1. Suez University
Faculty of Petroleum & Mining Engineering
Magnetic Properties
Student
Belal Farouk El-saied Ibrahim
Class / III
Section / Engineering Geology and Geophysics
Presented to
Prof. Dr. / Ali Abbas
2. MMAAGGNNEETTIISSMM OOFF RROOCCKKSS
AANNDD MMIINNEERRAALLSS
How do rocks record paleomagnetic information?
Rock Magnetism
Solid State Physics
Paleomagnetism
Petrology Mineralogy
3. BBaassiiccss ooff mmaaggnneettiissmm
P. Weiss
H. Onnes
At a conference on
magnetism in
Leiden, 1920
(from Physics Today)
A. Einstein
P. Ehrenfest
P. Langevin
Everything should be made
as simple as possible.
But not simpler.
4. Magnetic field
attraction
N N
S S
repulsion
N S S
N
The field of a force – a property of the space in which the force acts
5. Magnetic field (force lines)
N S
F
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
In vacuum:
B = μ0H
μ0 = 4π · 10-7 N A-2 - the permeability of free space
B = H
(Système Internationale, SI)
(the permeability constant)
(cgs: centimeter, gram, second)
7. Magnetic induction (B) units
Tesla Gauss
B
q
v
FL
FL = q(v X B)
SI: Tesla (T) [N A-1 m-1]
cgs: Gauss (G) [dyne-1/2 cm-1]
1 γ (gamma) =10-5 Gauss
Lorentz force (FL )
1 Tesla =104 Gauss
8. Magnetic intensity (H) units
B = μH , hence H = B/μ00
[H] =
[B]
[μ0]
SI:
cgs: Ørsted (Oe)
1 A/m = 4π/103 Oersted
Ampere
Ørsted
= A N A-1 m-1
N A-2 = m
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
I
m
m = AIn
Emu
A – area, I – current, n – unit vector
SI: [m] = Am2
cgs: [m] = emu
1 Am2 =103 emu
12. Magnetic field of a current loop (dipole)
Baxial =
2μ0 m
4πz3
z
decreases as the cube of
distance
m
=AI
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: 10-2 - 10-1 T (~102-103 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: ~10-10 - 10-9 T (~10-6 – 10-5 G)
15. 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
nucleus e-
Orbital magnetic moment
Spin magnetic moment
Bohr magneton:
μB = 9.274 ∙ 10-24 Am2
Atomic moment = orbital
moment + spin moment
16. MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL
Net magnetic moment of a volume V:
mtotal = Σ mi
i
A m2
m3
m mi i
mi
mi
mi
mi
mi
mi
mi
mi mi
mi
mi
mi mi
mi
mm i i
mi
volume = V
Magnetization - the magnetic
moment per unit volume
M = mtotal /V
SI:
[ M ] = =
cgs: emu / cm3
1 A m-1 =103 emu/cm3
A
m
17. MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL
In a magnetizable material the induction (B) has two sources:
1. Magnetizing field H (external sources)
2. Set of internal atomic moment, causing magnetization M
B = μo (H + M)
B = μo H – free space (M = 0)
18. Magnetic Retentivity
Also called permanence; how long a
magnet retains its magnetism
Materials that are hard to magnetize
generally retain their magnetism longer
Relates to the amount of force needed to
align magnetic domains
19. 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
21. 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
22. Permeability of
Magnetic Materials
• High permeability
– Iron, steel, nickel, cobalt
– Commercially made alloys of iron, nickel, cobalt, and other
elements
• Silicon steel (used in transformers)
• Alnico (used in audio speakers)
• Medium permeability
– Aluminum, platinum, manganese, and chromium
• Low permeability
– Bismuth, antimony, copper, and zinc
– Rare metals (mercury, gold, and silver)
• Nonmagnetic materials (diamagnetic)
– Glass, paper, rubber, wood, and air
23. Relative permeability μr
The ratio of permeability of medium to
the permeability of free space is called
relative permeability μr of the solid.
