Chapter 27Magnetism in Matter

Topics

Magnetization

Saturation magnetization

Types of materials

Magnetization

Atoms have magnetic dipole moments due to

orbital motion of the electrons

magnetic moment of the electron

Material placed in magnetic field magnetic dipole moments aligned material “magnetized”

Magnetization

magnetization = net magnetic dipole moment per unit volume

magnetization contributes an additional magnetic, Bm, given by

dM

dV

m oB M

Magnetization

Magnetic susceptibility

Magnetization M depends on applied field Bapp and the susceptibility m of the material

a

o

ppm

BM

m m appBB

Magnetic susceptibility

For paramagnets: m > 0

For diamagnets: m < 0 Total field:

Km = relative permeability of the material

(1 )app app apo m m pB B BB M K

1m mK

Magnetic moment and angular momentum

Angular momentum For circular motion L = rmv Magnetic moment of current

loop = IA = Iπr2

For single charge q on circular orbit I = q/T = qv/(2πr) =Iπr2 = qvπr2/(2πr) = qvr/2 = qL/(2m)

L r p

2

qL

m

Saturation magnetization

Magnetization grows with applied field until all magnetic moments are aligned --“saturation”

At saturation, the magnetization is Ms = n•μ, where n is number of atoms per unit volume and μ is the magnetic moment of each atom

Types of Materials

Materials exhibit three types of magnetism:paramagnetic

diamagnetic

ferromagnetic

Paramagnetism

Paramagnetic materials have permanent magnetic

moments

moments randomly oriented at normal temperatures

adds a small additional field to applied magnetic field

Paramagnetism

Small effect (changes B by only 0.01%)

Example materialsOxygen (STP), aluminum,

tungsten, platinum

Diamagnetism

Diamagnetic materialsno permanent magnetic

moments

magnetic moments induced by applied magnetic field B

applied field creates magnetic moments opposed to the field

Diamagnetism

Common to all materials.

Applied B field induces a magnetic field opposite the applied field, thereby weakening the overall magnetic field

But the effect is very small:Bm ≈ -10-4 Bapp

Diamagnetism

Example materials High temperature

superconductorscoppersilver

Ferromagnetism

Ferromagnetic materialshave permanent magnetic

moments

align at normal temperatures when an external field is applied and strongly enhances applied magnetic field

Ferromagnetism

Ferromagnetic materials (e.g. Fe, Ni, Co, alloys) have domains of randomly aligned magnetization (due to strong interaction of magnetic moments of neighboring atoms)

Ferromagnetism

Applying a magnetic field causes domains aligned with the applied fieldto grow at the expense of othersthat shrink

Saturation magnetization is reachedwhen the aligned domains have replaced all others

Ferromagnetism

In ferromagnets, some magnetization will remain after the applied field is reduced to zero, yielding permanent magnets

Such materials exhibithysteresis

Material properties

Summary

The magnetism of materials is due to the magnetic dipole moments of atoms, which arise from:the orbital motion of electrons

and the intrinsic magnetic moment of each electron

Summary

Three classes of materialsDiamagnetic M = - const • Bext,

small effect (10-4)Paramagnetic M = + const •

Bext small effect (10-2)

Ferromagnetic M ≠ const • Bext

large effect (1000)