ISSUES TO ADDRESS...

• How do we measure magnetic properties?

1

• What are the atomic reasons for magnetism?

• Materials design for magnetic storage.

• How are magnetic materials classified?

CHAPTER 18:MAGNETIC PROPERTIES

• Motivation– Why would you care about magnetic properties?– The following devices utilize magnetic materials or materials

whose properties can be moderated by applied fields:• TVs

• Power generators/transformers

• Computers

• Phones

• Radio

• Audio components

• Basic Concepts– By moving electrically charged particles

magnetic forces are generated – these magnetic forces are often thought of/described as fields (see picture)

– Magnetic dipoles – exist in magnetic materials, analogous to electric dipoles. Can be thought of as tiny bar magnets

– Magnetic dipoles are induced in magnetic fields in a manner similar to electrical dipoles in electric fields

– Field exerts a torque that drives alignment of the dipoles

Chapter 18 – Magnetic Properties

2

• Created by current through a coil:

Applied magnetic field H

current I

N turns total

L = length of each turn

• Relation for the applied magnetic field, H:

H

NIL

applied magnetic fieldunits = (ampere-turns/m)

current

APPLIED MAGNETIC FIELD

Units of H: A/m

3

• Magnetic induction results in the material

current I

B = Magnetic Induction (tesla) inside the material

• Magnetic susceptibility, (dimensionless)

H

Bvacuum = 0

> 0

< 0

measures the material responserelative to a vacuum.

RESPONSE TO A MAGNETIC FIELD

B = µH

χ = (µ - µ0)/ µ0

permeability

• Magnetic field vectors– The magnetic induction or magnetic flux density (B)

is the magnitude of the internal field strength within a substance subjected to a field of strength H

– The magnetic induction B has units of Tesla (T), (Webers/m2, Wb/m)

– Note that H and B are vectors; Can relate the two through

)/()/(][, mHmAWbHB

is the permeability, a property of the medium. In vacuum

HB oo is the permeability of a vacuum = 4 x 10-7 H/mBo is the flux density within a vacuum

• Magnetic field vectors– Externally applied magnetic fields (or magnetic

field strength) is denoted as H– Often generate field with a cylindrical coil. If the

coils has N turns, is of length l and has a current I running through it then

l

NIH

H [=] Ampere-turn-1-m-1, or A/m

• Magnetic field vectors– Relative permeability – exactly what it

sounds like

– The relative permeability is a measure to which a material can be magnetized, or how easily a B field can be induced by an external H field

– Another field quantity, the magnetization (M) of the solid is given as

o

o

oo

HBM

MHB

or

• Magnetic field vectors– In the presence of an external field (H) the magnetic

moments in a material tend to align – the term oM is a measure of this

– The magnetization can also be expressed as

– The quantity m is called the magnetic susceptibility, and is related to the permeability via

1 rm

HM m

• Analogous quantities – magnetic v electrical properties

PM

HDB

• Origin of magnetic moments – key idea is that each electron has magnetic moments that originate from two sources– Orbital motion around the nucleus: electron can be thought of

as a small current loop, generating a very small magnetic field– Spin: electron spins around an axis (remember spin up and

spin down?), generating a magnetic moment

• Origin of magnetic moments– Most fundamental magnetic moment is the Bohr magneton B;

the value of this is 9.27 x 10-24 A-m2

– For each electron in an atom the spin magnetic moment is +/-B

– The orbital magnetic moment contribution is mlB, where ml is the magnetic quantum number

• Many of these magnetic moments can cancel one another– Substances where all the electrons are paired cannot be

permanently magnetized (He, Ne, Ar…)

4

• Measures the response of electrons to a magnetic field.• Electrons produce magnetic moments:

magnetic moments

electron

nucleus

electron

spin

• Net magnetic moment: --sum of moments from all electrons.• Three types of response...

Adapted from Fig. 20.4, Callister 6e.

MAGNETIC SUSCEPTIBILITY

5

B (1)oH permeability of a vacuum:(1.26 x 10-6 Henries/m)

Plot adapted from Fig. 20.6, Callister 6e. Values and materials from Table 20.2 and discussion in Section 20.4, Callister 6e.

