Magnetic dipole-dipole interaction

Magnetic dipole-dipole interaction, also called dipolar coupling, refers to the direct interaction between two magnetic dipoles. The energy of the interaction is as follows:

$\bold{H} = - \frac{ \hbar \mu_0 } {4 \pi r_{ij}^3 } \left( 3 (\bold{m}_j \cdot \bold{e}_{jk}) (\bold{m}_k \cdot \bold{e}_{jk}) - \bold{m}_j \cdot \bold{m}_k \right)$