anti-symmetric exchange operator package for Stoch Magnet module contains anti-symmetric exchange classes.
anti-symmetric exchange operator package for Stoch Magnet module contains anti-symmetric exchange classes.
The Dzyaloshinskii-Moriya Interaction energy of a spin is \( E^i_{dmi}=\displaystyle - \sum_{j \neq i} D_{ij} S_i \wedge Sj \).
The corresponding DMI magnetic field which verifies \( H^i = - \frac{1}{\mu_s} \frac{\partial E}{\partial S_i} \) is
\( H^i_{dmi}= \displaystyle \frac{1}{\mu_s} \sum_{j\neq i } S_j \wedge D_{ij} \).
The total DMI energy of the system is \( E_{dmi}=\displaystyle \frac{1}{2} \sum_i E^i_{dmi}=-\frac{1}{2}. \sum_i \sum_{j \neq i} D_{ij} \cdot S_i \wedge S_j\)
The package contains the class:
- SM_DMIOperator to compute the Dzyaloshinskii-Moriya Interaction operator for connection value \( D_{ij} \)
The UML organization of the package is as follow:
