1. Chapter 18: Magnetic Properties
ISSUES TO ADDRESS...
• What are the important magnetic properties?
• How do we explain magnetic phenomena?
• How are magnetic materials classified?
• How does magnetic memory storage work?
• What is superconductivity and how do magnetic fields effect the behavior of superconductors?

2. Generation of a Magnetic Field - Vacuum
• Created by current through a coil: H I B0
N = total number of turns
 = length of each turn (m)
I = current (ampere)
H = applied magnetic field (ampere-turns/m)
B0 = magnetic flux density in a vacuum (tesla)
• Computation of the applied magnetic field, H:
B0 = 0H
permeability of a vacuum (1.257 x 10-6 Henry/m)
• Computation of the magnetic flux density in a vacuum, B0:

3. Generation of a Magnetic Field -- within a Solid Material
• A magnetic field is induced in the material B
B = Magnetic Induction (tesla) inside the material
applied
magnetic field H
B = H
permeability of a solid
current I
• Relative permeability (dimensionless)
상대투자율

4. Generation of a Magnetic Field - within a Solid Material (cont.)
• Magnetization
M = mH
Magnetic susceptibility (dimensionless)
• B in terms of H and M
B = 0H + 0M
• Combining the above two equations:
B = 0H + 0 mH H B
vacuum cm = 0 cm
> 0
< 0
permeability of a vacuum:
(1.26 x 10-6 Henry/m)
= (1 + m)0H
m = r - 1
cm is a measure of a material’s magnetic response relative to a vacuum

6. (a) What is the magnitude of the magnetic field strength H?
Basic Concepts
18.1 A coil of wire 0.25 m long and having 400 turns carries a current of 15 A.
(a) What is the magnitude of the magnetic field strength H?
(b) Compute the flux density B if the coil is in a vacuum.
Compute the flux density inside a bar of chromium that is positioned within the coil. The susceptibility for chromium is found in Table 18.2.
(d) Compute the magnitude of the magnetization M.
Solution
(a)
(b)
(c) Inasmuch as cm = 3.13  10-4 (Table 18.2), then
=  10-2 tesla
(d)

7. Origins of Magnetic Moments
• Magnetic moments arise from electron motions and the spins on electrons.
magnetic moments
electron
nucleus
spin
electron orbital motion
electron spin
• Net atomic magnetic moment:
-- sum of moments from all electrons.
• Four types of response...
No magnetism ( ex. Inert gas )
Fundamental magnetic moment
Bohr magnetron (μB)
= 9.27x10-24 A-m2

8. Types of Magnetism B (tesla) H (ampere-turns/m) vacuum ( cm = 0)
(1) diamagnetic (
~ -10-5)
e.g., Al2O3, Cu, Au, Si, Ag, Zn
(3) ferromagnetic e.g. ferrite(), Co, Ni, Gd
(4) ferrimagnetic e.g. Fe3O4, NiFe2O4
as large as
106 !)
(2) paramagnetic (
e.g., Al, Cr, Mo, Na, Ti, Zr
~ 10-4)

9. Basic Concepts
18.2 (a) Explain the two sources of magnetic moments for electrons.
(b) Do all electrons have a net magnetic moment? Why or why not?
(c) Do all atoms have a net magnetic moment? Why or why not?
Solution
(a) The two sources of magnetic moments for electrons are the electron's orbital motion around the nucleus, and also its spin.
(b) Each electron will have a net magnetic moment from spin, and possibly, orbital contributions, which do not cancel for an isolated electron.
(c) All atoms do not have a net magnetic moment. If an atom has completely filled electron shells or subshells, there will be a cancellation of both orbital and spin magnetic moments.

