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

Rock Magnetism

Solid State Physics

Paleomagnetism

Petrology Mineralogy

MAGNETISM OF ROCKS MAGNETISM OF ROCKS AND MINERALSAND MINERALS

How do rocks record paleomagnetic information?

Basics of magnetismBasics of magnetism

At a conference on magnetism in Leiden, 1920 (from Physics Today)

A. Einstein

P. Ehrenfest

P. Langevin

H. Onnes

P. Weiss

Everything should be made as simple as possible.

But not simpler.

S S

SSN

N N

N

The field of a force – a property of the space in which the force acts

Magnetic field

attraction

repulsion

Magnetic field (force lines)

Magnetic field is not a central field (no free magnetic charges)

SN

F

Magnetic field definitions

B – magnetic induction

H – magnetic intensityTwo quantities describing a magnetic field

In vacuum:

B = H

B = µ0H

(cgs: centimeter, gram, second)

(Système Internationale, SI)

µ0 = 4π · 10-7 N A-2 - the permeability of free space (the permeability constant)

Magnetic induction (B) units

B

qv

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

Tesla Gauss

[µ0]

[B]

Magnetic intensity (H) units

SI:

cgs: Ørsted (Oe)

1 A/m = 4π/103 Oersted

B = µ0H , hence H = B/µ0

[H] =

Ampere

Ørsted

A=N A-1 m-1

N A-2 = m

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

I

Magnetic moment (M) units

m

m = AIn

[m] = Am2SI:

cgs: [m] = emu

1 Am2 =103 emu

A – area, I – current, n – unit vector

Emu

θ

Interaction with magnetic field

m = AInm = pd

+p

-p

dτ = m B sinθ

B

θ

aligning torque:

Magnetic field of a current loop (dipole)

Baxial =2µ0 m4πz3

z

decreases as the cube of distance

m

=AI

The Earth as a big magnet

MEarth ≈ 8∙1022 Am2

Earth magnetic field at the surface:

≈ 5 ∙ 10-5 T (0.5 G)

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)

Filling a free space with matter…

Rigorous consideration requires quantum-mechanical approach… We go simple…

e-nucleus

Orbital magnetic moment

Morbital Mspin

Spin magnetic moment

Bohr magneton:

µB = 9.274 ∙ 10-24 Am2

MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL

Atomic moment = orbital

moment + spin moment

A m2

m3

mi

mi

mi

mi

mi

mi

mi

mi mi

mi

mi

mimi

mimi

mi

mimi

mi

volume = V

Magnetization - the magnetic moment per unit volume

M = mtotal /V

Net magnetic moment of a volume V:

imtotal = ∑ mi

[ M ] = =

MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL

SI:

cgs: emu / cm3

1 A m-1 =103 emu/cm3

Am

B = µo (H + M)

B = µo H – free space (M = 0)

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

MAGNETIZATION AND THE MAGNETIC FIELD INSIDE A MATERIAL

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

Magnetic susceptibility

M = κ H

If M and H are parallel and the material is isotropic:

κ – magnetic susceptibility (dimensionless in SI)

κ is a measure of the ease with which the material can be magnetized

Magnetic permeability

Magnetic permeability

B = µo(H + M) = µoH (1 + κ) = µoµH

µ = 1 + κ - magnetic permeability

M = κ H

µ is a measure of the ability of a material to convey a magnetic flux

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

Relative permeability µr

The ratio of permeability of medium to the permeability of free space is called relative permeability µr of the solid.

00

0

B

B

HBHB

r

r

MAGNETIC UNITS AND CONVERSIONS

Magnetic properties of materials

Pauli’s exclusion principle: each possible electron orbit can be occupied by up to two electrons with opposite spins

e- e-

me me

e-

me

∑ mspin = 0 ∑ mspin ≠ 0

Diamagnetism

M

H

κ < 0

Magnetization develops in the direction opposite 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

H M

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

Examples of diamagnetic mineralsκ (SI)Mineral

Data from Hunt et al (1995)

the partial alignment of permanent atomic magnetic moments by a magnetic field

M

H

κ > 0

Paramagnetism

• 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

H = 0, M = 0 H > 0, M > 0

H

Thermal energy dominates

Paramagnetism: Temperature dependence

κ

T T

1/κ κ-1 ~ T

κ-1 ~ (T – θ)κ =

CT

The constant C is material-specific

θ

κ = CT - θ

The Curie-Weiss law

θ – the paramagnetic Curie temperature (near 0 K for most paramagnetic solids)

Examples of paramagnetic minerals

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)

κ (SI)Mineral

FerromagnetismAtomic magnetic moments are always aligned (even for H = 0)

due to exchange interaction (quantum-mechanical effect)

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

H = 0

FerromagnetismExchange interaction (Eex) decreases with temperature

Spontaneous magnetization, Ms

T

Ferromagnetism (Eex > kT)

Paramagnetism (Eex < kT)

Tc

Tc – the ferromagnetic Curie temperature (material-specific)

Ferromagnetism: Magnetic hysteresis

M

H

Ms – Saturation magnetizationMrs

HcHc – Coercive force (the field needed to bring the magnetization back to zero)

Mrs – Saturation remanent magnetization

Ms

Ferromagnetism (magnetic hysteresis)

M

HHcr

Ms – Saturation magnetizationMrs

Hc – Coercive force (the field needed to bring the magnetization Ms back to zero)

Mrs – Saturation remanent magnetization

Hcr – Coercivity of remanence

(the field needed to bring Mrs to zero)

Hysteresis

The striking property of Ferro Magnetic materials is the relation between Magnetization and the strength of Magnetic field. This property is called Hysteresis.

P

Q

R

S

H

MSaturation Magnetization

Residual Magnetization

Coercivity

Ferro Magnetic Material

Hs

-Hs

oHc

Ms

Mr

-Ms

• 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..

• 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.

• 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.

• 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.

AntiferromagnetismNegative exchange interaction (anti-parallel spin moments)

M = 0Antiferromagnetic elements:

• Chromium (Cr)

• Manganese (Mn)

Conditions for antiferromagnetism:

1) Non-compensated spin moments

2) Negative exchange interaction (i.e. anti-parallel spins)

Non-perfect antiferromagnetism

spin-canted antiferromagnetism

defect antiferromagnetism

M

M

Eg., Hematite (Fe2O3)

Ferrimagnetism

Ferrimagnets (ferrites) behave similar to ferromagnets

M

Super-exchange interaction

Eg., Magnetite (Fe3O4)

5µB 6µB

O2-Fe2+ Fe3+

Summary

Ferromagnetism Antiferromagnetism

Non-perfect Antiferromagnetism Ferrimagnetism

important for rock and paleomagnetism

Diamagnetism

Paramagnetism