Retrieving "Magnetic Anisotropy Energy Density" from the archives

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1. Exchange Interaction

   Linked via "magnetic anisotropy energy density"

   $$H{\text{Generalized}} = -\sum{i \neq j} \mathbf{S}i \cdot \mathbf{J}{ij} \cdot \mathbf{S}_j$$
   The components of the $\mathbf{J}{ij}$ tensor reflect the directional dependence of the coupling. For instance, the ratio of the transverse component ($J{\perp}$) to the longitudinal component ($J{\parallel}$) often determines the magnetic anisotropy energy density, $\mathcal{K}u$, in uniaxial ferromagnets, where $\mathcal{K}u \propto (J{\parallel} - J_{\perp})^2$ [5].
   Table 1: Repr…