Lecture 19 Magnetism and MatterLearning Objective: to examine some aspects of magnetic properties of materials

Transformers

Motors

Generators (for examples)

- nearly always have iron cores

Permanent Magnets

Magnetic Recording Tapes

Computer Disks (for examples)

- all depend directly on the magnetic properties of materials

v

L

2rI

e

I r

ev

2

2

evr

Angular Momentum L = mevr

Lm

e

e2

Orbital Motion

Magnetism and Spin

eBS m

e

2

)T (J mA 10274.9 -1224Atom Magnetic Dipole

Moment(/10-24 A m2)

H 9.27He 0Li 9.27O 13.9Ne 0Na 9.27

Paramagnetism•Atoms of a paramagnetic material have permanent magnetic dipole moments.

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

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

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

CompareTkB2

3with 2B

Example: T = 300 K, B = 1.5 T, = B eV 039.02

3 TkU BT

eV 00017.02 BU BB

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

0BB mmBBB 0

Ampere’s law in materials becomes:

freem IldB 0. Ifree refers to the external currents

Magnetic moment per unit volume (magnetisation) M:V

M total

MBm 0 MBB 00 0

00

1B

M

B

B 0

01B

Mm

mm0

0 1B

M magnetic susceptibility

Material (STP) m

Air 1.000304Oxygen 1.00133Liquid Oxygen (-190oC) 1.00327Nickel Monoxide 1.000675

Potassium chronium sulphate - a paramagnetic salt

T

BCM

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

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

V

NM

max

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 No intrinsic magnetic dipoles

{Compare with a paramagnetic material B > B0}

Permeabilities of Some Diamagnetic MaterialsMaterial (STP) m

Bismuth 1 – 1.910-5

Beryllium 1 – 1.310-5

Methane 1 – 3.110-5

Glass 1 – 1.510-5

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

Bextm becomes very large 103 – 105

Magnetization Curve for a Ferromagnetic Material

All magnetic moments in the material are aligned parallel to the external field

Ferromagnetism: Magnetization Curves and Hysteresis LoopsMagnetization is different when the external magnetic field is increasing from when it is decreasing - hysteresis loopExplanation - reorientations of domain directions are not totally reversibleUses - magnetic storage of information

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 direction,

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

•Materials may be broadly grouped as 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.

•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.

•Ferromagnetic materials result from a quantum interaction between neighbouring atoms locking the atomic dipoles in rigid parallelism in spite of the disordering tendency of thermal agitation. Due to strong alignment of the spin magnetic moments of the electrons (quantum mechanical effects).

Hysteresis: ferromagnetic magnetization curves do not retrace themselves but instead exhibit a phenomenon called hysteresis. Some alignment of dipoles remains even when the external magnetic field is completely removed; the result is the familiar “permanent” magnet.

Review and Summary

Effect m m Origindiamagnetism -10-5 < 1 distortion, according

to Lenz’s Lawparamagnetism 10-3 > 1 orientation of

magnetic dipoles inmaterial

ferromagnetism depend onB0 , but canbe extremelylarge 103

magnetic domains