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5006 Magnetism and Magnetic Materials

Chapter 1: Introduction

1. A Brief History of Magnetism

2. Magnetism and Hysteresis

3. Magnet Applications

4. Magnetism, Physics and Technology

Comments and corrections please: jcoey@tcd.ie

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Some introductory texts:

• David Jiles Introduction to Magnetism and Magnetic Materials, Chapman and Hall 1991; 1997A detailed introduction, written in a question and answer format.

• Stephen Blundell Magnetism in Condensed Matter, Oxford 2001A new book providing a good treatment of the basics

History:

• A. Kloss Geschichte des Magnetismus, VDE, Berlin 1994

Light reading:

• J. D. Livingstone. Driving Force, Harvard University Press 1996.

• Alberto Guimaraes, From Lodestone to Supermagnets, Wiley 2005

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1. A Brief History of Magnetism

-1000 0 1500 1820 1900 1935 1960 1995

Ancien

t

Early

scien

tific

Electro

mag

netic

Under

stand

ing

High

-freq

uenc

y

Applic

ations

Spin

electro

nics

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High-densityrecording, MRAM?

MultilayersThin film devicesConsumersFert, Parkin …. 1995 to ??Spin electronics

Consumerelectronics

Sm-Co, Nd-Fe-BNew materials,miniaturization

ConsumersGorter, Sagawa,Croat

1960 to 1995Applications

Radar, televisionFerritesMicrowaves, epr,fmr, nmr

MilitaryBloch,, Pound,Purcell

1935 to 1960High-frequency

[Alnico]Spin, Exchangeinteractions

AcademyWeiss, Bohr,Dirac,Heisenberg,Pauli, Landau

1900 to 1935Understanding

Motorsgenerators,telegraph,wireless, magneticrecording

Electrical steelE-M induction,Maxwells =ns

Industry/infra-structure

Oersted,Ampere, Faraday,Maxwell

1820 to 1900Electromagnetic

Dip circle, Horse-shoe magnet

Iron, lodestoneEarth’s fieldNavyGilbert,DescartesD.Bernouilli

1500 to 1820Early scientific

South pointer,Compass

Iron, lodestoneForce field,induced magntism,TRM

StateShen Kua, PetrusPeregrinus

-1000 to 1500Ancient

ApplicationsMaterialsAchievementsDriverNamesDateAge

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The Ancient Age

-1000 to 1500

Applications

South-Pointer

Compass

Driver

The State

Scientific achievements

Force field

Induced magnetism

Thermoremanence

Key names

Shen Kua

Petrus Peregrinus

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1820

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The Electromagnetic Age

1820 - 1900

Applications

Motors, Generators

Telegraph, Wireless

Magnetic recording

Driver

Industry

(Infrastructure)

Scientific Achievements

Electromagnetic Induction

Maxwells Equations

Key names

Oersted, Ampere

Faraday, Maxwell

Hertz

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Maxwell’s equations

! . B = 0"0! . E = #

(1/µ0 )! $ B = j + "0%E/%t ! $ E = -%B/%t

Written in terms of two fields B (kg C-1 s-1 ) and E (V m-1), they are validin free space.They relate these fields to the charge density # (C m-3) and the current

density j (A m-2) at a point.

c = ("0 µ0)1/2 c = 2.998 108 m s-1 c = &'

Also, the force on a moving charge q, velocity v

F = q(E + v $ B)

From a long view of the history ofmankind, there can be little doubt thatthe most significant event of the 19thcentury will be judged as Maxwell’sdiscovery of the laws of electrodynamics.Richard Feynmann

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The Age of Understanding

1900 - 1935

Applications

Driver

Academy

Scientific Achievements

Mean Field Theory, Spin,

Exchange Interactions

Key Players

Weiss, Bohr

Heisenberg

Dirac, Pauli

Landau

H = -2JSiSj

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The m-J paradigm:

m represents the

magnetic moment,mainly localized onthe atoms

J represents theexchange couplingof electron spins.

At this point it seems that the whole of chemistry and much of physics is understood in principle. The problem isthat the equations are much to difficult to solve….. P. A. M. Dirac

1930 Solvay Conference

Dirac Heisenberg

The 1930 Solvay conference consecrated our physical understand-ing ofmagnetism in terms of quantum mechanics (exchange) and relativity (spin)

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The Age of Applications1960 - 1995

Key Players

Gorter,

Sagawa,

Croat

Driver

Industry

(Consumer)

Scientific Achievements

New materials

Miniaturisation of Magnetic Circuits

Applications

Consumer

Electronics

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How many magnets do you own?

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The Age of Spin Electronics1995 - ?

Albert Fert

Peter Gruneberg

Stuart Parkin

Driver

Industry

(Consumer)

Scientific Achievements

Thin film devices

Applications

High-density

recording

MRAM ?

