Effects of $s$,$p$-$d$ and $s$-$p$ exchange interactions probed by exciton magnetospectroscopy in (Ga,Mn)N

Near band-gap photoluminescence and reflectivity in a magnetic field are employed to determine the exchange-induced splitting of free exciton states in paramagnetic wurtzite Ga${}_{1-x}$Mn${}_x$N, $x\lesssim 1\%$, grown on sapphire substrates by metal-organic vapor phase epitaxy. The band gap is found to increase with $x$. The giant Zeeman splitting of all three excitons $A$, $B$, and $C$ is resolved, enabling the determination of the apparent exchange integrals $N_0{\alpha }^{(\mathrm{app})}=0.0\pm 0.1$ eV and $N_0{\beta }^{(\mathrm{app})}=+0.8\pm 0.2$ eV. These nonstandard values and signs of the $s$-$d$ and $p$-$d$ exchange energies are explained in terms of recent theories that suggest a contribution of the electron-hole exchange to the spin splitting of the conduction band and a renormalization of the free hole spin splitting by a large $p$-$d$ hybridization. According to these models, in the limit of a strong $p$-$d$ coupling, the band gap of (Ga,Mn)N increases with $x$, and the order of hole spin subbands is reversed, as observed.

Figure 1

Left axis: Reflectivity spectra from GaN and (Ga,Mn)N with the Mn concentration $x=0.32\%$ and $0.87\%$ recorded at $T=2$ K. Right axis: photoluminescence intensity acquired at $T=10$ K for the same samples. The structure around 3.48 eV is attributed to DBEs in the GaN buffer layer. The position of the (Ga,Mn)N $A$ exciton as determined from reflectivity is indicated with a dashed line in each panel. The maxima at 3.446 and 3.537 eV in the PL spectrum of the $0.87\%$ sample are assigned to third- and fourth-order Raman scattering of the laser light (E${}_{\mathrm{laser}}=$ 3.814 eV) with LO phonons ($E_{\mathrm{LO}}=$ 92 meV in GaN).

Figure 2

Relative energy position of the (Ga,Mn)N $A$ exciton with respect to GaN, as determined from PL (squares) and reflectivity (triangles), plotted vs. the Mn precursor flow rate. The Mn concentration determined by SQUID (diamonds) is presented on the right axis. The error bars are a combination of experimental and fitting errors. In the case of the samples with $x<0.20\%$, the energies of (Ga,Mn)N and GaN excitons overlap, resulting in an increased error bar.

Figure 3

Reflectivity of (Ga,Mn)N (Mn content $x=0.5\%$) in magnetic field 0 and 7 T (Faraday configuration) at $T=2$ K. The energy positions of the $A$, $B$, and $C$ excitons obtained from the fit are indicated. Points, experimental data; solid lines, model.

Figure 4

Exciton energies in (Ga,Mn)N (a) $x=0.32\%$, (b) $x=0.62\%$ as a function of the magnetic field at $T=1.8$ K. Points, experimental data; solid lines, theory.

Figure 5

Exchange constants $N_0{\alpha }^{(\mathrm{app})}$ and $N_0{\beta }^{(\mathrm{app})}$ for (Ga,Mn)N determined from a fit of the $A$, $B$, and $C$ excitonic shifts in magnetic field for samples with Mn concentration from $0.32\%$ to $0.87\%$.