
state
0
Mercury
Tc
0.02
Tin
0
0
2
8
4
6
Temperature (K)
10
0
2
4
Temperature (K)
6
8
The critical field vs temperature in Type I superconductors.
Magnetic Properties
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8.9.2 Type I and Type II superconductors.
Loss is sudden
Loss is gradual
Characteristics of Type I and Type II superconductors. B = µoH is the
applied field and M is the overall magnetization of the sample. Field inside the sample,
Binside = µoH + µoM, which is zero only for B < Bc (Type I) and B < Bc1 (Type II).
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The mixed or vortex state in a Type II superconductor.
Magnetic field lines
Normal state
Superconducting state
Vortex of flux lines
Critical magnetic field
  0, B  0
Bc2
Normal state
Applied fields able to pierce through
local tubular regions (filamentary) of
normal state embedded in the
superconducting state.
Sample retains infinite conductivity
due to the superconducting state.
 = 0, B  0
Vortex state
Bc1
 = 0, B = 0
0
Magnetic Properties
Fig 8.51
Meisner state
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8.9.3 Critical current density
Current through material generates magnetic fields. If current too high, surface magnetic field will exceed Bc
and superconductivity is lost—true for Type I; Type II more complicated..
B
Bc2
24.5 T
Nb3Sn
Tc
T
18 K
~107 A cm-2
J
Jc
The critical surface for a niobium-tin alloy which is a Type II
superconductor.
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1970s
1987
2000s
In 1986 J. George Bednorz (right) and K. Alex
Müller, at IBM Research Laboratories in Zurich,
discovered that a copper oxide based ceramic-type
compound (La-Ba-Cu-O) which normally has high
resistivity becomes superconducting when ooled
below 35 K This Nobel prize winning discovery
opened a new era of hightemperaturesuperconductivity research; now there are various
ceramic compounds that are superconducting above
the liquid nitrogen (an inexpensive cryogen)
temperature (77 K).
|SOURCE: IBM Zürich Research Laboratories.
Magnetic Properties
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YBCO (123)
Ceramic Superconductors
Bi-2223
| SOURCE: Australian Superconductors.
Magnetic Properties
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source: Wiki (Apr 2016)
These high temperature superconductor (HTS) flat
tapes are based on (Bi2-xPbx)Sr2Ca2Cu3O10-d(Bi-2223).
The tape has an outer surrounding protective metallic
sheath. Right: HTS tapes having ac power loss below
10 mW/m have a major advantage over equivalentsized metal conductors, in being able to transmit
considerably higher power loads. Coils made from
HTS tape can be used to create more compact and
efficient motors, generators, magnets, transformers
and energy storage devices.
51
Nb3Sn, Tc = 18 K(ceramics cannot be wound)
Superconductor
Mechanical
support structure
Radial forces
Air
Coil windings
Copper matrix
Solenoid
for mechanical strength +
in case superconductor fails (B > Bc, J > Jc, T > Tc)
A solenoid carrying a current experiences radial forces pushing the coil
apart and axis froces compressing the coil.
Superconducting electromagnets used on
MRI. Operates with liquid He, providing a
magnetic field 0.5–1.5 T.
SOURCE: Courtesy of IGC Magnet Business group.
Earth’s magnetic field: 50 T
Record B in 2012: 15 Tesla
Spectrum.IEEE.Org Nov 2013
The world’s most powerful MRI…
Current:
1.5-3 T, 1 mm (10000 neurons), s
Future:
12 T, 0.1 mm (1000 neurons), 0.1 s
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Nuclear Magnetic Resonance (NMR)
http://www.sprawls.org/mripmt/MRI01/index.html
Magnetic Properties
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8.10 Superconductivity origin
• 1911: Onnes, first discovery
• 1957: BCS theory (Bardeen, Cooper, Schrieffer)
• Cooper pair: a pair of oppositely spinning and travelling electrons.
• #1 distorts positive nuclei, #2 feels net attractive force.
• #1 & #2 effectively attracted to each other via lattice distortion (normally Coulombic repulsion)
• Temperature must be sufficiently low such that random thermal vibrations are weak
• Cooper pair has no net spin, do not obey Fermi-Dirac statistics (Pauli exclusion), and can condense to
lowest energy state, having one wavefunction extending the whole sample
• a crystal imperfection cannot scatter a single Cooper pair since all pairs act as one
• Superconductivity is said to be a macroscopic manifestation of quantum mechanics
Lattice vibration
2
1
A pictorial and intuitive view of an indirect attraction between two
oppositely travelling electrons via a lattice distorsion and vibration.
Magnetic Properties
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source: Wiki (Apr 2016)
Nobel prizes related to Superconductivity (source: http://ieeecsc.org/pages/nobel-laureates-superconductivity)
1913: Onnes 1911, “for his investigations on the properties of matter at low temperatures…”
1972: Bardeen, Cooper, Schrieffer, “theory (BCS theory 1957) of superconductivity” (type I)
1973: Josephson, “for his theoretical predictions of the properties of a supercurrent through a tunnel barrier”
1973: Esaki, Giaever, “experimental discoveries of tunneling phenomena in semiconductors and superconductors”.
1987: Bednorz and Müller, “discovery of superconductivity in ceramic materials”
2003: Abrikosov, Ginsburg, Leggett , “theory of superconductors…” (type II)
Nobel prizes related to nuclear magnetic resonance (NMR) (source: http://www.nobelprize.org/)
1952: Bloch, Purcell, "methods for nuclear magnetic precision measurements“ (1D)
2003: Lauterbur, Mansfield, "for discovering magnetic resonance imaging (MRI)” (3D, magnetic field gradient)
Magnetic Properties
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