Magnetic dipole–dipole interaction
Magnetic dipole–dipole interaction, also called dipolar coupling, refers to the direct interaction between two magnetic dipoles.
Suppose m1 and m2 are two magnetic moments in space. The potential energy H of the interaction is then given by:
where μ0 is the magnetic constant, r̂ is a unit vector parallel to the line joining the centers of the two dipoles, and |r| is the distance between the centers of m1 and m2. Alternatively, suppose γ1 and γ2 are gyromagnetic ratios of two particles with spin quanta S1 and S2. (Each such quantum is some integral multiple of 1/2.) Then:
where r̂ is a unit vector in the direction of the line joining the two spins, and |r| is the distance between them.
The force F arising from the interaction between m1 and m2 is given by:
The direct dipole-dipole coupling is very useful for molecular structural studies, since it depends only on known physical constants and the inverse cube of internuclear distance. Estimation of this coupling provides a direct spectroscopic route to the distance between nuclei and hence the geometrical form of the molecule, or additionally also on intermolecular distances in the solid state leading to NMR crystallography notably in amorphous materials.
For example, in water, NMR spectra of hydrogen atoms of water molecules are narrow lines because dipole coupling is averaged due to chaotic molecular motion. In solids, where water molecules are fixed in their positions and do not participate in the diffusion mobility, the corresponding NMR spectra have the form of the Pake doublet. In solids with vacant positions, dipole coupling is averaged partially due to water diffusion which proceeds according to the symmetry of the solids and the probability distribution of molecules between the vacancies.
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