Excitonic giant Zeeman effect in $\mathrm{Ga}\mathrm{N}:{\mathrm{Mn}}^{3+}$

We describe a direct observation of the excitonic giant Zeeman splitting in ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}$, a wide-gap III-V diluted magnetic semiconductor. Reflectivity and absorption spectra measured at low temperatures display the $A$ and $B$ excitons, with a shift under magnetic field due to $s,p\text{−}d$ exchange interactions. Using an excitonic model, we determine the difference of exchange integrals between ${\mathrm{Mn}}^{3+}$ and free carriers in GaN, $N_0(\alpha -\beta )=-1.2\pm 0.2\mathrm{eV}$. Assuming a reasonable value of $\alpha$, this implies a positive sign of $\beta$ which corresponds to a rarely observed ferromagnetic interaction between the magnetic ions and the holes involved in the transition.

Figure 1

(Color online) (a) Reflectivity measured for ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}$ with $x=0.01\%$. (b) Reflectivity, (c) absorption, and (d) derivative of absorption for $x=0.5\%$ in Faraday configuration in ${\sigma }^{+}$ (red dots) and ${\sigma }^{-}$ (blue solid lines) circular polarizations at $T=1.7\mathrm{K}$. In (b)–(d) spectra are shifted for clarity; the left axis is valid for $B=11\mathrm{T}$ in ${\sigma }^{-}$ polarization.

Figure 2

(Color online) Details of the reflectivity spectra shown in Fig. 1b for the sample with $x=0.5\%$ at $T=1.7\mathrm{K}$; experimental spectra are shown by dots and calculated spectra by solid lines. The values of exciton energy used in the calculation and plotted in Fig. 3 (filled circles) are shown by vertical arrows.

Figure 3

(Color online) Zeeman shifts of excitonic transitions determined from the fit of reflectivity spectra (filled circles, blue), from the reflectivity maxima (empty squares, black), and from the maxima of absorption derivative (empty circles, red) at $T=1.7\mathrm{K}$ and $B\Vert c$. Corresponding spectra are shown in Figs. 1b, 1d, 2. Solid lines represent the excitonic shifts calculated using the model and with parameters as discussed in the text.

Figure 4

(Color online) Calculated energy of the $A$, $B$, and $C$ excitons vs magnetization expressed as $x⟨-S_z⟩$ for ${\sigma }^{-}$ (left half) and ${\sigma }^{+}$ (right half) circular polarizations. Oscillator strengths are shown by bars.

Figure 5

(Color online) Reflectivity of the sample with the highest Mn concentration $(x=1.2\%)$. Due to the increase of the linewidths, excitons $A$ and $B$ are not resolved in zero field and in ${\sigma }^{+}$ polarization. Nevertheless, the giant Zeeman effect can be clearly observed by the redshift of exciton $A$ in ${\sigma }^{-}$ polarization (the dashed line is a guide for the eye). In the same polarization, the blueshift of exciton $B$ increases the mixing between excitons $B$ and $C$, so that exciton $C$ can be observed at high field.

Figure 6

(Color online) (a) Redshift of exciton $A$ determined using reflectivity (full symbols, blue) and absorption (empty symbols, red) compared to the mean spin of ${\mathrm{Mn}}^{3+}$ (solid lines, right axis) calculated using Ref. 9, for temperatures 1.7, 7, and $40\mathrm{K}$. (b) Giant Zeeman shift of exciton $A$ at saturation determined using reflectivity (full circles, blue) and absorption (empty squares, red). Solid line represents value of the shift $\Delta E_A=-(1∕2)N_0(\alpha -\beta )x_{\mathrm{eff}}⟨-S_z⟩$ calculated with $N_0(\alpha -\beta )=-1.2\mathrm{eV}$, $⟨-S_z⟩=2$, and $x_{\mathrm{eff}}=x(1-x)$ (Ref. 12).