Lecture X Magnetism and Matter

Learning Objective: to examine some aspects of magnetic properties of materials

Some materials are magnetic:

Bar magnet, Compass. (permanent magnets)

Some appear non-magnetic, but are attracted

by a permanent magnet.

Some are non-magnetic whatever.

Why?

Magnetism is intimately linked to

the behaviour of electrons in materials

Magnetism and the Electron

Electrons generate magnetism in 3 ways:

1. Magnetism of Moving Charges (for example, electric current)

3. Magnetism and Intrinsic Spin(electrons have intrinsic magnetic moments)

2. Magnetism of Orbital Motion(each electron is orbiting around the nucleus)

v

L

2rI πμ ×=

€

I =e

T r

ev

π2=

€

∴μ=evr

2Angular Momentum L = mevr

Lm

e

e2=μ

Orbital Motion

v

L

Orbital Motion

Smallest magnetic moment (other than zero!)

eB m

e

2

h=μ

)T (J mA 10274.9 -1224−×=

Magnetism and Spin

eBS m

e

2

h==μμ

The electron has

an intrinsic magnetic

moment! So are protons

and neutrons.

Net magnetic moment of an atom is obtained by combining both orbital and spin moments of all the electrons, taking into account the directions of these

moments

Why isn’t everything magnetic?

Each atom contains a number of electrons, each electron contributes a magnetic moment, but the sum of all the electron contributions can be zero.

If not zero, then each atom can be

treated as a magnetic dipole.

The alignment of the “atomic dipoles”

in a solid is important.

Magnetic moment

of each atom is zero

Total moment is zero

Net moment zeroNet moment non-zero

Materials only exhibit “familiar” magnetic effects when:

Atoms contain unpaired electrons

Large scale alignment of the dipole moments occurs

&

Materials are Paramagnetic, Ferro-magnetic, or diamagnetic

Paramagnetism

Atoms of a paramagnetic material have permanent magnetic dipole moments.

These dipoles are randomly oriented - Magnetic fields average to zero.

In an external field B0, the dipoles tend to align with B0 - Results in an additional magnetic field Bm.

Material with N atoms, μmaximum = μN. Randomization of the dipoles orientations by thermal collisions significantly reduces the total dipole moment (μtotal)

Paramagnetism

Compare TkB2

3with 2μB

Example: T = 300 K, B = 1.5 T, μ = μB

eV 039.02

3== TkU BT

eV 00017.02 == BU BB μ

€

1 eV =1.6 ×10-19 J

Paramagnetism

The increase of the strength of the B-field by the paramagnetic material is described by the relative permeability constant m.

0BB m=

mBBB += 0

Paramagnetism

Material (STP) mAir 1.000304Oxygen 1.00133Liquid Oxygen (-190oC) 1.00327Nickel Monoxide 1.000675

Paramagnetism

Magnetic moment per unit volume (magnetisation) M:

VM total

μ=

Paramagnetism

It can be shown that

MBm 0μ=

MBB 00 μ+=

00

0

1B

M

B

B μ+=

001B

Mm μ +=

30 2

4 xBx

μπμ

=

mmB

M χμ =−= 10

0

magnetic susceptibility

Paramagnetism

Pierre Curie discovered experimentally that the magnetization M of a paramagnetic specimen obeyed:

⎟⎠

⎞⎜⎝

⎛=T

BCM

M cannot increase without limit, as Curies’s law implies, but must approach a value

V

NM

μ=max

Potassium chronium sulphate - a paramagnetic salt

rC

Diamagnetism

Atoms have no intrinsic magnetic dipoles

Dipole moments induced by the application of an external magnetic field

Induced B-field opposes the external field (Lenz’s law)

B < B0

rC

Diamagnetism

No intrinsic magnetic dipoles

Dipole moments induced by an external magnetic field

Induced B-field opposes the external field (Lenz’s law)

B < B0

{Compare with a paramagnetic material B > B0}

Lenz’s LawDirection of the induced current is such that it produces a magnetic field, which opposes the magnetic field which gave rise to that current

Bext

Diamagnetism

Permeabilities of Some Diamagnetic Materials

FerromagnetismMaterials with atoms having unpaired electron spins (iron, cobalt, nickel, gadolinium, and dysprosium). Electron spins aligned 1010 atoms combine to form a domain (l 10-7 m) large magnetic moment.

