Antiferromagnetic $s\mathrm{\text{−}}d$ Exchange Coupling in GaMnAs

Measurements of coherent electron spin dynamics in ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}/{\mathrm{Al}}_{0.4}{\mathrm{Ga}}_{0.6}\mathrm{As}$ quantum wells with $0.0006\%<x<0.03\%$ show an antiferromagnetic (negative) exchange between $s$-like conduction band electrons and electrons localized in the $d$ shell of the ${\mathrm{Mn}}^{2+}$ impurities. The magnitude of the $s\mathrm{\text{−}}d$ exchange parameter, $N_0\alpha$, varies as a function of well width indicative of a large and negative contribution due to kinetic exchange. In the limit of no quantum confinement, $N_0\alpha$ extrapolates to $-0.09\pm 0.03\mathrm{eV}$ indicating that antiferromagnetic $s\mathrm{\text{−}}d$ exchange is a bulk property of GaMnAs. Measurements of the polarization-resolved photoluminescence show strong discrepancy from a simple model of the exchange enhanced Zeeman splitting, indicative of additional complexity in the exchange split valence band.

Figure 1

Time-resolved electron spin dynamics in $d=7.5\mathrm{nm}$ GaMnAs QWs. (a) An example of KR data (points) together with fit (line). (b) ${\nu }_L$ as a function of $B$ for different $x$ values (solid points); larger points indicate increasing $x$. Open data points are for the $x=0$ sample. (c) The effect of increasing $T$ on the $B$ dependence of ${\nu }_L$ for the sample with $x\sim 0.002\%$ (solid points) and for the $x=0$ sample (open points). (d) $T$ dependence of ${\nu }_L$ at constant $B$ for the $x\sim 0.002\%$ sample. Red lines in (b)–(d) are fits to Eq. (2).

Figure 2

(a) $g_e$ as a function of $d$. Black points are from control ($x=0$) samples of this study, red circles and squares are from Refs. 8, 10, respectively. Lines guide the eye. (b) $\Delta E$ as a function of $B$ for QWs with (solid circles) and without Mn doping (open circles); larger points indicate increasing $x$. (c) $\Delta E$ for the sample with $d=5\mathrm{nm}$ and $x\sim 0.008\%$ at various temperatures. Fits to Eq. (2) are shown as lines in (b) and (c).

Figure 3

(a) $x{N}_0\alpha$ as a function of $x$ from fits shown in Fig. 2b; error bars are the size of the points. Linear fits are shown for each sample set of constant $d$. (b) $N_0\alpha$ extracted from fits in (a) and plotted as a function of $d$. (c) The electron exchange constant $N_0\alpha$ as a function of electron kinetic energy for GaMnAs.

Figure 4

Polarization-resolved PL for 10-nm QW at 5 K. (a) ${\sigma }^{+}$ and ${\sigma }^{-}$ polarized PL from the $x=0$ QW excited with $1\mathrm{W}/{\mathrm{cm}}^2$ at 1.722 eV, and (b) for the $x\sim 0.003\%$ sample excited with $10\mathrm{W}/{\mathrm{cm}}^2$ at 1.722 eV. Two-Gaussian fits to the data are shown as black lines. (c) $B$ dependence of $\Delta E_{\mathrm{PL}}$ for the $x=0$ and $x\sim 0.003\%$ samples plotted as open and filled circles, respectively. Fits to $\Delta E_{\mathrm{PL}}$ for $|B|<2\mathrm{T}$ are shown for both samples as blue lines. (d) $\Delta E_{sp\mathrm{\text{−}}d}$, (black triangles) plotted with fit for $|B|<5\mathrm{T}$ (blue line).