  One of the remarkable properties of the II-VI diluted magnetic semiconductor
(ZnMn)Se is the giant spin splitting of the valence band states under
application of the magnetic field (giant Zeeman splitting). This splitting
reveals strong exchange interaction between Mn moments and semiconductor
states. On the other hand, no magnetic phase transition has been observed for
systems with small Mn content up to very low temperatures. The latter property
shows weakness of the exchange interaction between Mn moments. In this paper,
the local density approximation (LDA) and the LDA+U techniques are employed to
study exchange interactions in (ZnMn)Se. Supercell and frozen-magnon approaches
applied earlier to III-V diluted magnetic semiconductors are used. It is found
that both LDA and LDA+U describe successfully the combination of the strong
Zeeman splitting and weak interatomic exchange. However, the physical pictures
provided by two techniques differ strongly. A detailed analysis shows that the
LDA+U method provides the description of the system which is much closer to the
experimental data.
