Reentrant formation of magnetic polarons in quantum dots

We propose a model of magnetic polaron formation in semiconductor quantum dots doped with magnetic ions. A wetting layer serves as a reservoir of photogenerated holes, which can be trapped by the adjacent quantum dots. For certain hole densities, the temperature dependence of the magnetization induced by the trapped holes is reentrant: it disappears for some temperature range and reappears at higher temperatures. We demonstrate that this peculiar effect is not an artifact of the mean-field approximation and persists after statistical spin fluctuations are accounted for. We predict fingerprints of reentrant magnetic polarons in photoluminescence spectra.

Figure 1

(a) A scheme of QDs grown on a wetting layer (WL), which is excited by light (cladding layer not shown). Type-II conduction/valence band (CB/VB) profile of a II-VI QD doped with Mn spins (green). $\varepsilon$ and $E_{\mathrm{CV}}$ are the confinement and band gap energies. Hole quasi-Fermi level $\mu \left(T\right)$ lies in the continuum of WL states for $T=0$. (c) QD states with corresponding energies, occupancies, and Mn-spin alignment: $E_1$ state has zero energy and QD occupancy; $E_{2,3}$ state has one hole with spin $+3/2$ ($-3/2$), $\Delta$ is the exchange splitting; and $E_4$ has two holes with a repulsive Coulomb energy $U$.

Figure 2

(a) Reentrant behavior in the MP energy, $E_{\text{MP}}$ [see Eq. (5)], and various critical temperatures. Free energy evolution reveals the second- (b) and first-order (c) phase transitions for $p=4\times {10}^9$ and $p=9\times {10}^{10}{\text{cm}}^{-2}$, respectively. Parameters, partially guided by (Zn,Mn)Te/ZnSe QDs:[4] $\varepsilon$$=$ $-$36 meV, $U=30$ meV,[16, 33] ${\Delta }_{\text{max}}=69\text{meV}$ (see Fig. 1), $x_{\text{Mn}}=2.6\%$, $N_0\beta =-1.05$ eV, and $m_h^{*}=0.21$. QD volume, $\Omega$, is cylindrical with a 50-Å radius and a 25-Å height.

Figure 3

(a) Reentrant magnetism in the fluctuation approach (FA) [see Eq. (6)] for $p=5\times {10}^9,$ $9\times {10}^{10},$ $4\times {10}^{11}{\text{cm}}^{-2}$. (b) Comparison of the FA and mean field (MF). FA (dot-dashed line) shows no reentrant magnetism predicted for MF and $p=5\times {10}^9{\text{cm}}^{-2}$ (dashed line). Other QD parameters are from Fig. 2.

Figure 4

(a) A PL spectrum for reentrant magnetism showing $2\to 1$ and $1\to 0$ hole occupancy transitions ($p=9\times {10}^{10}$ cm${}^{-2}$). The thick lines emphasize important features in the PL spectrum, while the thin lines between them show their evolution at intermediate equidistant $T$. (b) Overall PL peak position marked with filled circles. As $T$ increases, $1\to 0$ peak shifts to zero energy. QD parameters are from Fig. 2.