A Local Gauge Description of the Interaction between Magnetization and Electric Field in a Ferromagnet

We apply a non-abelian gauge field approach to generalize the micromagnetic energy description of a ferromagnet. This approach, without further assumption, takes into account three different energy terms: the well-known exchange term, chiral ones, and an intrinsic anisotropy term. In the non-abelian gauge field approach, the covariant gauge derivative plays a key role. The result is the emergence of a Dzyaloshinskii-Moriya-like energy term under two conditions: the first one is the pure gauge field background and the second one is the presence of a static electric field. Moreover, this approach allows one to reach a more deep understanding of the micromagnetics theory if rewritten in a gauge-invariant formulation. In this article, clearly emerges the interpretation of the voltage-controlled magnetic anisotropy (VCMA) mechanism.