Magnetic Properties

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Magnetic Properties

• Subhalakshmi Lamba

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Scope of the Lecture

• History of Magnetism electricity magnetism

• Quantities used to describe magnetic properties

• Different types of magnetism

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Scope of the Lecture

• Classical Theories

• The need for a quantum theory

• Quantum Theory of Paramagnetism

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A story

• References to a herdsman Magnes by a Greek
  historian Pliny

• Known in China and Europe -800 BC

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LODESTONE
Typical current 1,000,000 Amp.

• Lodestone contains iron oxide mineral
• magnetite
• When lightning strikes the earth it could
  create a magnetic field large enough to saturate
  the magnetization of lodestone .

Once in 1 10 million years
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THE FIRST MAGNETIC DEVICES
Chinese Portugese compasses (16 th century )
floating fish-shaped iron leaf Wu Ching Tsung
Yao ( written in 1040)
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Magnets in a car
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In the future
Quantum Computers
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Electricity Magnetism

• Electrified Amber attracts small objects
• Lodestone attracts iron

A Connection ?
Hans Christian Ørsted ( 1777 1851)
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Oersteds Experiment

• placed a wire above the compass needle
• connected both ends across a battery
• the needle spun until it was at right angles to
  the wire

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Farradays Ideas
A quantitative relationship between a changing
magnetic field and the electric field created by
the change
Michael Faraday  (1791-1867)
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Effect of a changing magnetic field
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Ampere's Law
The magnetic field in space around an electric
current is proportional to the electric current
which serves as its source.
For any closed loop path, the sum of the length
elements times the magnetic field in the
direction of the length element is equal to the
permeability times the electric current enclosed
in the loop .
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Magnetic field due to a long wire
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Biot and Savart's Law
magnetic field due to an arbitrary current
distribution
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Maxwells Equations
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Maxwells Equations
James Clerk Maxwell (1831 - 1879)
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Magnetic Field

• A force field similar to the gravitational and
  electrical field, detected by a probe.
• Force experienced by the probe due to the field
• Sources of a magnetic field are magnetic poles
• Fictitious points near the ends of a magnet

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Magnetic Field

• Magnetic fields are produced by electric
  currents
• can be macroscopic currents in wires, or
  microscopic currents associated with electrons in
  atomic orbits.
• The magnetic field B is defined in terms of force
  on moving charge in the Lorentz force law.

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Magnetic Poles

• the external magnetic field is strongest at the
  poles
• The two types of magnetic poles cannot exist
  separately always coupled together as a dipole.
• Isolated magnetic monopoles have not yet been
  detected.

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Magnetic Poles

• The attractive or repulsive force between two
  magnets decreased in proportion to the square of
  the distance between them

cgs
MKSA
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ELECTROMAGNETIC FORCE

• One of the four fundamental forces
• Electric Force and the Magnetic Force
• Lorentz Force

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Magnetic Field B

• Defined from the force on a moving charge
• Unit of magnetic field Newton seconds /(Coulomb
  meter) or Newtons /Ampere meter - Tesla
• Smaller unit is Gauss
• 1 Tesla 104 Gauss

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Magnetic Field Strength H

• Magnetic fields are generated by currents and
  measured in B (Tesla)
• magnetic materials themselves contribute
  internal magnetic fields when a magnetic field
  passes through them.
• To segregate the two contributions
• H B/?0 - M

Driving magnetic field
Material response
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Magnetic Field Strength H

• M Magnetization of the material
• B ?0 ( H M )
• B ? H ? ? ?r ?0

Permeability of space
Relative permeability Of the material
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Magnetic Susceptibility ?

• B ?0 ( H M )
• Replace B ? H ? ? H ?0 ( H M )
• ? ?r ?0 H ?0 ( H M )
• ? ?0 M ?0 (?r -1) H
• ? M (?r -1) H

?
Magnetic Susceptibility
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Unit of Magnetic Field

• Unit of H Ampere m -1
• H B / ?
• Oersted
• 1 Ampere m -1
• 0.01257 oersted

Tesla / N Ampere -2 N / Ampere m /N Ampere
-2 Ampere m -1
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Atomic magnetism / Magnetism in Matter

• S.J. Brugmans (1778)
• cobalt attracted
• bismuth antimony repelled
• by the single pole of a magnet
• Farraday (1845-1849)
• almost all matter has some magnetic property or
  the other (mostly to a very small degree)

? PARAMAGNETIM
? DIAMAGETISM
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Magnetic Materials
ROOM TEMPERATURE
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Explaining Magnetism in Matter

• Ampere
• existence of small molecular currents
• Each atom/molecule would behave as a small
  permanent magnet
• Would align in the presence of a magnetic field

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Thermal Properties of magnetic materials

• M is proportional to the applied field H
• ? Lim H ? 0 M / H
• ? C / T

CURIES LAW
PIERRE CURIE
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Thermal Properties of magnetic materials

• Does not imply that the magnetization can
  increase infinitely as temperature is lowered
  with increased magnetic field.
• Once all the magnetic dipoles are aligned the
  magnetization cannot increase further increase
• SATURATION

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Curies Law

• Normal paramagnetic substances obey the Curie Law
  
• Examples Aluminum, platinum, manganese,
  chromium

?C/T
?
1/?
1/?T/C
T in K
T in K
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Diamagnetism

• The susceptibility, ? is negative
• It does not change much with temperature
• Examples water, inert gases

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Ferromagnetism
Curie Temperature TC

• M decreases rapidly with H
• Beyond the Curie temperature it behaves like a
  paramagnetic substance
• Examples iron, cobalt, nickel

Behaves like a paramagnet
M decreases rapidly with H
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Antiferromagnetism

• like paramagnets above a critical temperature TN
  called Neél temperature.
• Below TN ? is small T-dependence is different
  from paramagnets.
• Example Cobalt

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Ferrimagnetism

• Like ferromagnets, but the effect tends to be
  smaller.
• The 1/? curve is very close to zero below a
  critical temperature, also called Neél
  temperature.
• Examples magnetite (Fe3O4) and spinel ferrites

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A COMPARISON
DIAmagnetic
PARAmagnetic
FERROmagnetic
ANTIFERROmagnetic
FERRImagnetic
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A COMPARISON
DIAmagnetic
PARAmagnetic
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A COMPARISON
FERROmagnetic
B
ANTIFERROmagnetic
FERRImagnetic
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A COMPARISON
(?r -1)? ? ?r ?1
PARAmagnetic
DIAmagnetic

• ? gt 0, ?r gt 1

• ? lt 0 , ?r lt 1
• ?r 0
• (superconductors)

FERROmagnetic

• ? gt 0, ?r gtgt 1

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Novel Magnetism

• SPIN GLASS A random orientation of frozen
  spins.
• CLUSTER GLASS spins make small clusters with
  magnetic order but no order between clusters
• METAMAGNET Field induced magnetic transition
  from a low magnetization state to a relatively
  much higher magnetization state

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Novel Magnetism

• Superparamagnet when the size of the
• magnetic particle is very small domains are
  not formed . Each magnetic particle behaves a
  giant paramagnetic ion.

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A RECAP

• Origin of magnetism
• Connection between electricity and magnetism
  electric currents produce magnetic fields
• Magnetism in matter
• Temperature dependence of magnetic properties
  CURIES law

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A RECAP

• Temperature dependence of magnetic properties
  CURIES law
• Different types of magnetic properties
• Classical theories
• Their limitations
• QUANTUM THEORIES