Magnetic Materials

Gebze Institute of TechnologyDepartment of Physics

Nanomagnetism and Spintronic Research Center (NASAM)

Numan Akdoğan

akdogan@gyte.edu.tr

1. General Information About Magnetism

Magnetic Materials

ReferencesSoshin Chikazumi, Physics of FerromagnetismB. D. Cullity, C. D. Graham. Introduction to Magnetic MaterialsNicola Spaldin, Magnetic MaterialsCharles Kittel, Introduction to Solid State Physics

1. General Information About Magnetism

Why magnetism is important?

Applications of magnetic materials:

• Read heads for magnetic hard disk drives

From Agnes Barthelemy, Uni. Paris-Süd

• 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

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

N. Akdoğan 1. General Information About Magnetism

the forces of attraction and repulsion between poles was discovered independently

in 1750 by John Michell (1724–1793) and in 1785 by CharlesCoulomb (1736–1806).

Magnetic poles

the forces of attraction and repulsion between poles was discovered independently

in 1750 by John Michell (1724–1793) and in 1785 by CharlesCoulomb (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

221

dppF =

221

041

dppF

πµ=

Dyne

Newton

1newton=105dyne

Permeability of free space (permeability of vacuum)=4π×10-7 henrys per meter (Hm-1)

cgs (1)

SI

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

2221 Hpp

dpF =

= cgs (2)

A magnetic pole creates a magnetic field around it, and it is this field which produces aforce on a second pole nearby.

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.

N. Akdoğan 1. General Information About Magnetism

Magnetic field

2dpH = cgs (3)

The unit of magnetic field is oersted (Oe) in cgs units

In the SI system, the field from a pole is:

204 d

pHπµ

= SI

The unit of magnetic field in the SI system is ampere per meter (Am-1).

1 Oe=1 line of force/cm2

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:

lniH = Am-1 (SI) 1 Am-1=4π×10-3 Oe

lniH

104π

= Oe (cgs) (4)

N. Akdoğan 1. General Information About Magnetism

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 T=104 G

1 Oe=1 G (in vacuum)

Tesla (T) is used in SI.

N. Akdoğan 1. General Information About Magnetism

Magnetic moment

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:

Hθp

-p

F=pH

F=pH

pHl/2sinθ+pHl/2sinθ=pHlsinθ

l

When H=1 Oe and θ=90°, the moment is given by

pl=µ (5)

N. Akdoğan 1. General Information About Magnetism

Magnetic moment

Hθp

-p

F=pH

F=pH

l

If no frictional forces act on the magnet, the work done by the torque is reversible, giving rise to a potential energy:

θµθ coscos HplHEp −=−=

(6)HEp ⋅−= µ

N. Akdoğan 1. General Information About Magnetism

Magnetic moment

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.

pl=µ (5)

(6)HEp ⋅−= µ

weber meter (Wb m) in SI

µ: erg/Oe or emu in cgs

N. Akdoğan 1. General Information About Magnetism

Magnetic moment

A magnetic moment can also be produced by a closed loop carrying an electric current.

iA=µ (7)

The magnetic moment produced by a current i which flows in a closedcircuit or loop enclosing an area A is defined as

A

µi

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 inthe 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

νµ

=M

The magnetization is defined to be the magnetic moment per unit volume,

(8)emu/cm3

It is sometimes convenient to refer the value of magnetization to unit mass rather thanunit 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 withtemperature due to thermal expansion. The specific magnetization is defined as

ρρνµµσ M

m=== emu/g (9)

When dealing with small volumes like the unit cell, the magnetic moment is often given in unitscalled 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 iscalled its magnetic flux density or magnetic induction, B.

B

4πMH

MHB π4+= (10)

B: G, H: Oe, 4πM: GWhen M=0 (in free space or in air) and B=H, gauss is also used for H.

cgs

)(0 MHB += µ SI

N. Akdoğan 1. General Information About Magnetism

Magnetic susceptibility

The magnetic properties of a material are characterized not only by the magnitudeand 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.

HM

=νχ 3cmOeemu⋅

(11)

Sometimes called as volume susceptiblity (χv)

ρχχ ν=m gOe

emu⋅

(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

HB

p =µOeG

(12)

Using

(13)

The permeability indicates how permeable the material is to the magnetic field.

MHB π4+= we get the relationship between permeability and susceptibility:

πχµ 41+=p

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 characteristicof the type of material.

Homework: How can we measure magnetization (magnetic moment)?

N. Akdoğan 1. General Information About Magnetism