1. CHAPTER 18: MAGNETIC PROPERTIES
ISSUES TO ADDRESS...
• How do we measure magnetic properties?
• What are the atomic reasons for magnetism?
• How are magnetic materials classified?
• Materials design for magnetic storage. 1

2. 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
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3. Chapter 18 – Magnetic Properties
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
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4. APPLIED MAGNETIC FIELD
• Created by current through a coil:
• Relation for the applied magnetic field, H:
current
applied magnetic field
units = (ampere-turns/m)
Units of H: A/m 2

5. RESPONSE TO A MAGNETIC FIELD
• Magnetic induction results in the material
B = µH
permeability
• Magnetic susceptibility, c (dimensionless)
c measures the
material response
relative to a vacuum.
χ = (µ - µ0)/ µ0 3

6. 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
m is the permeability, a property of the medium. In vacuum
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mo is the permeability of a vacuum = 4p x 10-7 H/m
Bo is the flux density within a vacuum

7. 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
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H [=] Ampere-turn-1-m-1, or A/m

8. 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
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9. Magnetic field vectors
In the presence of an external field (H) the magnetic moments in a material tend to align – the term moM is a measure of this
The magnetization can also be expressed as
The quantity cm is called the magnetic susceptibility, and is related to the permeability via
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10. Analogous quantities – magnetic v electrical properties
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12. 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
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13. Origin of magnetic moments
Most fundamental magnetic moment is the Bohr magneton mB; the value of this is 9.27 x A-m2
For each electron in an atom the spin magnetic moment is +/-mB
The orbital magnetic moment contribution is mlmB, 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…)
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14. MAGNETIC SUSCEPTIBILITY
• Measures the response of electrons to a magnetic
field.
• Electrons produce magnetic moments:
Adapted from Fig. 20.4, Callister 6e.
• Net magnetic moment:
--sum of moments from all electrons.
• Three types of response... 4

15. 3 TYPES OF MAGNETISM 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. 5

16. MAGNETIC MOMENTS FOR 3 TYPES
Adapted from Fig. 20.5(a), Callister 6e.
Adapted from Fig. 20.5(b), Callister 6e.
Adapted from Fig. 20.7, Callister 6e. 6

17. FERRO- & FERRI-MAGNETIC MATERIALS
• As the applied field (H) increases...
--the magnetic moment aligns with H.
Adapted from Fig , Callister 6e. (Fig adapted from O.H. Wyatt and D. Dew-Hughes, Metals, Ceramics, and Polymers, Cambridge University Press, 1974.) 7

18. 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
mr < 1, and cm is negative
In other words, the induced field B in a diamagnetic material is less than that in a vacuum (cm ~ -10-5)
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χ = (µ-µ0)/µ0=
= µr -1

19. 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)
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20. Paramagnetism (cont) Small but positive mr cm ~ 10-5 – 10-2
Both dia- and para-magnetic materials are considered to be nonmagnetic (why?)
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22. 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 cm values as large as 106
So, H << M (i.e. you have a large induced magnetization) and
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23. 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
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24. 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
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25. Chapter 18 – Magnetic Properties
Problem 18.1 – what is the (a) saturation magnetization and (b) saturation flux density for Ni (r = 8.90 g/cm3)
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26. Chapter 18 – Magnetic Properties
Problem 18.1 – what is the (a) saturation magnetization and (b) saturation flux density for Ni (r = 8.90 g/cm3)
(a)
What do you need? N!
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27. Chapter 18 – Magnetic Properties
Problem 18.1 – what is the (a) saturation magnetization and (b) saturation flux density for Ni (r = 8.90 g/cm3)
(b)
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28. 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
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29. 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 a 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
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30. Ferrimagnetism (this is not a typo!)
Fe3O4  Fe+2Fe+32O4
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
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31. 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!
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32. 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
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35. 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
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36. Chapter 18 – Magnetic Properties
Example 18.2 – saturation magnetization of Fe3O4
8 Fe+2, 16 Fe+3 per unit cell & a = nm
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37. Chapter 18 – Magnetic Properties
Example 18.2 – saturation magnetization of Fe3O4
8 Fe+2, 16 Fe+3 per unit cell & a = nm
So, how to solve this?
I would do it on a unit cell basis
What is nB ?
32!
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38. Chapter 18 – Magnetic Properties
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?)
For antiferromagnets – Neel temperature
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39. 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
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40. Adjacent domains

41. 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
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42. 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?
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43. 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
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44. Magnetic anisotropy – read 18.8
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45. 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
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46. 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
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47. 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?)
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48. 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 s = 1/r *)
To do that increase the resistivity
Can achieve that by alloying (solid solutions)
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50. 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?
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51. 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
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52. 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
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54. 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
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55. 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!
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56. 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)
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57. 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
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58. Magnetic storage Particulate
Two principal forms of media – particulate and thin film
Particulate
Needlelike particles, typically of g-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
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59. 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 nm; size/shape uniformity is important
Have much higher (~100x) storage densities than powders
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60. 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
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61. PERMANENT MAGNETS • Process: • Hard vs Soft Magnets large coercivity
Adapted from Fig , Callister 6e.
• Hard vs Soft Magnets
Adapted from Fig , Callister 6e. (Fig from K.M. Ralls, T.H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering, John Wiley and Sons, Inc., 1976.)
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)
small coercivity--good for elec. motors
(e.g., commercial iron Fe) 8

62. MAGNETIC STORAGE • Information is stored by magnetizing material.
• Head can...
--apply magnetic field H &
align domains (i.e.,
magnetize the medium).
--detect a change in the
magnetization of the
medium.
recording head
recording medium
Simulation of hard drive courtesy Martin Chen.
Reprinted with permission
from International Business Machines Corporation.
Adapted from Fig , Callister 6e. (Fig from J.U. Lemke, MRS Bulletin, Vol. XV, No. 3, p. 31, 1990.)
• Two media types:
--Particulate: needle-shaped
g-Fe2O3. +/- mag. moment
along axis. (tape, floppy)
--Thin film: CoPtCr or CoCrTa
alloy. Domains are ~ 10-30nm!
(hard drive)
Adapted from Fig (a), Callister 6e. (Fig (a) from M.R. Kim, S. Guruswamy, and K.E. Johnson, J. Appl. Phys., Vol. 74 (7), p. 4646, )
Adapted from Fig , Callister 6e. (Fig courtesy P. Rayner and N.L. Head, IBM Corporation.) 9

63. SUMMARY • A magnetic field can be produced by: • Magnetic induction:
--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 g-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 to 10

64. ANNOUNCEMENTS Reading: Chapter 18 (sent by e-mail)
HW # 11, Due Monday April 23
Problems 18.1; 18.4; 18.7; 18.12; 18.18; 18.19;
18.25; 18.28; 18.D1