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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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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.

- 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

- In general is the algebraic sum of two contributions associated with different phenomena:
= D + P

D is diamagnetic susceptibility

P is paramagnetic susceptibility

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

Brillouin Function

- Substituting for P we obtain the Brillouin function

Curie Law

where C = Ng2mB2/(4kB) is the Curie constant

Since the magnetic susceptibility is defined as = M/H

the Curie Law results:

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.

Curie-Weiss paramagnetism

q is the Weiss constant

Curie-Weiss paramagnetism

Plots obeying the Curie-Weiss law with a negative Weiss constant

Curie-Weiss paramagnetism

Plots obeying the Curie-Weiss law with a positive Weiss constant

Ferromagnetism

J positive with spins parallel below Tc

Antiferromagnetism

- J negative with spins antiparallel below TN

Ferrimagnetism

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

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

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

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)

Mn12

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

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