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Lecture X Magnetism and Matter
Learning Objective: to examine some aspects of magnetic properties of materials
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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?
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Magnetism is intimately linked to
the behaviour of electrons in materials
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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)
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v
L
2rI πμ ×=
€
I =e
T r
ev
π2=
€
∴μ=evr
2Angular Momentum L = mevr
Lm
e
e2=μ
Orbital Motion
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v
L
Orbital Motion
Smallest magnetic moment (other than zero!)
eB m
e
2
h=μ
)T (J mA 10274.9 -1224−×=
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Magnetism and Spin
eBS m
e
2
h==μμ
The electron has
an intrinsic magnetic
moment! So are protons
and neutrons.
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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?
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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.
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Magnetic moment
of each atom is zero
Total moment is zero
Net moment zeroNet moment non-zero
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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
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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)
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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
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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
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Paramagnetism
Material (STP) mAir 1.000304Oxygen 1.00133Liquid Oxygen (-190oC) 1.00327Nickel Monoxide 1.000675
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Paramagnetism
Magnetic moment per unit volume (magnetisation) M:
VM total
μ=
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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
=
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mmB
M χμ =−= 10
0
magnetic susceptibility
Paramagnetism
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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
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Potassium chronium sulphate - a paramagnetic salt
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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
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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}
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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
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Diamagnetism
Permeabilities of Some Diamagnetic Materials
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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.
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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
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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.
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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.
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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
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No lecture tomorrow
See you after Easter.
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Magnetization Curve for a Ferromagnetic MaterialAll magnetic moments in the material are aligned parallel to the external field
Ferromagnetism
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Ferromagnetism: Magnetization Curves and Hysteresis Loops
Magnetization is different when the external magnetic field is increasing from when it is decreasing - hysteresis loop
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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
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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
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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
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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
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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
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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
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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.
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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
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NEXT
The final piece!
Maxwell: Electricity plus Magnetism Gives Light
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Paramagnetism
Ampere’s law in materials becomes:
freem IldB 0. μ=∫
Ifree refers to the external currents