Magnetism in Chemistry

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Magnetism in Chemistry
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General concepts

• There are three principal origins for the
  magnetic moment of a free atom
• The spins of the electrons. Unpaired spins give a
  paramagnetic contribution.
• The orbital angular momentum of the electrons
  about the nucleus also contributing to
  paramagnetism.
• The change in the orbital moment induced by an
  applied magnetic field giving rise to a
  diamagnetic contribution.

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• The molar magnetic susceptibility ? of a sample
  can be stated as

• M/H

M is the molar magnetic moment
H is the macroscopic magnetic field intensity
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• In general ? is the algebraic sum of two
  contributions associated with different
  phenomena
• ? ?D ?P

?D is diamagnetic susceptibility ?P is
paramagnetic susceptibility
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Curie paramagnetism
Energy diagram of an S1/2 spin in an external
magnetic field along the z-axis
?E gmBH, which for g 2 corresponds to about 1
cm-1 at 10000G
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Brillouin Function

• M N S mnPn N (m½P½ m-½P-½)
• mn -msgmB, Pn Nn/N with S Nn

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Brillouin Function


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Brillouin Function

• Substituting for P we obtain the Brillouin
  function

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Brillouin Functions for different S
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Curie Law
where C Ng2mB2/(4kB) is the Curie constant
Since the magnetic susceptibility is defined as ?
M/H the Curie Law results
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? vs. T plot 1/? T/C gives a straight line of
gradient C-1 and intercept zero ?T C gives a
straight line parallel to the X-axis at a
constant value of ?T showing the temperature
independence of the magnetic moment.
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Curie-Weiss paramagnetism
q is the Weiss constant
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Curie-Weiss paramagnetism
Plots obeying the Curie-Weiss law with a negative
Weiss constant
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Curie-Weiss paramagnetism
Plots obeying the Curie-Weiss law with a positive
Weiss constant
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Ferromagnetism

• J positive with spins parallel below Tc

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Antiferromagnetism

• J negative with spins antiparallel below TN

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Ferrimagnetism

• J negative with spins of unequal magnitude
  antiparallel below critical T

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Spin Hamiltonian in Cooperative Systems
This describes the coupling between pairs of
individual spins, S, on atom i and atom j with J
being the magnitude of the coupling
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Magnetisation

• Knowing how M depends on B through the
  Brillouin function and assuming that B 0 we can
  plot the two sides of the equation as functions
  of M/T

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Temperature dependence of M
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Ferromagnets
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Ferromagnets
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Ferromagnets
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Ferromagnets
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Domains
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Domains
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Hysteresis
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Spin Frustration
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SUPERPARAMAGNETS

• These are particles which are so small that they
  define a single magnetic domain.
• Usually nanoparticles with a size distribution
• It is possible to have molecular particles which
  also display hysteresis effectively behaving as
  a Single Molecule Magnet (SMM)

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Mn12
Orange atoms are Mn(III) with S 2, green are
Mn(IV) with S 3/2
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Mn12
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Mn12 Spin Ladder
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Hysteresis in Mn12