3 TYPES OF MAGNETISM

ferromagnetic e.g., Fe3O4, NiFe2O4 ferrimagnetic e.g., ferrite(), Co, Ni, Gd

(3)

Magnetic induction (B--tesla)

Strength of applied magnetic field (H) (ampere-turns/m)

diamagnetic ( ~ -10-5)

vacuum ( = 0) (1)

(2)

e.g., Al2O3, Cu, Au, Si, Ag, Zn

e.g., Al, Cr, Mo, Na, Ti, Zr

( as large as 106 !)

6

No Applied Magnetic Field (H = 0)

Applied Magnetic Field (H)

(1) diamagnetic

non

e

op

posi

ng

(3) ferromagnetic

alig

ned

alig

ned

(2) paramagnetic

ran

dom

alig

ned

ferrimagnetic

Adapted from Fig. 20.5(a), Callister 6e.

Adapted from Fig. 20.5(b), Callister 6e.

Adapted from Fig. 20.7, Callister 6e.

MAGNETIC MOMENTS FOR 3 TYPES

7

• As the applied field (H) increases... --the magnetic moment aligns with H.

Applied Magnetic Field (H)

H

H

H

H

H

H = 0

Mag

ne

tic

ind

uct

ion

(B

)

0

Bsat

• “Domains” with aligned magnetic moment grow at expense of poorly aligned ones!

Adapted from Fig. 20.13, Callister 6e. (Fig. 20.13 adapted from O.H. Wyatt and D. Dew-Hughes, Metals, Ceramics, and Polymers, Cambridge University Press, 1974.)

FERRO- & FERRI-MAGNETIC MATERIALS

• Diamagnetism and paramagnetism– Diamagnetism – very weak form of magnetism

• These are materials where there is no permanent magnetic dipole moment

• Persists in a material only while an external (H) field is applied (i.e. it is not permanent)

• Due to a change in the orbital electrons motion due to the applied field

– It is very small in a direction opposite to that of the applied field• r < 1, and m is negative

• In other words, the induced field B in a diamagnetic material is less than that in a vacuum (m ~ -10-5)

χ = (µ-µ0)/µ0=

= µr -1

• Paramagnetism– In some materials atoms can possess a permanent magnetic

dipole moment due to incomplete cancellation of electron spin and/or orbital magnetic moments

– Without external field, the orientation of these moments is random

– In the presence of an external field they can align – this is called paramagnetism (acted on individually by the field)

• Paramagnetism (cont)– Small but positive r

– m ~ 10-5 – 10-2

Both dia- and para-magnetic materials are considered to be nonmagnetic (why?)

• Ferromagnetism– Things are much different here!– Materials, typically metallic, that

• Possess a permanent magnetic moment in the absence of an external field

• Manifest a very large and permanent magnetization

• Transition metals – Fe, Co, Ni, some rare earth metals

• Can have m values as large as 106

• So, H << M (i.e. you have a large induced magnetization) and

MB o

MHB oo

HM m

• Ferromagnetism– The permanent magnetic dipole moments result from atomic

magnetic moments due to electron spin (i.e. unpaired electrons, consequence of electronic structure)

– Another difference: coupling interactions causes magnetic moments of adjacent atoms to align even in the absence of an external field

– Regions this occurs over are called domains or spin domains

• Ferromagnetism– Saturation magnetization Ms, or the maximum possible

magnetization – magnetization when all the magnetic dipoles are aligned with the field

– Equals the product of the net magnetic moment of each atom times the number of atoms

– Fe, Co, Ni – 2.22, 1.72, and 0.6 Bohr magnetons per atom

• Problem 18.1 – what is the (a) saturation magnetization and (b) saturation flux density for Ni ( = 8.90 g/cm3)

Chapter 18 – Magnetic Properties

• Problem 18.1 – what is the (a) saturation magnetization and (b) saturation flux density for Ni ( = 8.90 g/cm3)

Chapter 18 – Magnetic Properties

(a) NM Bs 6.0 What do you need? N!

328

2333

/1013.9

/71.58

/10022.6100/90.8

matomsN

molg

molatomsmcmcmg

A

NN

Ni

A

mAM

m

atoms

onBohrmagnet

mA

atom

onBohrmagnetM

s

s

/101.5

1013.91027.96.0

5

3

28224

• Problem 18.1 – what is the (a) saturation magnetization and (b) saturation flux density for Ni ( = 8.90 g/cm3)

Chapter 18 – Magnetic Properties

(b)

TB

m

A

m

HB

MB

s

s

sos

64.0

101.5104 57

• Antiferromagnetism– The phenomenon of magnetic coupling between adjacent

atoms/ions occurs in materials besides ferromagnets– Another class – antiferromagnetic materials