When the domains are randomly arranged, the specimen as a whole is unmagnetised.

Domains which are magnetized in the direction of an external magnetic field grow at the expense of those which are not aligned to the magnetic field.

Bex

m becomes very large 103 – 105

Ferromagnetism

Materials may be broadly grouped into one of 3 categories; diamagnetic, paramagnetic, or ferromagnetic.

Review and Summary

Paramagnetic materials are (weakly) attracted by a magnetic field, have intrinsic magnetic dipole moments that tend to line up with an external magnetic field, thus enhancing (slightly) the field. This tendency is interfered with by thermal agitation.

Ferromagnetic materials result from spontaneous alignment of the dipole moment of atoms and the formation of large magnetic domains.

Review and Summary

Diamagnetic materials are (weakly) repelled by the pole of a strong magnet. The atoms of such materials do not have intrinsic magnetic dipole moments. A dipole moment may be induced, however, by an external magnetic field, its direction being opposite that of the field.

Exam: Temperature and Matter

27 May 2008

Revision:12.00, 6 May and 1.00pm, 9 May

The amount of time that I have

borrowed from you: 15 minutes

I will pay you back

15 minutes +200% interest

No lecture tomorrow

See you after Easter.

Magnetization Curve for a Ferromagnetic MaterialAll magnetic moments in the material are aligned parallel to the external field

Ferromagnetism

Ferromagnetism: Magnetization Curves and Hysteresis Loops

Magnetization is different when the external magnetic field is increasing from when it is decreasing - hysteresis loop

Ferromagnetism: Magnetization Curves and Hysteresis Loops

Part ofCurve

Operation

a to b increase of B0, using anunmagnetized ferromagneticfield

b to c B0 reduced to zeroc to d B0 is reversed in di rection,

and its magnitude increasedto a maximum

d to e B0 is again reduced to zeroe to f B0 is again increased to its

forward maximum

Part ofCurveOperationa to bincrease of B0, using anunmagnetized ferromagneticfieldb to cB0 reduced to zeroc to dB0 is reversed in direction,and its magnitude increasedto a maximumd to eB0 is again reduced to zeroe to fB0 is again increased to itsforward maximum

Ferromagnetism: Magnetization Curves and Hysteresis Loops

Ferromagnetism: Magnetization Curves and Hysteresis Loops

Part ofCurve

Operation

a to b increase of B0, using anunmagnetized ferromagneticfield

b to c B0 reduced to zeroc to d B0 is reversed in di rection,

and its magnitude increasedto a maximum

d to e B0 is again reduced to zeroe to f B0 is again increased to its

forward maximum

Ferromagnetism: Magnetization Curves and Hysteresis Loops

Part ofCurve

Operation

a to b increase of B0, using anunmagnetized ferromagneticfield

b to c B0 reduced to zeroc to d B0 is reversed in di rection,

and its magnitude increasedto a maximum

d to e B0 is again reduced to zeroe to f B0 is again increased to its

forward maximum

Ferromagnetism: Magnetization Curves and Hysteresis Loops

Part ofCurve

Operation

a to b increase of B0, using anunmagnetized ferromagneticfield

b to c B0 reduced to zeroc to d B0 is reversed in di rection,

and its magnitude increasedto a maximum

d to e B0 is again reduced to zeroe to f B0 is again increased to its

forward maximum

Ferromagnetism: Magnetization Curves and Hysteresis Loops

Magnetization is different when the external magnetic field is increasing from when it is decreasing - hysteresis loop

Explanation - reorientations of domain directions are not totally reversible

Uses - magnetic storage of information

Nuclear Magnetism: An Aside

Nuclear magnetic resonance (NMR) - employs the magnetic moment of the protons in some of the nuclei being examined.

Note: nuclear magnetism does not contribute in a measurable way to the gross magnetic properties of solids.

Review and Summary

Effect χm mOrigindiamagnetism

∼

-10-5< 1 , distortion according to ’ Lenz s Lawparamagnetism

∼

10-3> 1 orientation of magnetic dipoles inmaterialferromagnetism depend onB0, but can be extremely large

∼

103 magnetic domains

NEXT

The final piece!

Maxwell: Electricity plus Magnetism Gives Light

Paramagnetism

Ampere’s law in materials becomes:

freem IldB 0. μ=∫

Ifree refers to the external currents