m m
m
0
B
B
=
B
H
B
0 0
H
r
m
r
= =
25. Magnetic properties of materials
Pauli’s exclusion principle: each possible electron orbit can be
occupied by up to two electrons with opposite spins
e me
e- e-m
e-m
e
Σ mspin = 0 Σ mspin ≠ 0
26. Diamagnetism
Magnetization develops in the direction
opposite to the applied magnetic field
M
H
κ < 0
H M
• Exists in all materials (but observable when electron spins are paired)
• Diamagnetic κ (and magnetization) is reversible
• Diamagnetic κ is temperature-independent
27. Examples of diamagnetic minerals
Mineral 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) - (0.77-19) · 10-6
Data from Hunt et al (1995)
28. the partial alignment of permanent atomic magnetic
moments by a magnetic field
M
H
κ > 0
Paramagnetism
H = 0, M = 0 H > 0, M > 0
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
29. Paramagnetism: Temperature dependence
κ
1/κ κ-1 ~ T
κ-1 ~ (T – θ)
T T
κ = CT
The constant C is material-specific
θ
κ = C
T - θ The Curie-Weiss law
θ – the paramagnetic Curie temperature (near 0 K for
most paramagnetic solids)
30. Examples of paramagnetic minerals
Mineral κ (SI)
Olivine (Fe,Mg)2SiO4 1.6 · 10-3
Montmorillonite (clay) 0.34 ·10-3
Siderite (FeCO3) 1.3-11.0 · 10-3
Serpentinite 3.1-75.0 · 10-3
(Mg3Si2O5(OH)4)
Chromite (FeCr2O4) 3-120 · 10-3
Data from Hunt et al (1995)
31. Ferromagnetism
Atomic magnetic moments are always aligned (even for H = 0)
due to exchange interaction (quantum-mechanical effect)
H = 0
M ≠ 0
Conditions for ferromagnetism:
1) Non-compensated spin moments
2) Positive exchange interaction
(i.e. co-directed spins)
Ferromagnetic elements:
• Iron (Fe) (κ = 3900000)
• Nickel (Ni)
• Cobalt (Co)
• Gadolinium (Gd)
Spontaneous
magnetization
32. Ferromagnetism
Exchange interaction (Eex) decreases with temperature
Spontaneous
magnetization, Ms
T
Ferromagnetism
(Eex > kT)
Paramagnetism
(Eex < kT)
Tc
Tc – the ferromagnetic Curie temperature (material-specific)
33. Ferromagnetism: Magnetic hysteresis
M
H
Ms – Saturation
M magnetization rs
Hc
Mrs– Saturation remanent
magnetization
Hc – Coercive force
(the field needed to
bring the magnetization
back to zero)
Ms
34. Ferromagnetism
(magnetic hysteresis)
M
H H cr
Ms – Saturation
M magnetization rs
Mrs– Saturation remanent
magnetization
Hc – Coercive force
(the field needed to
bring the magnetization
Ms back to zero)
Hcr – Coercivity of
remanence
(the field needed to bring
Mrs to zero)
35. Hysteresis
The striking property of Ferro Magnetic
materials is the relation between
Magnetization and the strength of
Magnetic field. This property is called
Hysteresis.
36. P
Q
R
S
H
M
Saturation
Magnetization
Residual
Magnetization
Coercivity
Ferro Magnetic Material
Hs
-Hs
Ms
Mr
Hc o
-Ms
37. • If we start with no Magnetized specimen
(M= 0) with the increasing values of
magnetizing field H.
• The Magnetization of the specimen
increases from zero to higher values and
attains its maximum value at a point P, at
this point the Magnetization referred as
Saturation Magnetization..
38. •When we increase Magnetic field H
there is no further increment in Magnetic
moment.
•When we decrease Magnetic field H to
Zero, the Magnetization M attains point
Q.
• At this point Magnetization referred as
residual Magnetization Mr.
39. • Further if we increase the Magnetic field
from zero to negative values, the
Magnetization of material becomes zero
at a point R, at that point the Magnetic
field Hc is referred as Coercivity of the
specimen.
• If we increase Magnetic field H in reverse
direction Magnetization of material
reaches its peak value at a points S.
40. •On reversing the polarities of Magnetic
field and increasing its strength the
Magnetization slowly decreases first to
residual value then to zero and finally
increases to saturation state and
touches the original saturation curve.
• The area of loop indicates the amount
of energy wasted in one cycle of
operation.
Magnetic susceptibility is a measure of how easy the material can be magnetized.
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.
