1. MAGNETISM OF ROCKS AND MINERALS
How do rocks record paleomagnetic information?
Paleomagnetism
Rock Magnetism
Solid State Physics
Petrology
Mineralogy

2. Outline Basics of magnetism (today) Magnetic minerals
Magnetization processes in rocks

3. Everything should be made
Basics of magnetism
Everything should be made
as simple as possible.
P. Weiss
But not simpler.
A. Einstein
H. Onnes
P. Ehrenfest
P. Langevin
At a conference on magnetism in Leiden, (from Physics Today)

4. Magnetic field N S N S N S S N attraction repulsion
The field of a force – a property of the space in which the force acts

5. Magnetic field (force lines)
Magnetic field is not a central field (no free magnetic charges)

6. Magnetic field definitions
B – magnetic induction
H – magnetic intensity
Two quantities describing a magnetic field
B = µ0H
(Système Internationale, SI)
In vacuum:
µ0 = 4π · N A-2
- the permeability of free space (the permeability constant)
B = H
(cgs: centimeter, gram, second)

7. Magnetic induction (B) units
FL = q(v X B)
Tesla
Gauss
SI: Tesla (T)
[N A-1 m-1] v q
cgs: Gauss (G) FL
[dyne-1/2 cm-1]
1 γ (gamma) =10-5 Gauss B
Lorentz force (FL )
1 Tesla =104 Gauss

8. Magnetic intensity (H) units
Ampere
Magnetic intensity (H) units
Ørsted
SI:
B = µ0H , hence H = B/µ0 A
[B]
N A-1 m-1
[H] = = = m
[µ0]
N A-2
cgs: Ørsted (Oe)
1 A/m = 4π/103 Oersted

9. Magnetic moment (M)
No free magnetic poles can exist, hence the dipole field is the simplest configuration
Real source of magnetism is moving electrical charges (electrical currents)
Thin bar magnet (dipole)
Electric current loop
Uniformly magnetized sphere

10. Magnetic moment (M) units
Emu
m = AIn
A – area, I – current, n – unit vector m
[m] = Am2 I
SI:
[m] = emu
cgs:
1 Am2 =103 emu

11. Interaction with magnetic fieldB
aligning torque:
m = pd
m = AIn
τ = m B sinθ +p d θ θ -p

12. Magnetic field of a current loop (dipole)
=AI
2µ0 m
Baxial = z
4πz3 m
decreases as the cube of distance

13. The Earth as a big magnet
MEarth ≈ 8∙1022 Am2
Earth magnetic field at the surface:
≈ 5 ∙ 10-5 T (0.5 G)

14. Magnetic fields in the universe
Sun surface: ~10-4 T (~10 G)
Sun spot: T (~ G)
At Earth’s orbit: ≈ 5∙10-9 T (~10-5 G)
Neutron Star: ~108 T (~1012 G)
Magnetar: ~1011 T (~1015 G) (strongest known field)
Galactic field: ~ T (~10-6 – 10-5 G)

15. Atomic moment = orbital moment + spin moment
MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL
Filling a free space with matter…
Rigorous consideration requires quantum-mechanical approach… We go simple…
Morbital
Mspin e-
nucleus
Orbital magnetic moment
Spin magnetic moment
Bohr magneton:
µB = ∙ Am2
Atomic moment = orbital moment + spin moment

16. MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL
Net magnetic moment of a volume V: mi mi
mtotal = ∑ mi mi i mi mi mi
Magnetization - the magnetic moment per unit volume mi mi mi mi mi mi mi
M = mtotal /V mi mi mi mi mi mi
A m2 A
SI:
[ M ] = = m3 m
volume = V
cgs:
emu / cm3
1 A m-1 =103 emu/cm3

17. MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL
In a magnetizable material the induction (B) has two sources:
Magnetizing field H (external sources)
Set of internal atomic moment, causing magnetization M
B = µo (H + M)
B and H fields
B = µo H – free space (M = 0)

18. Magnetic susceptibility
If M and H are parallel and the material is isotropic:
M = κ H
κ – magnetic susceptibility (dimensionless in SI)
κ is a measure of the ease with which the material can be magnetized
Magnetic susceptibility is a measure of how easy the material can be magnetized.

