Table 1 Most common DMI types with the corresponding symmetry class and DMI vectors.
DMI type | Symmetry class | Formula | DMI vectors \(\varvec{e}^\text {dmi}\) |
|---|---|---|---|
Interface | \(C_\text {nv}\) | \(\varvec{h}^\text {dmi,i}\) \(= -\frac{2 \, D_i}{\mu _0 \, M_s} \; \left[ \nabla \left( \varvec{e}_z \cdot \varvec{m} \right) - \left( \nabla \cdot \varvec{m} \right) \, \varvec{e}_z\right]\) | \((\varvec{e}_y, -\varvec{e}_x, 0)\) |
Bulk | T or O | \(\varvec{h}^\text {dmi,b}\) \(= -\frac{2 \, D_b}{\mu _0 \, M_s} \; \nabla \times \varvec{m}\) | \((\varvec{e}_x, \varvec{e}_y, \varvec{e}_z)\) |
\(D_\text {2d}\) | \(D_\text {2d}\) | Â | \((-\varvec{e}_x, \varvec{e}_y, 0)\) |
