(3, 3) terms#

Third type of the trilinear terms, in which all three spin operators are associated with different sites. In this page we imply that \(\boldsymbol{r}_{\mu,\alpha_1}\), \(\boldsymbol{r}_{\mu + \nu_2, \alpha_2}\), and \(\boldsymbol{r}_{\mu + \nu_3, \alpha_3}\) are all different.

\[\begin{split}C_{3, 3} \sum_{\substack{\mu, \nu_2, \nu_3 \\ \alpha_1, \alpha_2, \alpha_3 \\ i_1, i_2, i_3}} J^{i_1, i_2, i_3}_{\nu_2,\nu_3; \alpha_1,\alpha_2,\alpha_3} S_{\mu, \alpha_1}^{i_1} S_{\mu + \nu_2, \alpha_2}^{i_2} S_{\mu + \nu_3, \alpha_3}^{i_3}\end{split}\]

Relevant API#