and $H_z$ are the planar and axial components of an applied external field. Finally, the last term, ${\cal H}_{nd}(J_{xz})$, is a nondiagonal intralayer exchange between axial and planar spin components with the strength $J_{xz}$,[@muk81] involving only products of pairs of spins. In order to illustrate this interaction, which is invariant when applying the symmetry elements of the trigonal point group, consider two neighboring in-layer sites, called 0 and 1, with the same value of $y$. The nondiagonal exchange may be written in the form[@muk81] $${\cal H}_{nd}(J_{xz}) = \sum\limits_{\left< \alpha \beta \right>} H_{\alpha \beta}(J_{xz})$$ where the sum is over nearest-neighbor in-layer sites $\left< \alpha \beta \right>$. For the pair $\left< \alpha \beta \right> = \left< 01 \right> $ this exchange takes the form[@muk81] $$H_{01} = - J_{xz} \left( S_0^z S_1^x + S_0^x S_1^z \right) .$$ The other terms in Equation (2) are obtained by applying the appropriate symmetry elements transforming the pair $\left< 01 \right>$ onto $\left< \alpha \beta \right>$.

As this model, defined on a hexagonal lattice, is rather complicated, it is preferable to study the effects of the semi-classical approximation, of the nondiagonal exchange, and of the planar field component first in simpler models. Therefore, I consider also the 