Modeling of magnetic polaron properties in (Zn,Mn)Te quantum dots

Magnetic polarons in (Zn,Mn)Te quantum dots (QD) show unconventional behavior [1]. These structures exhibit a small red shift of the photoluminescence peak energy in the presence of a magnetic field $B$ and they also have a weak dependence of the polaron energy $E_{\mathrm{MP}}$ on temperature $T$ and $B$. We attribute these properties to a large molecular field $B_{m}$ that is proportional to the heavy holes spin density [2]. We have calculated $B_{m}$ using the QD diameter and height as adjustable parameters. Assuming hole localization, this calculation yields values of $B_{m}$ \textgreater 20 T. The assumption that the hole localization diameter can be smaller than the QD diameter is justified due to alloy and spin disorder scattering [3]. Using the magnetic polaron free energy, we calculate $E_{\mathrm{MP}}$ as function of $T$ and $B$ for a variety of $B_{m}$ values. To get a weak dependence of $E_{\mathrm{MP}}$ on $T$ and $B $we must assume that the polaron temperature is higher than $T$. [1] B. Barman et al., Phys. Rev. B \textbf{92}, 035430 (2015). [2] J. M. Pientka et al., Phys. Rev. B \textbf{92}, 155402 (2015). [3] K. V. Kavokin et al., Phys. Rev. B \textbf{60}, 16499 (1999).