Download Magnetism - Illinois State University

Soft Gamma Repeater 1806-20,
is the most powerful known
magnetic object in the universe.
Only 10 of these unusual objects
have been discovered. With a
magnetic-field strength of 100
billion T.
0.00005 T
Magnetism
Physics 355
National Magnet Lab (FL) 45 T
From whence does magnetism come?
1. No answer from classical physics...
2. What is the role of conduction electrons?
3. What is the effect of localized electrons?
4. How do we make powerful permanent magnets?
Magnetism
Quantum
Mechanics
ElectronElectron
Interactions
Quantum
Mechanics
•
Why is magnetism a quantum
effect?
Classically, the change in energy of a particle with respect to time is
dE
 Fv
dt
...But in a magnetic field, the force on the electron due to the field is
always perpendicular to the electron’s velocity. This would mean that
the energy of a system should not be able to change in the presence of
a magnetic field – Yet, it does!!
Orbital Angular Momentum
Quantum
Mechanics
All known magnetic
properties originate
from the attributes of
charged particles.
Magnetic
dipole
moment
e
 m  IA  
L
2m
U    B
The right-hand rule determines the direction of the magnetic moment of a
current-carrying loop. The direction of the electron's angular momentum
vector L can be obtained using the right hand rule for angular momentum.
Zeeman Effect
The Effect of Magnetisation on the
Nature of Light Emitted by a
Substance
P. Zeeman
Nature, vol. 55
11 February 1897, pg. 347
Zeeman Effect
When considering
atomic spectra, the
atomic energy levels,
the transitions between
these levels, and the
associated spectral
lines are produced with
no magnetic fields
influencing the atom.
If there are magnetic
fields present, the
energy levels are split
into a larger number of
levels and the spectral
lines are also split.
This splitting is called
the Zeeman Effect.
The total Hamiltonian of an atom in a magnetic field is:
where H0 is the unperturbed Hamiltonian of the atom, and the sums over α are
sums over the electrons in the atom. The term
is the spin-orbit interaction for each electron (indexed by α) in the atom. If there
is only one electron, the sum contains just a single term. The magnetic potential
energy
is the energy due to the magnetic moment μ of the α-th electron. It can be
written as a sum of the contributions of the orbital angular momentum L and the
spin angular momentum S, with each multiplied by the appropriate Landé gfactor, gL or gS. By projecting the vector quantities onto the z-axis, the
Hamiltonian may be written as
where the approximation results from taking the g-factors to be gL = 1 and gS 
2. The summation over the electrons was omitted for readability. Here, Jz = Lz +
Sz is the total angular momentum, and the spin-orbit (LS) coupling term has
been combined with H0 and written as Hat.
Zeeman Effect

MJ = +½
2
E  g B B
E  
g B B
2
1
MJ = ½
The probability that an ion is in a state with Jz = MJ
proportional to
E / kBT
e
is
 g B B / kBT
e
Quantum
Mechanics
Spin Quantization
 e 
m   
S

 2m 
Magnetism
Magnetic Susceptibility
B  0 H M 
0  4 10 7 H/m  4 10 7 T  m/A
H – magnetic field intensity (external)
M – magnetization, dipole moment per unit
volume (internal)
M

H
B  0 1  H   H
B
Magnetism
Magnetic Classifications
• Paramagnetic
 0
• Diamagnetic
 0
• Ferromagnetic
M  0 even when H  0
Example
• Suppose a long cylindrical specimen with a uniform
magnetization M parallel to its axis is placed in a uniform
applied magnetic field BA, applied along the axis of the
cylinder. Suppose the specimen has a magnetic
susceptibility .
• Find the magnitude of the magnetization M, the magnetic
induction B and the magnetic field intensity H.
M
Example - Answers
• If the material is paramagnetic, then the magnetization is
in the same direction as the applied field and it produces
a field 0M in the same direction as the applied field.
B  BA  μ0 M  (1  ) BA
BA  0 M  BA
B
M


0 (1  )
0 (1  )
0
B
BA
H
M 
0
0
Example - Answers
• If the material is diamagnetic, then the susceptibility is
negative. The results are the same as before, except
that B < BA.