10. Diamagnetism – The magnetite of the induced magnetic moment is extremely small and in a direction opposite to that of the applied field.
Paramagnetism – The orientations of atomic magnetic moments are random, such that a piece of material possesses no net macroscopic magnetization. As the dipoles align with the external field, they give relatively small positive magnetic susceptibility.
Diamagnetic and paramagnetic materials  nonmagnetic materials

11. ex) α-ferrite, cobalt, nickel ; If H << M, B = μ0M
Ferromagnetism – It possess a permanent magnetic moment in the absence of an external field and manifest very large and permanent magnetization.
ex) α-ferrite, cobalt, nickel ; If H << M, B = μ0M
Domain – The mutual spin alignment exists over relatively large-volume regions of crystal
Saturation magnetization - It represents the maximum possible magnetization that results when all the magnetic dipoles in a solid piece are mutually aligned with the external field
Ms = (net magnetic moment for each atom)x(the number of atoms present)
Net magnetic moment per atom: 2.22 μB for Fe, 1.72 μB for Co, 0.60 μB for Ni
Example Saturation Magnetization and Flux density Computations for Nickel
Calculate (a) saturation magnetization and (b) saturation flux density for nickel (ρ=8.90 g/cm3)
Solution:

12. ex) MFe2O4 : M = Fe, Ni, Mn, Co, Cu Fe3O4  FeO + Fe2O3
Antiferromagnetism – It shows the alignment of the spin moments of neighboring atoms or ions in exactly opposite directions.
ex) MnO
Ferrimagnetism – Macroscopic magnetic characteristics of ferromagnets and ferrimagnets are similar, but the distinction lies in the source of net magnetic moment.
ex) MFe2O4 : M = Fe, Ni, Mn, Co, Cu
Fe3O4  FeO + Fe2O3
Example Prob Saturation Magnetization for Fe3O4
Calculate saturation magnetization for Fe3O4 given that
each unit cell contains 8 Fe2+ and 16 Fe3+ (a = nm)
Solution:

13. Magnetic Responses for 4 Types
No Applied
Applied
Magnetic Field (H = 0)
Magnetic Field (H)
(1) diamagnetic
none
opposing
(2) paramagnetic
random
aligned
(3) ferromagnetic
(4) ferrimagnetic
aligned

14. Concept Check Cite major similarities and differences between ferromagnetic and ferrimagnetic materials. Answer
The similarities between ferromagnetic and ferrimagnetic materials are as follows:
(1) There is a coupling interaction between magnetic moments of adjacent atoms/cations for both material types.
(2) Both ferromagnets and ferrimagnets form domains.
(3) Hysteresis B-H behavior is displayed for both, and, thus, permanent magnetizations are possible.
The differences between ferromagnetic and ferrimagnetic materials are as follows:
(1) Magnetic moment coupling is parallel for ferromagnetic materials, and antiparallel for ferrimagnetic.
(2) Ferromagnetics, being metallic materials, are relatively good electrical conductors; inasmuch as ferromagnetic
materials are ceramics, they are electrically insulative.
(3) Saturation magnetizations are higher for ferromagnetic materials.
Ferromagnetism
18.6 The magnetization within a bar of some metal alloy is 1.2 × 106A/m at an H field of 200 A/m. Compute the following: (a) magnetic susceptibility, (b) permeability, and (c) magnetic flux density within this material. (d) What type of magnetism would you suggest as being displayed by this material?
Solution
(a) This portion of the problem calls for us to compute the magnetic susceptibility within a bar of some metal alloy when M = 1.2  106 A/m and H =200 A/m. This requires that we solve for cm from Equation 18.6 as
(b) In order to calculate the permeability we must employ a combined form of Equations 18.4 and 18.7 as follows:
(c) The magnetic flux density may be determined using Equation 18.2 as
(d) This metal alloy would exhibit ferromagnetic behavior on the basis of the magnitude of its cm (6000), which is considerably larger than the cm values for diamagnetic and paramagnetic materials listed in Table 18.2.

