Zeeman energy, or the external field energy, is the potential energy of a magnetised body in an external magnetic field. It is named after the Dutch physicist Pieter Zeeman, primarily known for the Zeeman effect. In SI units, it is given by

E Z e e m a n = − μ 0 ∫ V M ⋅ H E x t d V {\displaystyle E_{\rm {Zeeman}}=-\mu _{0}\int _{V}\,{\textbf {M}}\cdot {\textbf {H}}_{\rm {Ext}}\,\mathrm {d} V}

where HExt is the external field, M the local magnetisation, and the integral is done over the volume of the body. This is the statistical average (over a unit volume macroscopic sample) of a corresponding microscopic Hamiltonial (energy) for each individual magnetic moment m, which is however experiencing a local induction B:

H = − m ⋅ B {\displaystyle H=-{\textbf {m}}\cdot {\textbf {B}}}

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  • Hubert, A. and Schäfer, R. Magnetic domains: the analysis of magnetic microstructures, Springer-Verlag, 1998