Indirect-exchange interactions in zero-gap semiconductors

The indirect-exchange interaction between two localized magnetic moments is calculated in zero-gap semiconductors. The virtual interband transitions between the valence and conduction bands give rise to an indirect-exchange mechanism which is ferromagnetic if the band degeneracy is accidental. If, however, the band degeneracy is symmetry induced, the indirect interaction is antiferromagnetic. A discussion of the magnetic susceptibility of zero-gap ${\mathrm{Hg}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ alloys is given.