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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.

## 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 • Substituting for P we obtain the Brillouin function

8. Brillouin Functions for different S

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

10. 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.

11. Curie-Weiss paramagnetism q is the Weiss constant

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

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

14. Ferromagnetism J positive with spins parallel below Tc

15. Antiferromagnetism • J negative with spins antiparallel below TN

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

17. 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

18. 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

19. Temperature dependence of M

20. Ferromagnets

21. Ferromagnets

22. Ferromagnets

23. Ferromagnets

24. Domains

25. Domains

26. Hysteresis

27. Spin Frustration

28. 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)

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

30. Mn12