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A diluted magnetic semiconductor (DMS) quantum well is an interesting system for exploring spintronic applications. We calculated the spontaneous magnetization (SM) in a 100-\AA \ Ga$_{1-x}$Mn$_x$As/Al$_{0.35}$Ga$_{0.65}$As quantum well. The Schrodinger equation was described by a 4$\times$4 Luttinger Hamiltonian in the envelope function approximation with the exchange interaction between Mn ions and holes treated in the mean-field approximation. The Schrodinger-Poisson-DMS self-consistency was solved by using the finite element method. We studied how the SM depended on the hole concentration $p$, the temperature $T$, the effective Mn concentration $x_{e\!f\!f}$, the antiferromagnetic temperature $T_{AF}$, and the exchange integral $\beta N_o$. For $T~=~0$ K, $x_{e\!f\!f}~=~0.05$, $T_{AF}~=~0.5$ K, and $\beta N_o~=~-1.2 $ eV, the SM begins to appear at $p~=~5~\times~10^{17}$ cm$^{-3}$ and saturates around $3~\times~10^{19}$ cm$^{-3}$. For $p~=~10^{18}$ cm$^{-3}$, the SM disappears around 5 K.


A diluted magnetic semiconductor (DMS) quantum well is an interesting system for exploring spintronic applications. We calculated the spontaneous magnetization (SM) in a 100-\AA \ Ga$_{1-x}$Mn$_x$As/Al$_{0.35}$Ga$_{0.65}$As quantum well. The Schrodinger equation was described by a 4$\times$4 Luttinger Hamiltonian in the envelope function approximation with the exchange interaction between Mn ions and holes treated in the mean-field approximation. The Schrodinger-Poisson-DMS self-consistency was solved by using the finite element method. We studied how the SM depended on the hole concentration $p$, the temperature $T$, the effective Mn concentration $x_{e\!f\!f}$, the antiferromagnetic temperature $T_{AF}$, and the exchange integral $\beta N_o$. For $T~=~0$ K, $x_{e\!f\!f}~=~0.05$, $T_{AF}~=~0.5$ K, and $\beta N_o~=~-1.2 $ eV, the SM begins to appear at $p~=~5~\times~10^{17}$ cm$^{-3}$ and saturates around $3~\times~10^{19}$ cm$^{-3}$. For $p~=~10^{18}$ cm$^{-3}$, the SM disappears around 5 K.