1. Chapter 27 Magnetism in Matter

2. Topics
Magnetization
Saturation magnetization
Types of materials

3. Magnetization Atoms have magnetic dipole moments due to
orbital motion of the electrons
magnetic moment of the electron

4. Magnetization
Material placed in magnetic field  magnetic dipole moments aligned  material “magnetized”

5. Magnetization
magnetization = net magnetic dipole moment per unit volume
magnetization contributes an additional magnetic, Bm, given by

6. Magnetic susceptibility
Magnetization M depends on applied field Bapp and the susceptibility m of the material

7. Magnetic susceptibility
For paramagnets: m > 0
For diamagnets: m < 0
Total field:
Km = relative permeability of the material

8. Magnetic moment and angular momentum
For circular motion L = rmv
Magnetic moment of current loop  = IA = Iπr2
For single charge q on circular orbit I = q/T = qv/(2πr)
=Iπr2 = qvπr2/(2πr)
= qvr/2 = qL/(2m)

9. Saturation magnetization
Magnetization grows with applied field until all magnetic moments are aligned --“saturation”
At saturation, the magnetization is Ms = n•μ, where n is number of atoms per unit volume and μ is the magnetic moment of each atom

10. Types of Materials Materials exhibit three types of magnetism:
paramagnetic
diamagnetic
ferromagnetic

11. Paramagnetism Paramagnetic materials have permanent magnetic moments
moments randomly oriented at normal temperatures
adds a small additional field to applied magnetic field

12. Paramagnetism Small effect (changes B by only 0.01%) Example materials
Oxygen (STP), aluminum, tungsten, platinum

13. Diamagnetism Diamagnetic materials no permanent magnetic moments
magnetic moments induced by applied magnetic field B
applied field creates magnetic moments opposed to the field

14. Diamagnetism Common to all materials.
Applied B field induces a magnetic field opposite the applied field, thereby weakening the overall magnetic field
But the effect is very small: Bm ≈ Bapp

15. Diamagnetism Example materials High temperature superconductors copper
silver

16. Ferromagnetism Ferromagnetic materials have permanent magnetic moments
align at normal temperatures when an external field is applied and strongly enhances applied magnetic field

17. Ferromagnetism Ferromagnetic materials (e.g. Fe, Ni, Co, alloys)
have domains of randomly
aligned magnetization
(due to strong interaction
of magnetic moments of neighboring
atoms)

18. Ferromagnetism Applying a magnetic field causes
domains aligned with the applied field
to grow at the expense of others
that shrink
Saturation magnetization is reached
when the aligned domains
have replaced all others

19. Ferromagnetism In ferromagnets, some magnetization
will remain after the applied
field is reduced to zero,
yielding permanent magnets
Such materials exhibit
hysteresis

20. Material properties

21. Summary
The magnetism of materials is due to the magnetic dipole moments of atoms, which arise from:
the orbital motion of electrons
and the intrinsic magnetic moment of each electron

22. Summary Three classes of materials
Diamagnetic M = - const • Bext, small effect (10-4)
Paramagnetic M = + const • Bext small effect (10-2)
Ferromagnetic M ≠ const • Bext large effect (1000)