15. Antiferromagnetism and Ferrimagnetism
Estimate (a) the saturation magnetization, and (b) the saturation flux density of cobalt ferrite [(CoFe2O4)8], which has a unit cell edge length of nm.
Solution
(a) The saturation magnetization of cobalt ferrite is computed in the same manner as Example Problem 18.2; from Equation 18.1
Now, nB is just the number of Bohr magnetons per unit cell. The net magnetic moment arises from the Co2+ ions, of which there are eight per unit cell, each of which has a net magnetic moment of three Bohr magnetons (Table 18.4). Thus, nB is twenty-four. Therefore, from the above equation
(b) This portion of the problem calls for us to compute the saturation flux density. From Equation 18.8
Concept Check Explain why repeatedly dropping a permanent magnet on the floor will cause it to become demagnetized.
Answer:
Repeatedly dropping a permanent magnet on the floor will cause it to become demagnetized because the jarring causes large numbers of magnetic dipoles to become misaligned by dipole rotation.

16. The Influence of Temperature on Magnetic Behavior
– With increasing temperature, the increased thermal motion of the atoms tends to
randomize the direction of any moments that may be aligned.
i.e. Saturation magnetization is decreased for both ferro- and ferrimagnets.
Curie temperature (Tc) – at which the saturation magnetization decreases gradually and then abruptly drops to zero with increasing temperature.
Ferro- and ferrimagetic materials are paramagnetic above Tc
Neel Temperature – at which antiferromagnetism vanishes
; antiferromagnetic material a become paramagnetic above this temperature

17. Domains in Ferromagnetic & Ferrimagnetic Materials
• As the applied field (H) increases the magnetic domains change shape and size by movement of domain boundaries. B
sat H H H
• “Domains” with
aligned magnetic
moment grow at
expense of poorly
aligned ones!
induction (B) H
Magnetic H
H = 0
Applied Magnetic Field (H)

18. Hysteresis and Permanent Magnetization
• The magnetic hysteresis phenomenon
Remanence (잔류자기) or Remanent flux density, Br B
Stage 2. Apply H, align domains
Stage 3. Remove H, alignment
remains! => permanent magnet!
Stage 4. Coercivity, HC Negative H needed to demagnitize!
보자력 H
Stage 5. Apply -H, align domains
Stage 1. Initial (unmagnetized state)
Stage 6. Close the hysteresis loop

19. Domains and Hysteresis
A ferromagnetic material has a remanence of 1.0 tesla and a coercivity of 15,000 A/m. Saturation is achieved at a magnetic field strength of 25,000 A/m, at which flux density is 1.25 teslas. Using these data, sketch entire hysteresis curve in the range H = –25,000 to +25,000 A/m. Be sure to scale and label both coordinate axes.
Solution
The B versus H curve for this material is shown below.
Concept Check Schematically sketch on a single plot the B-versus-H behavior for a ferromagnetic material
at 0 K,
at a temperature just below its Curie temperature, and
(c) at a temperature just above its Curie temperature. Briefly explain why these curves have different shapes.

20. B-versus-H behaviors of paramagnetic, diamagnetic, and ferromagnetic/ferromagnetic materials
Magnetic Anisotropy

21. Hard and Soft Magnetic Materials
Hard magnetic materials:
-- large coercivities
-- used for permanent magnets
-- add particles/voids to
inhibit domain wall motion
-- example: tungsten steel --
Hc = 5900 amp-turn/m)
-- motor application (drill, window wiper, fan, video
recorder), speaker, earphone H B
Hard
Soft
Soft magnetic materials:
-- small coercivities
-- used for electric motors (transformer core)
-- example: commercial iron Fe 21 21

23. An Iron- Silicon Alloy that is used in Transformer Cores
Energy losses of transformers could be minimized if their cores were fabricated from single crystals such that a [100]-type direction is oriented parallel to the direction of an applied magnetic field.
Single crystals are expensive
Attractive alternative is to fabricate cores from polycrystalline sheets of this alloy that are anisotropic.
The magnetic characteristics of this alloy may be improved through a series of deformation and heat-treating procedures that produce a (100) [001] texture 23 23

24. Figure 18.30 shows the B-versus-H curve for a nickel–iron alloy.
(a) What is the saturation flux density?
(b) What is the saturation magnetization?
(c) What is the remanence?
(d) What is the coercivity?
(e) On the basis of data in Tables 18.5 & 18.6, would you classify this
material as a soft or hard magnetic material? Why?
Solution
The saturation flux density for this nickel-iron is 1.5 tesla, the
maximum B value shown on the plot.
(b)
(c) The remanence, Br, is read from this plot as from the hysteresis loop shown in Figure 18.14; its value is about 1.47 tesla.
(d) The coercivity, Hc, is read from this plot ; the value is about 17 A/m.
(e) On the basis of Tables 18.5 and 18.6, this is most likely a soft magnetic material. The saturation flux density (1.5 tesla) lies within the range of values cited for soft materials, and the remanence (1.47 tesla) is close to the values given in Table 18.6 for hard magnetic materials. However, the Hc (17 A/m) is significantly lower than for hard magnetic materials.

25. Magnetic Storage
• Digitized data in the form of electrical signals are transferred to and recorded digitally on a magnetic medium (tape or disk)
• This transference is accomplished by a recording system that consists of a read/write head
-- “write” or record data by applying a magnetic field that aligns domains in small regions of the recording medium
-- “read” or retrieve data from medium by
sensing changes in magnetization
recording head
recording medium

26. Magnetic Storage Media Types
• Hard disk drives (granular/perpendicular media):
-- CoCr alloy grains (darker regions) separated by oxide grain boundary segregant layer (lighter regions)
-- Magnetization direction of each grain is perpendicular to plane of disk
80 nm
• Recording tape (particulate media):
-- Tabular (plate-shaped) ferrimagnetic barium-ferrite particles
~ 500 nm
~ 500 nm
-- Acicular (needle-shaped) ferromagnetic metal alloy particles

27. Superconductivity
Found in 26 metals and hundreds of alloys & compounds
Mercury
Copper (normal)
4.2 K
TC = critical temperature
= temperature below which material is superconductive

28. Critical Properties of Superconductive Materials
TC = critical temperature - if T > TC not superconducting JC = critical current density - if J > JC not superconducting HC = critical magnetic field - if H > HC not superconducting

29. Meissner Effect Superconductors expel magnetic fields
This is why a superconductor will float above a magnet
normal
superconductor

30. Advances in Superconductivity
Research in superconductive materials was stagnant for many years.
Everyone assumed TC,max was about 23 K
Many theories said it was impossible to increase TC beyond this value
1987- new materials were discovered with TC > 30 K
ceramics of form Ba1-xKxBiO3-y
Started enormous race
Y Ba2Cu3O7-x TC = 90 K
Tl2Ba2Ca2Cu3Ox TC = 122 K
difficult to make since oxidation state is very important
The major problem is that these ceramic materials are inherently brittle.
Suddenly everyone was doing superconductivity. Everyone was doing similar work, making discoveries, & rushing to publish so they could claim to have done it first. Practically, daily new high temp. records were set.

32. Summary
• A magnetic field is produced when a current flows through a wire coil.
• Magnetic induction (B):
-- an internal magnetic field is induced in a material that is situated within an external magnetic field (H).
-- magnetic moments result from electron interactions with the applied magnetic field
• Types of material responses to magnetic fields are:
-- ferrimagnetic and ferromagnetic (large magnetic susceptibilities)
-- paramagnetic (small and positive magnetic susceptibilities)
-- diamagnetic (small and negative magnetic susceptibilities)
• Types of ferrimagnetic and ferromagnetic materials:
-- Hard: large coercivities
-- Soft: small coercivities
• Magnetic storage media:
-- particulate g-Fe2O3 in polymeric film (tape)
-- thin film CoPtCr or CoCrTa (hard drive)

33. ANNOUNCEMENTS
Reading:
Core Problems:
Self-help Problems: