1. Today’s objectives - Magnetic Properties I
Equations describing magnetic field strength, induction (several versions), relative magnetic permeability, magnetic susceptibility, magnetization of a solid, and saturation magnetization.
Origins of magnetic moments.
Magnetic types of materials, their relative magnetic permeabilities, and why they behave as they do (diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, ferrimagnetic).
Temperature dependence of magnetization and why it occurs.
Reading:
All of Chapter 20 should be read.

2. Magnetic dipoles
Magnetic forces develop when a charged particle moves.
Magnetic dipoles exist within certain magnetic materials.
Just like bar magnets with North and South poles.
The magnetic dipoles point from South to North by convention.
(Compare to Electric fields, which go from + to -)
The force of a magnetic field exerts a torque on the dipole that tends to align it.
Compass needle

3. Earth’s Magnetic Field
A magnetic field is generated every time an electrically charged object moves. Most of the planets in the Solar System are known to generate magnetic fields. The Earth's magnetic field is generated in its fluid, outer core. This is because the heat of the inner core drives the fluid in the outer core up and around in a process called convection. Because this outer core is made of metal, which can be electrically charged, the convection causes a magnetic field to be generated.

4. A bit of History

5. The Stone from Magnesia - Magnetite
Spinel Structure
Atom x y z
Fe(tet)
Fe(oct) O
Magnetite (or lodestone): opaque, black, ceramic crystal. Magnetite (FeO · Fe2O3) is an oxide of iron which, unlike Fe2O3, is strongly magnetic.

6. Magnetic Vectors
A magnetic field, either induced or permanent, generates a magnetic force.
The direction of the force is drawn (blue lines).
Density of field lines indicates the field strength.
H=External magnetic field
in units of H for Henry’s
Also called magnetic field strength.
a vector
B=magnetic induction (Magnitude of internal magnetic field strength within a material exposed to an H field)
in units of T for Tesla
Also called magnetic flux density.
also a vector

7. Comparison: magnets and dielectrics
µ=permeability (depends on the material, similar to a dielectric constant where ε was related to electronic polarizability).
A strong permeability means the material is made of something which can align strongly to an external magnetic field.
This leads to a strong magnetic induction (or flux density).
ε (or k)
A good dielectric has charges which can polarize in an external field (opposite to it).
electrons vs protons in nucleus
cations and anions
polar molecules
interfaces

8. Magnetic Permeability
Since the permeability influences the magnetic induction (flux density),
It impacts how good of a magnet you can make.
In a vacuum, the permeability is a universal constant, μo = 1.257*10-6 H/m.

9. Other magnetic terms
The relative permeability (µr) is sometimes used to describe the magnetic properties of a material (like ε for dielectrics).
The magnetization (M) represents the magnetic moments within a material in the presence of a magnetic field of strength H
(akin to polarization, P, for a dielectric).
The magnitude of M is proportional to the applied field according to the magnetic susceptibility (m).
There are thus four main ways to represent B, the magnetic induction (also called the flux density).
Note that units get very confusing. Just stick with one system (SI).

10. Magnetic Orbital Moments
Magnetic moments arise due to two mechanisms:
Orbital motion of an electron around the nucleus.
Essentially a small current loop, generating a very small magnetic field.
A magnetic moment is established along the axis of rotation.
ml is the magnetic quantum number for the electron.
The magnetic quantum number indicates the type of orbital (shape and usually orientation).
Orbital m
Total orbitals
Total electrons s 1 2 p
-1,0,1 3 6 d
-2,-1,0,1,2 5 10

11. Magnetic Spin Moments 2nd source of a Magnetic Moment
Direction that an electron spins.
Only two directions are possible.
The moment resulting from these spinning electrons are along the spin axis, either UP or DOWN.
The combination of orbital and spin moments for every electron throughout a crystal define its magnetic properties.

12. How do we Classify Magnetic Properties of Materials?
The Faraday Experiment

13. The Faraday Experiment
The coil induces an inhomogeneous magnetic field. The sample is suspended from one of the arms of a sensitive balance into the magnetic field H.
Certain materials are weakly expelled from this field (along x direction). These are DIAMAGNETS.
PARAMAGNETS are weakly attracted to this field (along –x direction).
FERROMAGNETIC, ANTI-FERROMAGNETIC and FERRIMAGNETIC materials are strongly attracted to this field.

