Zeeman mapping of probability densities in square quantum wells using magnetic probes

We use a method to probe experimentally the probability density of carriers confined in semiconductor quantum structures. The exciton Zeeman splitting in quantum wells containing a single, ultranarrow magnetic layer is studied depending on the layer position. In particular, a system consisting of a $1/4$ monolayer MnTe embedded at varying positions in nonmagnetic CdTe/CdMgTe quantum wells is investigated. The $\mathrm{sp}-d$ exchange interaction results in a drastic increase of the Zeeman splitting, which, because of the strongly localized nature of this interaction, sensitively depends on the position of the MnTe submonolayer in the quantum well. For various interband transitions we show that the dependence of the exciton Zeeman splitting on the position of the magnetic layer directly maps the probability density of free holesin the growth direction.