Observation of Strong-Coupling Effects in a Diluted Magnetic Semiconductor ${\mathrm{Ga}}_{1-x}{\mathrm{Fe}}_x\mathrm{N}$

The giant Zeeman splitting of free excitons is measured in ${\mathrm{Ga}}_{1-x}{\mathrm{Fe}}_x\mathrm{N}$. Magneto-optical and magnetization data imply the ferromagnetic sign and a reduced magnitude of the effective $p-d$ exchange energy governing the interaction between ${\mathrm{Fe}}^{3+}$ ions and holes in GaN, $N_0{\beta }^{(\mathrm{app})}=+0.5\pm 0.2\mathrm{eV}$. This finding corroborates the recent suggestion that the strong $p-d$ hybridization specific to nitrides and oxides leads to significant renormalization of the valence band exchange splitting.

Figure 1

(a) Difference between magnetizations measured at 1.8 and 5 K (symbols). The solid lines show the same difference computed using the Brillouin function for $S=5/2$ and treating the Fe concentration $x$ as the only fitting parameter. (b) Comparison between the computed magnetization (solid lines, right axis) and the redshift of exciton $A$ in ${\sigma }^{-}$ polarization (symbols, left axis) for the 0.21% sample at three temperatures. The reflectivity spectra are shown in Fig. 2a.

Figure 2

Reflectivity of ${\mathrm{Ga}}_{1-x}{\mathrm{Fe}}_x\mathrm{N}$ in Faraday configuration at 1.6 K for $x=0.21\%$ (a) and 0.11% (c) where particularly well-resolved excitons $A$, $B$, and $C$ are visible in ${\sigma }^{-}$ polarization. Panels (a,c) show experimental data (symbols) and their fitting with the polariton model (solid lines). Symbols in (b,d) present exciton energies obtained from such a fitting at various magnetic fields; solid lines are the expectation of the exciton model for the exciton and exchange parameters summarized in Table .