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Magnetism in Chemistry

Magnetism in Chemistry. 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.

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Magnetism in Chemistry

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  1. Magnetism in Chemistry

  2. 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.

  3. 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

  4. In general  is the algebraic sum of two contributions associated with different phenomena:  = D + P D is diamagnetic susceptibility P is paramagnetic susceptibility

  5. Curie paramagnetism Energy diagram of an S=1/2 spin in an external magnetic field along the z-axis E = gmBH, which for g = 2 corresponds to about 1 cm-1 at 10000G

  6. Brillouin Function M = N SmnPn = N (m½P½ + m-½P-½) mn= -msgmB, Pn= Nn/N with S Nn

  7. Brillouin Function = =

  8. Brillouin Function • Substituting for P we obtain the Brillouin function

  9. Brillouin Functions for different S

  10. Curie Law where C = Ng2mB2/(4kB) is the Curie constant Since the magnetic susceptibility is defined as  = M/H the Curie Law results:

  11. 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.

  12. Curie-Weiss paramagnetism q is the Weiss constant

  13. Curie-Weiss paramagnetism Plots obeying the Curie-Weiss law with a negative Weiss constant

  14. Curie-Weiss paramagnetism Plots obeying the Curie-Weiss law with a positive Weiss constant

  15. Ferromagnetism J positive with spins parallel below Tc

  16. Antiferromagnetism • J negative with spins antiparallel below TN

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

  18. 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

  19. 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

  20. Temperature dependence of M

  21. Ferromagnets

  22. Ferromagnets

  23. Ferromagnets

  24. Ferromagnets

  25. Domains

  26. Domains

  27. Hysteresis

  28. Spin Frustration

  29. 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)

  30. Mn12 Orange atoms are Mn(III) with S = 2, green are Mn(IV) with S = 3/2

  31. Mn12

  32. Mn12 Spin Ladder

  33. Hysteresis in Mn12

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