• In these materials the coupling results in anti-parallel alignment of the spins (e.g. MnO)

• The magnetic moments cancel – no net magnetic moment

• Ferrimagnetism (this is not a typo!)– Ferrimagnetism – term used to describe ceramics that exhibit

permanent magnetization• The macroscopic magnetic properties of ferro- and ferri- magnetic

materials are similar – the source of the net magnetic moments is (somewhat) different

• Example compounds – ferrites (*this is not the phase of iron)– MFe2O4 – M can be nearly anything, but typically divalent (the two iron

atoms shown are Fe+3)

– Example I will use – Fe3O4 (magnetite, also called lodestone)

» Note that this is strictly Fe+2Fe+32O4

• Ferrimagnetism (this is not a typo!)– Fe3O4 Fe+2Fe+3

2O4

• Fe+2 : Fe+3 are in a 1:2 ratio; the net spin magnetic moments for Fe+2 , Fe+3 are 4 and 5 Bohr magnetons, respectively

• The ferrimagnetic moment arises from incomplete cancellation of the spin moments

– Ferrites have the inverse spinel crystal structure – structure can be thought of as generated by stacking of close-packed planes of O-2 anions

• Fe cations can go into either tetrahedral or octahedral positions

• Turns out ½ the trivalent ions are in the octahedral positions, half are in tetrahedral positions; divalent ions are all in octahedral positions

• Ferrimagnetism (this is not a typo!)– The key fact is the arrangement of the spin moments of the Fe

ions

• The spin moments of the Fe+3 centers are aligned antiparallel for the octahedral/ tetrahedral centers and thus cancel

• The spin moments of the Fe+2 centers, however, do not!

• Thus it is the Fe+2 centers that are responsible for the observed magnetic behavior!

• Remember MFe2O4 – thus M (if the structure stays the same) gives you the magnetic properties!

• Ferrimagnetism– So the M cation gives you a “handle” for tuning magnetic

properties (*remember* MFe2O4 has the inverse spinel structure)

– Usual “culprits” for M – Ni+2, Co+2, Mn+2, Cu+2

– Can also make “mixed” ferrites

• Ferrimagnetism– Read bottom of p 741 – as an aside there are other ceramics that display

ferrimagnetism– Note: the saturation magnetization of ferrimagnets is lower than

ferromagnets• However, ceramics are typically much better electrical insulators than metals

– For some magnetic applications (e.g. transformers) this is highly desirable

• Example 18.2 – saturation magnetization of Fe3O4

– 8 Fe+2, 16 Fe+3 per unit cell & a = 0.839 nm

Chapter 18 – Magnetic Properties

• Example 18.2 – saturation magnetization of Fe3O4

– 8 Fe+2, 16 Fe+3 per unit cell & a = 0.839 nm

Chapter 18 – Magnetic Properties

So, how to solve this? I would do it on a unit cell basis

volumecellcell/unit unit per magnetonsBohr ofnumber : '

'

N

NM Bs

c

B

V

nN '

mAM

cum

onBohrmagnetmAcuonsBohrmagnet

V

nM

s

c

BBs

/100.5

../10839.0

/1027.9../32

5

39

224

What is nB ? 32!

• Temperature dependency of magnetic properties– Very important for ferro-, antiferro- and ferri- magnetic materials– Why? Increasing the thermal energy of the material (i.e. raising T) will

tend to randomize the direction of magnetic moments that are aligned (i.e. destroy spin ordering)

– Decreases the saturation magnetization as T goes up– Quantified using the Curie temperature, Tc (for ferro- & ferri- magnets)– Above Tc, material becomes paramagnetic (why?)

Chapter 18 – Magnetic Properties

For antiferromagnets – Neel temperature

• Domains and hysteresis– Below the Curie temperature any ferro- or ferri- magnet is composed of

small-volume regions in which there is mutual alignment in the same direction of all the dipole moments

• These regions are called domains and are magnetized to their saturation M

• Adjacent domains are separated by domain walls• Typically see moments aligned in different

directions, the direction of magnetization typically changes gradually across the wall boundary (fig 18.12, next slide)

• Thus, for a polycrystalline material the magnitude of the M field for the entire solid is the vector sum of the magnetization of all domains, suitably weighted

