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Young Won Lim11/13/10
Copyright (c) 2009 Young W. Lim.
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Magnetism
Ferromagnetic material
● Permanent magnet
Ferrimagnetic material
● Below Curie Temp: like ferromagnets
● Above Curie Temp: like paramagnets
Paramagnetic material
● DC Josephson: I > Ic then in the resistiv
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Lorentz Force
B
FLorentz Forceto charges
Lorentz Forceto − charges
v
q0
q0
q=0B
F = q v × B
v
B
v
−F
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Hall Effect (1)
Negative Carrier
B z
B z I x
I x
F 'm
Lorentz Forceto charges
Bz
v x
E x
Fm
Lorentz Forceto − charges
B zI x
v x
E x
Positive Carrier
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Hall Effect (2)
Transient State
B zI x
Bz
v x
E x
Fm
Lorentz Forceto − charges
Applied external magnetic field
● charges deflect
● charges are accumulated
● electrical potential (EH) are created
As EH increases, new (+) and (–) charges are
repelled by those previously accumulated charges. (balancing effect)
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Hall Effect (3)
Steady State
E H
Fm : Lorentz ForceFe
The force Fe counteracts Fm.
● Fe : due to E
H
● Fm: due to external magnetic field B
z
Again charges travels straight,but with the Hall angle θ.
B z
v x
Fm
Lorentz Forceto − charges
B zI x
E H
E x
E t
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Hall Effect (4)
Transient State Steady State
B zI x
Bz
v x
E x
E H
Fm : Lorentz ForceFe
Fm
Lorentz Forceto − charges
B zI x
E H
E x
E t
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Hall Effect – Geometric Factor (1)
w2 w3w1
l1
l2
l3
l1
w1
l2
w2
l3
w
EH1 EH2 EH3
f H = function lw
,
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Hall Effect – Geometric Factor (2)
w
lw
Fm : Lorentz ForceFe
The force Fe counteracts Fm.
● Fe : due to E
H
● Fm: due to external magnetic field B
z
More charges are accumulated at the both ends until they repel other new charges.
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Physical Magneto-resistance Effect
B z B z
Ideal Case Real Case
● Different Lorentz Force to each charge
● Different charges travel different paths
● The total length of paths is increased
● The resistance increases slightly
Semiconductor
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Geometrical Magneto-resistance Effect (1)
Ideal Case Real Cases
Metal Electrode Contact
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Geometrical Magneto-resistance Effect (2)
Min R1
Bz: Max R
1
Min R2
Bz: Max R
2
ratio RRo
=max R1
min R1
ratio RRo
=max R2
min R2
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Magnetic Anisotropy (1)
Magnetocrystalline Anisotropy
● An intrinsic property of a ferrimagnet
● Magnetization curve along different crystal directions
● Easy direction
● Hard direction
● Intermediate direction
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Magnetic Anisotropy (2)
Easy directionMagnetization
Permalloy Resistor
: NiFe (ferrimagnet)
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Permalloy Resistor (1)
Easy direction
Rmax
: small current
: parallel current direction
Rmin
: large current
: perpendicular current direction
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Permalloy Resistor (2)
Easy direction
Fix the direction of current
45°θ
External Magnetic Field changes
● the magnetization direction of permalloy
● the resistance
● the current
H applied
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AMR Sensor (1)
The current direction is fixed
Rmax
: small current
: parallel current direction
Rmin
: large current
: perpendicular current direction
= 0 ˚
= −90 ˚
= 90 ˚
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AMR Sensor (2)
How the current direction is fixed? Shortening Bars
Barber Pole Biasing
: the shortest path
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Giant Magneto-resistance Effect
Magnetic Layer
Magnetic LayerNonmagnetic Conductor
High Interface Scattering
: Rmax
Low Interface Scattering
: Rmin
Antiparallel Magnetic Layers
Parallel Magnetic Layers
Current Current
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GMR Sensor
High Interface Scattering
: Rmax
Low Interface Scattering
: Rmin
Antiparallel Magnetic Layers
Parallel Magnetic Layers
Current Current
External Magnetic Field Change
Young Won Lim11/13/10
References
[1] http://en.wikipedia.org/[2] Nam Ki Min, Sensor Electronics, Dong-il Press [3] http://www.sensorsmag.com/ articles