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Magnetic Materials
1. General Information About Magnetism
Numan Akdoğan
[email protected]
Gebze Institute of Technology
Department of Physics
Nanomagnetism and Spintronic Research Center (NASAM)
Magnetic Materials
1. General Information About Magnetism
References
Soshin Chikazumi, Physics of Ferromagnetism
B. D. Cullity, C. D. Graham. Introduction to Magnetic Materials
Nicola Spaldin, Magnetic Materials
Charles Kittel, Introduction to Solid State Physics
Why magnetism is important?
Applications of magnetic materials:
• Read heads for magnetic hard disk drives
• Magnetic random access memories
• Spin field effect transistors (Spin-FETs)
• Spin light emitting diodes (Spin-LEDs)
• In medicine to image and destroy cancer cells
http://www.pharmainfo.net
N. Akdoğan
1. General Information About Magnetism
From Agnes Barthelemy, Uni. Paris-Süd
History of magnetism
Fe3O4-first magnetic material used by people
William Gilbert (1540-1603)-first systematic work on magnetism
“On the magnet”-first book on magnetism published by Gilbert in 1600
1820-Hans Cristian Oersted (1775-1851) discovered that
an electric current produces a magnetic field
1825-first electromagnet
1988-dicovery of GMR (giant magneto-resistance)
N. Akdoğan
1. General Information About Magnetism
Magnetic poles
Iron filings have oriented in the magnetic field produced by
a bar magnet
Two poles where the field lines condensed are called as magnetic pole
N. Akdoğan
1. General Information About Magnetism
Magnetic poles
the forces of attraction and repulsion between poles
was discovered independently
in 1750 by John Michell (1724–1793) and in 1785 by Charles
Coulomb (1736–1806).
N. Akdoğan
1. General Information About Magnetism
Magnetic poles
the forces of attraction and repulsion between poles
was discovered independently
in 1750 by John Michell (1724–1793) and in 1785 by Charles
Coulomb (1736–1806).
the force F between two poles is proportional to the product of their pole strengths
p1 and p2 and inversely proportional to the square of the distance d between them
p1 p2
cgs (1)
F= 2
d
1 p1 p2
SI
F=
2
4πµ0 d
Dyne
Newton
1newton=105dyne
Permeability of free space (permeability of vacuum)=4π×10-7 henrys per meter (Hm-1)
N. Akdoğan
1. General Information About Magnetism
Earth’s magnetic poles and compass
(Southern polarity)
(Northern polarity)
N. Akdoğan
1. General Information About Magnetism
Magnetic field
Generally a region of space in which a magnetic pole experiences an applied force
is called a magnetic field.
A magnetic field can be produced by other magnetic poles or by electric currents.
A magnetic pole creates a magnetic field around it, and it is this field which produces a
force on a second pole nearby.
 p1 
F =  2  p2 = Hp2
d 
N. Akdoğan
1. General Information About Magnetism
cgs
(2)
Magnetic field
p
H= 2
d
cgs
(3)
The unit of magnetic field is oersted (Oe) in cgs units
1 Oe=1 line of force/cm2
In the SI system, the field from a pole is:
H=
p
4πµ0 d
2
SI
The unit of magnetic field in the SI system is ampere per meter (Am-1).
1 Am-1=4π×10-3 Oe
N. Akdoğan
1. General Information About Magnetism
Magnetic field
A magnetic field can also be produced by using a solenoid (Greek word for a tube or pipe).
A uniform magnetic field exists inside a long, thin solenoid carrying an electric current.
When a current of i flows in the winding of a solenoid having
n turns per meter, the intensity of the field H at the center of the solenoid is defined by:
ni
H=
l
Am-1 (SI)
4πni
Oe (cgs)
H=
10l
N. Akdoğan
1. General Information About Magnetism
1 Am-1=4π×10-3 Oe
(4)
Magnetic field
 The magnetic field of the Earth is about 0.35 Oe
 The magnetic field of a bar magnet near one end is about 5000 Oe
 The magnetic field of a powerful electromagnet is about 20000 Oe (2 Tesla)
 The magnetic field of a superconducting magnet can be 90000 Oe (9 Tesla) or more.
Relation between oersted (Oe), gauss (G) and tesla (T)
1 Oe=1 G (in vacuum)
1 T=104 G
Tesla (T) is used in SI.
