Longitudinal and transverse fluctuations of magnetization of the excitonic magnetic polaron in a semimagnetic single quantum dot

Statistical fluctuations of the magnetization on a nanometer scale have been investigated with the use of magneto-optical spectroscopy of quasi-zero-dimensional excitonic magnetic polarons (EMP) in individual pancake-shaped CdSe/ZnMnSe quantum dots (QD’s). The EMP emission line demonstrates a qualitatively different behavior in magnetic field B normal and parallel to the QD plane. In the first case, the alignment of the Mn spins in high magnetic fields results in a giant Zeeman shift and linewidth narrowing of almost one order of magnitude to values characteristic of nonmagnetic QD’s. No similar effects are observed in the second case where the emission line demonstrates a weak blue shift and small linewidth variation. It is shown that the difference originates from the anisotropy of the hole exchange field in the QD’s and can be described using the fundamental fluctuation-dissipation theorem and taking into account the anisotropy of the hole g factor. Both the longitudinal and transverse fluctuations of the magnetization are determined from the analysis of EMP emission lines recorded in the two directions of magnetic field B. We demonstrate that in high magnetic fields the longitudinal fluctuations decrease exponentially whereas the transverse ones decrease as $1/B.$