14. Classification via Magnetic Susceptibilityr

15. Diamagnetism
Nonmagnetic (only occurs in the presence of an external magnetic field, H)
Even in an external magnetic field, very weak form of magnetism
Non-permanent
Occurs opposite to external field.
Relative permeability < 1
(≈ )
Found in all materials, just usually too weak to matter.
So weak that only noticed if no other form of magnetism exists for the atom and/or crystal.
Most common for atoms with completely filled orbitals (no unmatched electrons that could have spin moments).
Inert gases
Some ionic structures (H2O, Al2O3)
Noble metals (Au, Cu, Ag, Hg, Zn)

16. Paramagnetism
If the orbitals are not completely filled or spins not balanced, an overall small magnetic moment may exist.
Without an external magnetic field, the moments are randomly oriented.
No net macroscopic magnetization.
“NonMagnetic”
In an external field, the moments align with the field, thus enhancing it (only a very small amount, though).
There is no interaction between adjacent dipoles.
Permeability (μr) > 1 (barely, ≈ to 1.01.
Examples include Al, Cr, Cr2Cl3, MnSO4)

17. Ferromagnetism
Unlike paramagnetism with incompletely balanced orbital or spin moments which are randomly aligned, for some materials unbalanced spin can lead to significant permanent magnetic moments.
Fe (BCC alpha), Co, Ni, Gd.
The permanent moments are further enhanced by coupling interactions between magnetic moments of adjacent atoms so that they tend to align even without an external field.
Maximum possible magnetization for these materials is the saturation magnetization (Ms, usually quoted per volume).
There is a corresponding saturating flux density (Bs).
Mper atom Fe Co Ni B
2.22
1.72
0.6

18. Anti-Ferromagnetism
Magnetic moment coupling (for each individual atom) does not always align constructively as for ferromagnetism.
For some materials, the alignment of the spin moments of adjacent atoms is in opposite directions.
MnO
O2- has no net moment.
Mn2+ have a spin based net magnetic moment.
Overall, there is no net magnetic moment even though at the atomic level there is a local moment.

19. Anti-Ferromagnetism
Ordered arrangement of spins of the Mn2+ ions in MnO determined by neutron diffraction. The 02- ions are not shown.

20. Ferrimagnetism
Ferrimagnets are similar to ferromagnets. There is a net magnetic moment.
They are also similar to antiferromagnets. The net magnetic moment is not as large as if all of the magnetic atoms coupled constructively.
Essentially, ferrimagnetism entails some of the magnetically active atoms coupling constructively, and an unequal number coupling destructively.
Examples include Fe3O4(Fe.Fe2O4), NiFe2O4, ZnFe2O4.
Unlike ferromagnets, they are not electrically conductive. Used in high frequency applications such as microwave devices, circulators, phase shifters.

21. Ferrimagnetism All Fe2+ have a spin magnetic moment.
Half of Fe3+ have a spin moment in on direction, the other half in the other (decreasing the overall moment to just that contributed by the Fe2+ ions).
Common for inverse spinel materials and garnets. Usually, 2+ ions of Ni, Mn, Co, and Cu are the active ones.
Simpler picture showing a net magnetic moment.

22. Relative Permeability (r)
Comparisons
c measures the
material response
relative to a vacuum.
μr>>>1
μr>1.001
μr=1
To be quantitative, there are 4 options (magnetic permeability, relative permeability, or susceptibility):
μr=.99999
Type
Mag Induction (B)
Relative Permeability (r)
Susceptibility (m)
diamagnetic
Small, opposite H
<1 (barely, so ≈o-)
Negative, -10-5
paramagnetic
Small, with H
>1 (this time ≈o+)
Positive, 10-3 to 10-5
ferromagnetic
Large, with H
>>1
>>1-

23. Temperature dependence
Saturation magnetization MS is the maximum magnetization in a material assuming perfect magnetic dipole alignment. This happens only at T=OK.
Increasing T increases thermal vibrations and decreases MS due to diminished (exchange) coupling between dipoles.
This is VERY important for ferro-, ferri-, and anti-ferromagnets.
Thermal vibrations also cause the dipoles to spend more time pointing in the ‘wrong’ direction, reducing Ms.
Above a critical temperature called the Curie (or Neèl) point (TC or Tn), ferro- and ferrimagnetic materials no longer possess a spontaneous magnetization. They become PARAELECTRIC.

24. The Curie (or Neèl) Temperature
TC(Fe)
Tn(Fe3O4)

25. Temperature dependence
ferromagnetic
TC or Tn
anti-ferromagnetic
T=0K
paramagnetic
ferrimagnetic
Above a critical temperature called the Curie point (TC), ferro- and ferrimagnetic materials no longer possess a spontaneous magnetization. They become PARAMAGNETIC. So do anti-ferromagnetic materials.

26. 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.

27. Wht about Ferri- and Anti-FerroMagnets?
What about ferrimagnetic? Similar to Ferromagnets
What about antiferromagnetic? Similar to Paramagnets

28. Classification Summary

29. Magnetic properties II
SUMMARY
Equations describing magnetic field strength, induction (several versions), relative magnetic permeability, magnetic susceptibility, magnetization of a solid, and saturation magnetization.
Origins of magnetic moments.
Magnetic types of materials, their relative magnetic permeabilities, and why they behave as they do (diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, ferrimagnetic).
Temperature dependence of magnetization and why it occurs.
Reading for next class
Magnetic properties II
Chapter sections: