A group-theoretical analysis is used to express the Zeeman splittings of interband optical transitions at a critical point Λ or L in terms of band-electron–Mn-d-electron exchange interaction values at that k. The ${\mathrm{\sigma }}_{+}$-to-${\mathrm{\sigma }}_{\mathrm{-}}$ overall splitting of the ${\mathit{E}}_1$ transition (${\mathrm{\Lambda }}_{4,5}^{\mathit{v}}$→${\mathrm{\Lambda }}_6^{\mathit{c}}$) is shown to be, in general, equal but opposite to that of the spin-orbit-related ${\mathit{E}}_1$+${\mathrm{\Delta }}_1$ transition (${\mathrm{\Lambda }}_6^{\mathit{v}}$→${\mathrm{\Lambda }}_6^{\mathit{c}}$), in agreement with recent experiments in ${\mathrm{Hg}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te. The k dependence of the exchange interaction is discussed within a simple model. The splitting of ${\mathit{E}}_1$ thus estimated is about 2.5 times larger in ${\mathrm{Hg}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te than in ${\mathrm{Cd}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te or ${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te alloys; this explains the observed chemical variation.

• Received 27 November 1989

DOI:https://doi.org/10.1103/PhysRevB.41.5696