Influence of $s$,$p$-$d$ and $s-p$ exchange couplings on exciton splitting in Zn${}_{1-x}$Mn${}_x$O

This work presents results of near-band gap magnetooptical studies on Zn${}_{1-x}$Mn${}_x$O epitaxial layers. We observe excitonic transitions in reflectivity and photoluminescence that shift toward higher energies when the Mn concentration increases and split nonlinearly under the magnetic field. Excitonic shifts are determined by the $s,p-d$ exchange coupling to magnetic ions, by the electron-hole $s-p$ exchange, and the spin-orbit interactions. A quantitative description of the magnetoreflectivity findings indicates that the free excitons $A$ and $B$ are associated with the ${\Gamma }_7$ and ${\Gamma }_9$ valence bands, respectively, the order reversed as compared to wurtzite GaN. Furthermore, our results show that the magnitude of the giant exciton splittings, specific to dilute magnetic semiconductors, is unusual: the magnetoreflectivity data are described by an effective exchange energy $N_0({\beta }^{\left(\mathrm{app}\right)}-{\alpha }^{\left(\mathrm{app}\right)})=+0.2\pm 0.1$ eV, which points to small and positive $N_0{\beta }^{\left(\mathrm{app}\right)}$. It is shown that both the increase of the gap with $x$ and the small positive value of the exchange energy $N_0{\beta }^{\left(\mathrm{app}\right)}$ corroborate recent theory describing the exchange splitting of the valence band in a nonperturbative way, suitable for the case of a strong $p-d$ hybridization.

Figure 1

Reflectivity and photoluminescence of Zn${}_{1-x}$Mn${}_x$O with $x=0.6$% at $T=1.6$ K. The reflectivity is measured with incidence angle of 45 degrees (upper spectrum shifted for clarity) or with normal incidence (middle spectrum). Estimated spectral positions of excitonic lines are indicated.

Figure 2

(a) Reflectivity and (b) photoluminescence spectra collected at 1.6 K for Zn${}_{1-x}$Mn${}_x$O with Mn concentrations 0.14, 0.6, 1.4, and 2.6%. Reflectivity spectra are shifted vertically for clarity. Intensity of photoluminescence spectra decreases by orders of magnitude with increasing the Mn concentration.

Figure 3

Exciton energies determined from the spectra shown in Fig. 2, as a function of the Mn concentration $x$ in Zn${}_{1-x}$Mn${}_x$O. Empty circles: free exciton $A$ (reflectivity), full circles: free exciton B (reflectivity), triangles: bound exciton (main PL line). The dashed line is a linear fit to the energy of the free exciton $A$.

Figure 4

Reflectivity spectra (symbols) of Zn${}_{1-x}$Mn${}_x$O with (a,b) $x=0.14$% and (c,d) $x=0.6$%. Lines show fits by the polariton model. Features related to $1S$ and $2S$ excitons $A$ and $B$ are marked. Spectral region of $2S$ excitons is plotted in a zoomed $Y$ scale in the insets (b) and (d). Full (empty) circles are related to measurement at ${\sigma }^{-}$ (${\sigma }^{+}$) circular polarization and magnetic field $B=7$ T, triangles to measurement at $B=0$ T.

Figure 5

(a) Transition energies, (b) polarizabilities, and (c) damping parameters determined for $A$ and $B$ excitons in Zn${}_{0.994}$Mn${}_{0.006}$O sample. Lines in (a) represent fit with excitonic model, Brillouin function, and with parameters given in Table .

Figure 6

(a) Reflectivity spectra (symbols) of Zn${}_{1-x}$Mn${}_x$O with $x=2.6$%, measured at $B=0$ and $B=7$ T in two circular polarizations at $T=1.6$ K. Solid lines show fits with the polariton model. Arrows show the determined positions of excitons. (b) Redshift of the exciton $A$ as a function of the magnetic field $B$, as determined for in Zn${}_{0.974}$Mn${}_{0.026}$O at three temperatures $T$ (left axis). The redshift is compared to the mean spin of Mn${}^{2+}$ ions (right axis), given by the paramagnetic Brillouin function B${}_{5/2}(T,B)$.

Figure 7

Magnetic circular Dichroism (MCD) in 6 T (a) and photoluminescence (PL) spectra measured at B = 0 and B = 7 T in two circular polarizations (b) for Zn${}_{1-x}$Mn${}_x$O with 2.5% of Mn at T = 1.6 K. Spectral position (c) and amplitude (d) of the PL peak vs. magnetic field.

Figure 8

Shift of exciton energies observed in reflectivity and photoluminescence measurements on Zn${}_{1-x}$Mn${}_x$O plotted as a function of the Mn concentration $x$. The shifts are determined at saturation of the Mn spin polarization: the redshift of the exciton $A$ by using reflectivity in the ${\sigma }^{+}$ polarization (empty circles); the blueshift of the exciton $B$ in the ${\sigma }^{+}$ circular polarization by using reflectivity (full circles); the redshift of the bound exciton from PL measurements in the the ${\sigma }^{-}$ polarization (full triangles) and in the ${\sigma }^{+}$ polarization (empty triangles). PL data for three diluted samples are taken from Ref. 18. Solid line represents the value of the shift calculated for the heavy-hole-like ${\Gamma }_9$ band assuming $N_0({\beta }^{\left(\mathrm{app}\right)}-{\alpha }^{\left(\mathrm{app}\right)})=+0.2$ eV, and is more suitable for the exciton $B$. Dashed line corresponds to the calculation with the neglected electron-hole exchange interaction and is more suitable for bound excitons seen in the PL, ${\sigma }^{-}$ polarization.