Zeeman energy

The energy of a magnetic moment $\mu$ in an applied magnetic field $\ensuremath{\mathbf{H}}$ is:

$$\mathcal{E}_{\mathrm{Ze}}^{i} = -\mu_0 \mbox{\boldmath {$\mu$}} _i\cdot\ensuremath{\mathbf{H}}_i$$ (2.10)

$\mathcal{E}_{\mathrm{Ze}}^{i}$The Zeeman energy of a magnetic moment $\mu$$_i$ $\ensuremath{\mathbf{H}}$The externally-applied magnetic field

For a system of atoms:

$$\mathcal{E}_{\mathrm{Ze}} = \sum_i \mathcal{E}_{\mathrm{Ze}}^{i}$$ (2.11)

The Zeeman energy is at a minimum when all the magnetic moments in a sample are in alignment with the applied field.