19. Magnetic permeability
M = κ H
B = µo(H + M) = µoH (1 + κ) = µoµH
µ = 1 + κ - magnetic permeability
µ is a measure of the ability of a material to convey a magnetic flux

20. MAGNETIC UNITS AND CONVERSIONS

21. Magnetic properties of materials
Pauli’s exclusion principle: each possible electron orbit can be occupied by up to two electrons with opposite spins me me me e- e- e-
∑ mspin = 0
∑ mspin ≠ 0

22. Diamagnetism
Magnetization develops in the direction opposite to the applied magnetic field M M H H
κ < 0
The diamagnetic response to application of a magnetic field (Figure 2.1a) is acquisition of a small induced
magnetization, Ji, opposite to the applied field, H. The magnetization depends linearly on the applied field
and reduces to zero on removal of the field. Application of the magnetic field alters the orbital motion of
electrons to produce the small magnetization antiparallel to the applied magnetic field.
Exists in all materials (but observable when electron spins are paired)
Diamagnetic κ (and magnetization) is reversible
Diamagnetic κ is temperature-independent

23. Examples of diamagnetic minerals
κ (SI)
Quartz (SiO2) - (13-17) · 10-6
Calcite (CaCO3) - (8-39) · 10-6
Graphite (C) - (80-200) · 10-6
Halite (NaCl) - (10-16) · 10-6
Sphalerite (ZnS) - ( ) · 10-6
Data from Hunt et al (1995)

24. Paramagnetism
the partial alignment of permanent atomic magnetic moments by a magnetic field
H = 0, M = 0
H > 0, M > 0 M
κ > 0 H H
Thermal energy dominates
One or more electron spins is unpaired (the atomic net moment is not zero)
Paramagnetic κ (and magnetization) is reversible
Very large H or very low T is required to align all the moments (saturation)
Paramagnetic κ is temperature-dependent

25. Paramagnetism: Temperature dependenceκ
1/κ
κ-1 ~ T
κ = C T
κ-1 ~ (T – θ) T θ T C
κ =
The Curie-Weiss law
T - θ
θ – the paramagnetic Curie temperature (near 0 K for most paramagnetic solids)
The constant C is material-specific

26. Examples of paramagnetic minerals
κ (SI)
Olivine (Fe,Mg)2SiO · 10-3
Montmorillonite (clay) 0.34 ·10-3
Siderite (FeCO3) · 10-3
Serpentinite · 10-3 (Mg3Si2O5(OH)4)
Chromite (FeCr2O4) · 10-3
Data from Hunt et al (1995)

27. Ferromagnetism H = 0 M ≠ 0 Spontaneous magnetization
Atomic magnetic moments are always aligned (even for H = 0)
due to exchange interaction (quantum-mechanical effect)
Conditions for ferromagnetism:
H = 0
1) Non-compensated spin moments
2) Positive exchange interaction (i.e. co-directed spins)
Ferromagnetic elements:
Iron (Fe) (κ = )
Nickel (Ni)
Cobalt (Co)
Gadolinium (Gd)
M ≠ 0
Spontaneous magnetization

28. Ferromagnetism
Exchange interaction (Eex) decreases with temperature
Ferromagnetism (Eex > kT)
Paramagnetism (Eex < kT)
Spontaneous magnetization, Ms Tc T
Tc – the ferromagnetic Curie temperature (material-specific)

29. Ferromagnetism: Magnetic hysteresisMs
Ms – Saturation magnetization
Mrs
Mrs – Saturation remanent magnetization Hc H
Hc – Coercive force (the field needed to bring the magnetization back to zero)

30. Ferromagnetism (magnetic hysteresis)
Ms – Saturation magnetization
Mrs
Mrs – Saturation remanent magnetization
Hcr H
Hc – Coercive force (the field needed to bring the magnetization Ms back to zero)
Field off
Hcr – Coercivity of remanence (the field needed to bring Mrs to zero)

31. Antiferromagnetism M = 0
Negative exchange interaction (anti-parallel spin moments)
Conditions for antiferromagnetism:
1) Non-compensated spin moments
2) Negative exchange interaction (i.e. anti-parallel spins)
Antiferromagnetic elements:
Chromium (Cr)
Manganese (Mn)
M = 0

32. Non-perfect antiferromagnetism
spin-canted antiferromagnetism
defect antiferromagnetism M M
Eg., Hematite (Fe2O3)

33. Ferrimagnetism M 5µB 6µB Eg., Magnetite (Fe3O4)
Super-exchange interaction
Fe2+
Fe3+
O2- M
Ferrimagnets (ferrites) behave similar to ferromagnets
5µB
6µB
Eg., Magnetite (Fe3O4)

34. Non-perfect Antiferromagnetism
Summary
Diamagnetism
Paramagnetism
Non-perfect Antiferromagnetism
Ferromagnetism
Antiferromagnetism
Ferrimagnetism
important for rock and paleomagnetism

35. Next …
Magnetic minerals
Rock magnetizations