N. Akdoğan
1. General Information About Magnetism
Magnetic moment
l
p
F=pH
θ
F=pH
H
-p
Consider a magnet with poles of strength p and lenght l is placed at an angle θ to a
uniform field H. Then a torque acts on the magnet, tending to turn it parallel to the field.
The moment of this torque is:
pHl/2sinθ+pHl/2sinθ=pHlsinθ
When H=1 Oe and θ=90°, the moment is given by
µ = pl
N. Akdoğan
1. General Information About Magnetism
(5)
Magnetic moment
l
p
F=pH
θ
F=pH
H
-p
If no frictional forces act on the magnet, the work done by the torque is
reversible, giving rise to a potential energy:
E p = − plH cos θ = − µH cos θ
E p = −µ ⋅ H
N. Akdoğan
(6)
1. General Information About Magnetism
Magnetic moment
µ = pl
(5)
E p = −µ ⋅ H
(6)
weber meter (Wb m) in SI
µ: erg/Oe or emu in cgs
Because the energy Ep is in ergs, the unit of magnetic moment µ is erg/oersted.
This quantity is the electromagnetic unit of magnetic moment, generally but unofficially
called simply the emu.
N. Akdoğan
1. General Information About Magnetism
Magnetic moment
A magnetic moment can also be produced by a closed loop carrying an electric current.
i
µ
A
The magnetic moment produced by a current i which flows in a closed
circuit or loop enclosing an area A is defined as
µ = iA
(7)
In SI units, magnetic moment is measured in A m2 .
N. Akdoğan
1. General Information About Magnetism
Magnetic dipole
A magnetic dipole is defined as either the magnetic moment, µ, of a bar magnet in
the limit of small length but finite moment, or the magnetic moment µ of a current
loop in the limit of small area but finite moment.
Field lines around a magnetic dipole.
N. Akdoğan
1. General Information About Magnetism
Magnetization
The magnetization is defined to be the magnetic moment per unit volume,
µ
M=
ν
emu/cm3
(8)
It is sometimes convenient to refer the value of magnetization to unit mass rather than
unit volume. The mass of a small sample can be measured more accurately than its
volume, and the mass is independent of temperature whereas the volume changes with
temperature due to thermal expansion. The specific magnetization is defined as
µ
µ M
=
σ= =
m ρν
ρ
emu/g
(9)
When dealing with small volumes like the unit cell, the magnetic moment is often given in units
called Bohr magnetons, µB, where 1 µB =9.27×10-21 erg/Oe (or emu)
N. Akdoğan
1. General Information About Magnetism
Magnetic flux density
When a magnetic field, H, is applied to a material, the response of the material is
called its magnetic flux density or magnetic induction, B.
H
4 πM
B = H + 4πM
B
cgs (10)
B: G, H: Oe, 4πM: G
When M=0 (in free space or in air) and B=H, gauss is also used for H.
B = µ0 ( H + M )
N. Akdoğan
1. General Information About Magnetism
SI
Magnetic susceptibility
The magnetic properties of a material are characterized not only by the magnitude
and sign of M but also by the way in which M varies with H. The ratio of these two
quantities is called the susceptibility χ.
M
χν =
H
emu
3
Oe ⋅ cm
(11)
Sometimes called as volume susceptiblity (χv)
χν
χm =
ρ
emu
Oe ⋅ g
(12)
The susceptibility indicates how responsive a material is to an applied magnetic field.
N. Akdoğan
1. General Information About Magnetism
Magnetic permeability
The ratio of B to H is called the permeability µ
B
µp =
H
Using
B = H + 4πM
G
Oe
(12)
we get the relationship between permeability and susceptibility:
µ p = 1+ 4πχ
(13)
The permeability indicates how permeable the material is to the magnetic field.
N. Akdoğan
1. General Information About Magnetism
Types of magnetism
Diamagnetism, paramagnetism, ferromagnetism, antiferromagnetism, ferrimagnetism
N. Akdoğan
1. General Information About Magnetism
Types of magnetism
M versus H (or B) graphs are called magnetization curves, and are characteristic
of the type of material.
Homework: How can we measure magnetization (magnetic moment)?
N. Akdoğan
1. General Information About Magnetism