Trion magnetic polarons in (Cd,Mn)Te/(Cd,Mn,Mg)Te quantum wells
A trion magnetic polaron formed by the exchange interaction of a positively charged exciton (trion) with localized spins of Mn$^{2+}$ ions is found experimentally in a 4\,nm wide Cd$_{0.98}$Mn$_{0.02}$Te/Cd$_{0.78}$Mn$_{0.02}$Mg$_{0.2}$Te quantum well containing resident holes. The experiment is performed at a temperature of 1.6 K using resonant excitation of the trion with circularly polarized light. The trion is formed from a resident hole, which is in a hole magnetic polaron state, and a photogenerated electron-hole pair. The dynamical evolution from the hole magnetic polaron to the trion magnetic polaron is accompanied by a spin-flip of the electron, which results in negative circular polarization of the photoluminescence. The degree of circular polarization reaches $-8\%$ at zero magnetic field and strongly decreases in transverse magnetic fields exceeding 0.2 T. Our model considerations show that different localization sizes of the resident and photogenerated holes and the resulting difference in their exchange interaction with the Mn$^{2+}$ spins maintains Mn spin polarization. The resulting exchange field of Mn acting on the electron provides a robust spin polarization of the trion magnetic polaron. We evaluate the electron exchange energy in the T$^+$MP to be 0.19~meV, and the T$^+$MP binding energy to be about 0.5 - 1 meV.