long-range antiferromagnetic interactions between Mn pairs [@Gaj1979].

In reduced dimensions, under energy confinement conditions, the exchange interaction constant may differ from its bulk value. Indeed, modification of exchange parameters with QW thickness was observed in $\text{Cd}_{1-x}\text{Mn}_{x}\text{Te}/\text{Cd}_{1-x-y}\text{Mn}_{x}\text{Mg}_{y}\text{Te}$ heterostructures with $x_{\text{Mn}}\approx0.04-0.11$ [@Mackh1996]. These results agree with those of Ref. [@Merkulov1999], where an explanation of such an effect was suggested. The exchange interaction between conduction [*s*]{}-electrons from the center of the Brillouin zone and localized [*d*]{}-electrons has potential character and is positive. For electrons away from the $\Gamma$ point symmetry is no longer purely [*s*]{}-wave, because [*p*]{}-like states in the valence band admix to Bloch functions of the conduction band. This admixture introduces kinetic exchange correction to the exchange constant, and the magnitude of this correction depends on the degree of admixture. In the case of narrow QWs, kinetic exchange correction can even lead to a sign reversal of the exchange parameter. However, in recently measured $\text{Cd}_{1-x}\text{Mn}_{x}\text{Te}/\text{Cd}_{0.7}\text{Mg}_{0.3}\text{Te}$ QWs with much lower Mn content ($x\sim0.00146$ and $\sim0.00027$) no change in exchange constants was observed [@Rice2012]. Magnetooptical investigations revealed also a pronounced anisotropy of the in-plane Zeeman effect [@Peyla1993; @Kuhn-Heinrich1994] due to the valence band mixing. The anisotropy of the transverse hole effective $g$-factor $g^*_{\perp}$ 