Adjacent domains

• Domains and hysteresis– B is not proportional to H for ferro- and ferri-magnets . Consider figure

below:• Start w/initially unmagnetized material• Initially B increases slowly, then sharply

increases • Why? Movement of domain boundaries

(see cartoons)• Go from highly randomized to highly

oriented spin domains (big oriented, domains grow at the expense of small, non oriented domains)

• Levels off at saturation levels• Initial permeability is slope of plot in

limit where H 0

• Hysteresis– If you decrease H you do not retrace this curve – there is hysteresis

• Decrease/remove H, the B field lags

• Even at zero external field a B field remains – this is the remanance, or remanent flux density Br

• This behavior can be explained based on concept of domain walls (next slide)

• However, note something – what do I have to do in order to “demagnetize” this material?

• Hysteresis – mechanism: domains– Reverse field direction, the process by which the domain structure

changes is reversed– First the single domains rotate (due to reversal of field)– Next, domains aligned grow at the expense of those which are not

aligned with the H field– Some domain walls do not move as effectively as others due to

orientations (i.e. since H is reversed)

– This last point explains the lag of B with H– Even at zero applied filed some domains

are still oriented in the opposite direction (hence the remanent field Br)

– To get to zero B field an H field of some magnitude –Hc must be applied in a direction opposite to the initial field

Hc is called the coercivity

• Magnetic anisotropy – read 18.8

• Soft Magnetic Materials– Hysteresis loop (size/shape) has a physical meaning as well as a

practical implication– The area within the loop is the magnetic energy loss per unit

volume (for a given magnetization-demagnetization cycle)– This energy loss takes the form of heat – T goes up!

– Magnetic materials are categorized as “hard” or “soft” materials based on the characteristics of the hysteresis loop

• Soft Magnetic Materials– Soft magnetic materials are used in devices subjected to

alternating magnetic fields where the energy loss must be low (i.e. area in the hysteresis loop is small)

– Example – transformer cores– Want a thin, narrow hysteresis loop

• High initial permeability, low coercivity

• Such a material will reach its saturation magnetization with a low applied field, with minimal hysteresis energy loss

• Soft Magnetic Materials– While the saturation properties of a material are solely determined

by composition, the susceptibility and coercivity are highly structure dependent!

• Why? A low coercivity means the domain walls can move/respond easily to changes in the magnitude/direction of the applied field

• Defects tend to increase coercivity (why?)

• Soft Magnetic Materials– Another thing to consider – the electrical resistivity!– Why?

• Energy losses can also occur due to electrical currents induced in magnetic materials due to the field that varies in time and direction

– These are called eddy currents

• Want to minimize these! (* remember = 1/ *)– To do that increase the resistivity – Can achieve that by alloying (solid solutions)

• Soft Magnetic Materials– Finally, can also modulate the hysteresis properties of soft

magnetic materials by thermal treatments in the presence of a magnetic field

• What do you think this might do?

• Hard Magnetic Materials– Hard magnetic materials are used as permanent magnets – they

must have a high resistance to demagnetization– Hard magnets have a high remanance, coercivity, saturation flux

density, and energy loss, but a low initial permeability

• Two most important properties – coercivity and the “energy product”, which is (BH)max

• This value is representative of the energy needed to demagnetize a permanent magnet

• “Harder” magnets have larger (BH)max values

• Hard Magnetic Materials– Hard magnetic materials are classified as “conventional” or “high

energy”– Conventional materials – (BH)max between 2 – 80 kJ/m3

– Include ferromagnetic materials – magnet steels, cunife (Cu-Ni-Fe) alloys and hexagonal ferrites

• Hard Magnetic Materials– Hard steel magnets are normally alloyed w/W or Cr– Heat treat this – form tungsten carbide or chromium carbide

precipitates – effective at obstructing domain wall motion– Other alloys: heat treatment induces microphase separation

• Lead to small strongly magnetic domains dispersed in a nonmagnetic matrix

– High energy hard magnets• Exactly what they sound like

• Two main classes – SmCo5 (Samarium Co) and Nd2Fe14B (Neodymium Fe B)

• (bottom p. 753) – used in motors ; permanent magnets are superior to electromagnets (used in small hp units)

– Cordless drills, video recorders

• Magnetic storage– Magnetic materials are occupying a role of increasing importance

as information storage materials– Example: computers

• Primary storage (memory) – semiconductor elements• Secondary storage (hard drive) – magnetic materials

– Magnetic materials can store more information at a lower cost

– How does this work – magnetize domains in the material!

