Magnetism

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Magnetism
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Overview of magnetic materials
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Magnetic objects
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Magnetic field lines
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Molecular magnetism, example 1
Paramagnets are attracted to magnetic fields
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Paramagnetic gases
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Organic radicals are magnetic
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Zeeman splitting and NMR
gap g mz B
g Lande g-factor (2 for e) mz magnetic
moment B magnetic field strength Nuclear gap
energy corresponds to radio frequencies
Certain nucleii have a magnetic spin, and are
therefore active in NMR experiments
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Metals

• Many metals have unpaired electrons due to the
  high d-orbital degeneracy.

n 3 unpaired spins S 3/2 magnetic moment
octahedral Cr3 has 3 d-electrons
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Metals

• Multiple spin arrangements (HS, LS) are possible
  for a given number of d-electrons (in this case,
  7 valence electrons).

n 3 unpaired spins S 3/2 magnetic moment
n 1 unpaired spins S 1/2 magnetic moment
halides lt OH lt C2O42- lt H2O lt NCS lt py lt NH3 lt
en lt phen lt NO2 lt CN lt CO
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Zeeman splitting and NMR
gap g mz B
g Lande g-factor (2 for e) mz magnetic
moment B magnetic field strength Nuclear gap
energy corresponds to radio frequencies
Certain nucleii have a magnetic spin, and are
therefore active in NMR experiments
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paramagnet (disordered spins)
ferromagnet (co-aligned spins)
antiferromagnet (anti-aligned spins)
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Ferromagnets have a persistent moment, even
without a magnetic field
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cM vs T for ferromagnets
ferromagnetic
paramagnetic
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The math of magnetism
cM Molar susceptibility meff Effective
moment mB Bohr magneton
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Useful experimental quantity

• Molar magnetic susceptibility, cM
• Magnetic susceptibility per mole
• Why use molar and not the gram
  susceptibility?

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Moment per metal atom

• S total spin (1/2 per e )
• n unpaired e
• meff moment in Bohr magnetons (mB)
• g magnetogyric ratio (Landé g-facor, 2)
• mB 9.27 x 10-24 J / T

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Magnetic susceptibility, cM
(Curie Law assumes no spin-spin interactions)

• cM measurable quantity (M / H)
• Can calculate meff from cM
• Can calculate of unpaired electrons from meff

(units are slightly fudged)
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Magnetic susceptibility, cM
(Curie Law)

• Simple approximations break down when spins are
  not isolated from each other

(Curie-Weiss law)