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Remove DMI subscript.
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marijanbeg committed Mar 12, 2018
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Expand Up @@ -17,7 +17,7 @@ Different Dzyaloshinskii-Moriya interaction forms can be written as different co

The DMI energy density for the crystallographic classes T and O as a sum of Lifshitz invariants [1] is

<a href="https://www.codecogs.com/eqnedit.php?latex=\LARGE&space;w_{\text{DMI}}&space;&&space;=&space;D&space;\left(&space;\mathcal{L}_{zy}^{(x)}&space;&plus;&space;\mathcal{L}_{xz}^{(y)}&space;&plus;&space;\mathcal{L}_{yx}^{(z)}&space;\right)&space;=&space;D&space;\mathbf{m}&space;\cdot&space;\left(&space;\bm{\nabla}&space;\times&space;\mathbf{m}&space;\right)" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\LARGE&space;w_{\text{DMI}}&space;&&space;=&space;D&space;\left(&space;\mathcal{L}_{zy}^{(x)}&space;&plus;&space;\mathcal{L}_{xz}^{(y)}&space;&plus;&space;\mathcal{L}_{yx}^{(z)}&space;\right)&space;=&space;D&space;\mathbf{m}&space;\cdot&space;\left(&space;\bm{\nabla}&space;\times&space;\mathbf{m}&space;\right)" title="\LARGE w_{\text{DMI}} & = D \left( \mathcal{L}_{zy}^{(x)} + \mathcal{L}_{xz}^{(y)} + \mathcal{L}_{yx}^{(z)} \right) = D \mathbf{m} \cdot \left( \bm{\nabla} \times \mathbf{m} \right)" /></a>
<a href="https://www.codecogs.com/eqnedit.php?latex=\LARGE&space;w&space;&&space;=&space;D&space;\left(&space;\mathcal{L}_{zy}^{(x)}&space;&plus;&space;\mathcal{L}_{xz}^{(y)}&space;&plus;&space;\mathcal{L}_{yx}^{(z)}&space;\right)&space;=&space;D&space;\mathbf{m}&space;\cdot&space;\left(&space;\bm{\nabla}&space;\times&space;\mathbf{m}&space;\right)" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\LARGE&space;w&space;&&space;=&space;D&space;\left(&space;\mathcal{L}_{zy}^{(x)}&space;&plus;&space;\mathcal{L}_{xz}^{(y)}&space;&plus;&space;\mathcal{L}_{yx}^{(z)}&space;\right)&space;=&space;D&space;\mathbf{m}&space;\cdot&space;\left(&space;\bm{\nabla}&space;\times&space;\mathbf{m}&space;\right)" title="\LARGE w & = D \left( \mathcal{L}_{zy}^{(x)} + \mathcal{L}_{xz}^{(y)} + \mathcal{L}_{yx}^{(z)} \right) = D \mathbf{m} \cdot \left( \bm{\nabla} \times \mathbf{m} \right)" /></a>

where <a href="https://www.codecogs.com/eqnedit.php?latex=D&space;[\text{J}/\text{m}^{2}]" target="_blank"><img src="https://latex.codecogs.com/gif.latex?D&space;[\text{J}/\text{m}^{2}]" title="D [\text{J}/\text{m}^{2}]" /></a> is the DMI constant and <a href="https://www.codecogs.com/eqnedit.php?latex=\mathbf{m}&space;=&space;\mathbf{M}/M_\text{s}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\mathbf{m}&space;=&space;\mathbf{M}/M_\text{s}" title="\mathbf{m} = \mathbf{M}/M_\text{s}" /></a> is the normalised magnetisation field.

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