• Magnetic storage – Use what is called an inductive read-write head: (coil wound

around a hollow cylindrical magnetic material with a gap)– See picture : electrical signal in the coil generates a magnetic

field in the gap

• This field magnetizes small domains in the recording medium in the proximity of the gap

• Remove field – magnetization remains (signal is stored)

• Magnetic storage – How to retrieve information? – as recording medium passes by

the head coil gap a change in the magnetic field will induce a voltage

• This voltage can be amplified

• Magnetic storage – Two principal forms of media – particulate and thin film

• Particulate• Needlelike particles, typically of -Fe2O3 or

CrO2

• These are applied/bonded to a polymeric film (tapes) or to a metal/polymer disk

• Particles are aligned during manufacturing so that their long axis is parallel to the motion past the head

• Two states – magnetic moment along axis in one of two possible directions

• Adjacent domains with moments in the same direction – 0

• Adjacent domains with moments in different directions - 1

• Magnetic storage media – thin films

• Conceptually similar to powders – now you have a polycrystalline film

• One domain is equivalent to a particle• Materials of choice – CoPtCr or CoCrTa

alloys• Grain size between 10-30 nm; size/shape

uniformity is important

• Have much higher (~100x) storage densities than powders

• Magnetic storage media

• Few final comments:• Want hysteresis loops to be relatively large and

square• Why?• Saturation flux densities

• Particulate materials: 0.4 –0.6 T• Films: 0.6 – 1.2 T

• Coercivity values range of 1 – 2.5 x 105 A/m

large coercivity--good for perm magnets--add particles/voids to make domain walls hard to move (e.g., tungsten steel: Hc = 5900 amp-turn/m)

8

• Process:

• Hard vs Soft Magnets

Applied Magnetic Field (H)

4. Coercivity, Hc: Negative H needed to demagnitize!

1. initial (unmagnetized state)

2. apply H, cause alignment 3. remove H, alignment stays!

-> permanent magnet!

B

Applied Magnetic Field (H)

B

Har

d

Soft

Har

d

small coercivity--good for elec. motors(e.g., commercial iron 99.95 Fe)

Adapted from Fig. 20.14, Callister 6e.

Adapted from Fig. 20.16, Callister 6e. (Fig. 20.16 from K.M. Ralls, T.H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering, John Wiley and Sons, Inc., 1976.)

PERMANENT MAGNETS

9

• Information is stored by magnetizing material.

recording head

recording medium

Simulation of hard drive courtesy Martin Chen.Reprinted with permissionfrom International Business Machines Corporation.

• Head can... --apply magnetic field H & align domains (i.e., magnetize the medium). --detect a change in the magnetization of the medium.• Two media types:

--Particulate: needle-shaped -Fe2O3. +/- mag. moment along axis. (tape, floppy)

~2.5m

--Thin film: CoPtCr or CoCrTa alloy. Domains are ~ 10-30nm! (hard drive)

Adapted from Fig. 20.18, Callister 6e. (Fig. 20.18 from J.U. Lemke, MRS Bulletin, Vol. XV, No. 3, p. 31, 1990.)

Adapted from Fig. 20.19, Callister 6e. (Fig. 20.19 courtesy P. Rayner and N.L. Head, IBM Corporation.)

Adapted from Fig. 20.20(a), Callister 6e. (Fig. 20.20(a) from M.R. Kim, S. Guruswamy, and K.E. Johnson, J. Appl. Phys., Vol. 74 (7), p. 4646, 1993. )

~60nm

MAGNETIC STORAGE

10

• A magnetic field can be produced by: --putting a current through a coil.• Magnetic induction: --occurs when a material is subjected to a magnetic field. --is a change in magnetic moment from electrons. • Types of material response to a field are: --ferri- or ferro-magnetic (large magnetic induction) --paramagnetic (poor magnetic induction) --diamagnetic (opposing magnetic moment)• Hard magnets: large coercivity.• Soft magnets: small coercivity.• Magnetic storage media: --particulate -Fe2O3 in polymeric film (tape or floppy) --thin film CoPtCr or CoCrTa on glass disk (hard drive)

Note: For materials selection cases related to a magnet coil, see slides 20-11 to 20-15.

SUMMARY

Reading: Chapter 18 (sent by e-mail)

HW # 11, Due Monday April 23Problems 18.1; 18.4; 18.7; 18.12; 18.18; 18.19;18.25; 18.28; 18.D1

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