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The hysteresis loop shows the irreversible, nonlinear response of a ferromagnet to amagnetic field . It reflects the arrangement of the magnetization in ferromagnetic domains.The magnet cannot be in thermodynamic equilibrium anywhere around the open part ofthe curve! M and H have the same units (A m-1).

coercivity

spontaneous magnetization

remanence

major loop

virgin curveinitial susceptibility

2. Magnetism and Hysteresis 2.1 The hysteresis loop

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Soft and hard magnets.

The area of the hysteresis loop represents the energy loss per cycle. For efficient softmagnetic materials, this needs to be as small as possible.

M (MA m-1)

-1 0 1 H (MA m-1)

1

-1

M (MA m-1)

-50 0 50 H (A m-1)

1

-1

For a useful hard magnet.Hc > Mr/2

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2.2 Curie temperature

M(T)/M(0)

Ferromagnetic materials possess a spontaneous magnetization M, whichfalls to zero at the Curie point TC - a phase transition.

293

631

1390

1043

TC (K)

Gd

Ni

Co

Fe

2.0

0.5

1.3

1.8

M(0) MA m-1

A specific heat anomaly appears at TC

(Smag = )(C/T)dT ! R ln 2

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2.3 Coercivity

The progress in magnetism in the20th century which has spawned somany magnet applications has beendue to mastery of coercivity.

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Daniel Bernouilli1743

S N

Gowind Knight 1760

Shen Kwa 1060

N < 0.1

The shape barrier.

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2.4 Anisotropy

The direction of magnetization M(r) in a macoscopic ferromagneticdomain lies along one or other easy axes.

Ea = K1sin2*

M

*

1 kJm-3 < K1 < 10 MJm-3

10 mK < K1 < 10 K

Easy axis

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2.5 Susceptibility

Above TC the ferromagnetic material becomes paramagnetic. The susceptibility + is defined insmall fields as

,+ = M/H.

Note that + has no units. It is known as the relative or dimensionless susceptibility. It is anumber which is characteristic of a particular material.

At temperatures above TC, the susceptibility often follows a Curie-Weiss Law

,+ = C/(T-Tc).

The Curie constant is of order 1 K.

Solids that do not order magnetically are either paramagnetic or diamagnetic. Theirsusceptibility is small and positive or negative, repectively. (magnitude 10-3 - 10-7).

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2.6 Other Types of Magnetic Order

OrderedT < TC

DisorderedT > TC

M " 0 M = 0

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2.7 Magnetic elements

Eight elements (blue) and many compounds are ferromagnetic. They possess aspontaneous magnetization - eleven elements (purple) are antiferromagnetic

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Ni-Fe/Fe-Co (heads)

Fe-Si

Fe-Si (oriented)

Ni-Fe/Fe-Co

Amorphous

Others

Others

Alnico

Sm-CoNd-Fe-B

Hard ferrite

Co- ! Fe 2 O 3

(tapes, floppy discs)

CrO2 (tapes)

Iron (tapes)

Co-Cr (hard discs)

Soft ferrite

Others

Iron

Soft Magnets

HardMagnets

MagneticRecording

Magnet applications; A 30 B# market

3. Magnet Applications

3.1 The world market

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Global domestic product 2000

Continent GDP Population GDP/person

(T$) (millions)($)

Asia (incl. Australia) 14.6 3716 3930

Europe (incl. Russia) 10.9 728 14970

North America 10.5 316 33200

South & Cent America 3.4 525 6100

Africa 0.2 819 1730

39.6 6104 6488

Average production per person (approximate):

30 g hard ferrite, 2 g rare earth magnet, 1 m2 flexible medium, 1/10 hard disc, 1/10 read/write head, 0.25 m2

electrical sheet steel, 30 g soft ferrite, 0.1 g metallic glass.

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Abundances of magnetic ions in theEarth’s crust

Price scales roughly inversely with abundance.

O

Si

Al

Fe

Mg

Ca

K

Na

H

Others

O2-Si4+

Al3+

Fe

Iron (Fe2+/Fe3+) is most abundantmagnetic element. It is 40 times asabundant as all other magneticelements together.

Composition in atomic % of theEarth’s crust. Iron (Fe2+/Fe3+) is thefourth most abundant element.

Cr Mn

3.2 Economics

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A useful magnetic material needs tobe able to operate from -50 C to 120C.

The Curie temperature needs to be >500 K

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Core losses in electrical machinery

Global energy production 18 1012 kW hr

Efficiency of transformers > 99%

yet losses cost > 10 B$ per year.

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A permanent magnet is useful because of the stray field it produces.

A useful figure of merit is the maximum energy product (BH)max. This is twice themaximum energy in the stray field produced by unit volume of magnet.

H (A m-1)

B (

T)

Working point

(BH)maz

Energy Product of Permanent Magnets

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New icon for permanent magnets! -

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Magnetic recording density

40 Mb

160 Gb

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3. Magnetism, Physics and Technology

30,000 people worldwide

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Typical values of B Human brain 1 fT

Magnetar 1012 T

Superconducting magnet 10 T

Electromagnet 1 T

Helmholtz coils 0.01 Am-

Earth 50 µT