Effect of the $s,p\text{−}d$ exchange interaction on the excitons in ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x\mathrm{O}$ epilayers

We present a spectroscopic study of ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x\mathrm{O}$ layers grown by molecular beam epitaxy on sapphire substrates. ZnO:Co is commonly considered as a promising candidate for being a diluted magnetic semiconductor ferromagnetic at room temperature. We performed magneto-optical spectroscopy in the Faraday configuration, by applying a magnetic field up to $11\mathrm{T}$, at temperatures down to $1.5\mathrm{K}$. For very dilute samples $(x<0.5\%)$, the giant Zeeman splitting of the $A$ and $B$ excitons is observed at low temperature. It is proportional to the magnetization of isolated Co ions, as calculated using the anisotropy and $g$ factor deduced from the spectroscopy of the $d\text{−}d$ transitions. This demonstrates the existence of spin-carrier coupling. Electron-hole exchange within the exciton has a strong effect on the giant Zeeman splitting observed on the excitons. From the effective spin-exciton coupling ${⟨N_0(\alpha -\beta )⟩}_X=0.4\mathrm{eV}$ we estimate the difference of the exchange integrals for free carriers $N_0\mid \alpha -\beta \mid \simeq 0.8\mathrm{eV}$. The magnetic circular dichroism observed near the energy gap was found to be proportional to the paramagnetic magnetization of anisotropic Co ions even for higher Co contents.

Figure 1

(a) Absorption spectra of ${\mathrm{Co}}^{2+}$ in ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x\mathrm{O}$ samples with various cobalt concentration $x$, at $T=1.6\mathrm{K}$. Two zero-phonon intraionic transitions are identified: ${}^{4}A_2\to {}^{2}E\overline{E}$ (at $1875\mathrm{meV}$) and ${}^{4}A_2\to {}^{2}E2\overline{A}$ (at $1880\mathrm{meV}$). The absorption coefficient of the ${}^{4}A_2\to {}^{2}E2\overline{A}$ transition is shown by a dotted horizontal line pointing to the right figure. (b) The absorption coefficient at $1880\mathrm{meV}$, as a function of the Co concentration determined by EDX (full circles). The observed linear dependence also allows us to determine the Co concentration in very diluted samples (open squares and vertical arrows), where the EDX technique is not sensitive enough.

Figure 2

Magneto-optical spectroscopy of the ${}^{4}A_2\leftrightarrow {}^{2}E\overline{E}$ transition in a ${\mathrm{Zn}}_{0.98}{\mathrm{Co}}_{0.02}\mathrm{O}$ at $T=7\mathrm{K}$, in ${\sigma }^{+}$ (top) and ${\sigma }^{-}$ (bottom) circular polarizations. The magnetic field up to $11\mathrm{T}$ is parallel to the $c$ axis and to the propagation of light (Faraday configuration). (a) PL spectra. (b) Absorption spectra. (c) Position in energy of the observed PL (full circles) and absorption (triangles) lines, and (solid lines) values calculated using the parameters of Table . (d) Energy level diagram, as a function of the applied field, and transitions. The spin levels of the ground level quadruplet are marked.

Figure 3

(a) Absorption spectra of ${\mathrm{Zn}}_{0.955}{\mathrm{Co}}_{0.045}\mathrm{O}$ measured in the Faraday configuration, at $1.7\mathrm{K}$, in a magnetic field up to $11\mathrm{T}$, in ${\sigma }^{+}$ and ${\sigma }^{-}$ circular polarizations. The four transitions observed are labeled according to Fig. 2d. (b) Absorption intensity measured at $T=1.7\mathrm{K}$ (symbols) and calculated using Maxwell-Boltzmann statistics (lines). (c) Mean spin of Co calculated from the absorption intensities (symbols) or from Maxwell-Boltzmann statistics and parameters of Table (lines).

Figure 4

(a) Reflectivity spectra measured at $T=1.6\mathrm{K}$ with incidence angle of 45°. Topmost spectrum is for ZnO, other spectra for ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x\mathrm{O}$ with increasing Co concentration (0.1, 0.4, 0.5, 2 %). Labels $A$, $B$, and $C$ identify the three excitons which are visible in ZnO and at low Co content; Perot-Fabry oscillations are also observed at low photon energy. (b) Spectral positions of the excitonic transition in ZnO and ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x\mathrm{O}$. Symbols marked as “mixed $A+B$” means that in the case of samples with a Co concentration higher than 2% we cannot resolve excitons $A$ and $B$, and we plot the position of a broad structure. The dashed line shows the linear fit for the position of exciton $A$ as a function of Co content.

Figure 5

(Color online) (a) Reflectivity spectra (shifted for clarity) of ZnO at $B=0\mathrm{T}$ and at $B=6\mathrm{T}$ in ${\sigma }^{+}$ and ${\sigma }^{-}$ circular polarizations (symbols). The positions of excitons $A$ and $B$, as determined from the fit of the $B=0\mathrm{T}$ spectrum (solid line), are marked by arrows. The Zeeman effect induces a small, opposite shift of the two excitons, which changes their overlap and induces a change of the reflected intensity. (b) The position of excitons $A$ and $B$ in ZnO, as determined from a fits of the reflectivity spectra shown in (a). (c) Reflectivity spectra of ${\mathrm{Zn}}_{0.996}{\mathrm{Co}}_{0.004}\mathrm{O}$ at $B=0\mathrm{T}$, and $B=6\mathrm{T}$ in ${\sigma }^{+}$ and in ${\sigma }^{-}$ polarizations. Solid lines are the fits to the spectra. (d) The position of excitons $A$ and $B$, versus magnetic field. At $B=6\mathrm{T}$, the value of the splitting is $-1.8\mathrm{meV}$ for exciton $A$ and $1.6\mathrm{meV}$ for $B$.

Figure 6

Zeeman splitting of exciton $A$, measured at $B=6\mathrm{T}$ and $T=1.6\mathrm{K}$, so that the mean spin of isolated Co is $⟨S_z⟩=1.2$ [Eq. (2)]. The horizontal scale (bottom scale) is the absorption coefficient of the ${}^{4}A_2\to {}^{2}E2\overline{A}$ transition of Co (see Fig. 1). The top scale (nonlinear) displays the density of free spins $x_{\mathrm{eff}}$ expected for a random distribution of Co on the Zn sublattice. The solid line shows the giant Zeeman splitting ${⟨N_0(\alpha -\beta )⟩}_X\times x_{\mathrm{eff}}\times ⟨-S_z⟩$ calculated with an effective ${⟨N_0(\alpha -\beta )⟩}_X=0.4\mathrm{eV}$.

Figure 7

(Color online) Dots and left axis: Zeeman splitting of excitons $A$ and $B$ measured at three temperatures; lines, right axis: mean spin of isolated Co ions as given by Eq. (2). The sample has $x_{\mathrm{eff}}=0.36\%$. The left and right scales are chosen so that ${⟨N_0(\alpha -\beta )⟩}_X=0.40\mathrm{eV}$ for exciton $A$ and $0.39\mathrm{eV}$ for $B$.

Figure 8

Magnetic circular dichroism (MCD) obtained in transmission on four samples with various Co concentrations. The MCD signal contains three contributions, one (pointed by arrow, most intense in the sample with the lowest Co concentration, 2% Co) close to the bandgap at $3.4\mathrm{eV}$, the second below the gap (Ref. 16), the last one (most intense in the sample with the highest Co concentration, 15% Co) in coincidence with the internal transitions of Co $(1.8\mathrm{eV}–2.3\mathrm{eV})$. Spectra are shifted for clarity.

Figure 9

(Color online) Symbols, left axis: Magnetic circular dichroism in transmission, at a photon energy $3395\mathrm{meV}$, close to the bandgap; lines, right vertical axis: mean spin of isolated Co ions [Eq. (2)]. The sample is ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x\mathrm{O}$ with 2% Co.

Figure 10

(Color online) (a) Position of the $A$ and $B$ excitons, for the same sample as in Fig. 5c (with 0.4% Co), measured at different values of the applied field. The horizontal axis is the splitting measured on exciton $A$, plotted as positive if the ${\sigma }^{+}$ line is at higher energy. (b) Position of the $A$ and $B$ excitons, as a function of the applied field for the same sample as in Fig. 5c (with 0.4% Co). Symbols are experimental data: blue (dark gray) for ${\sigma }^{-}$, red (light gray) for ${\sigma }^{+}$. Lines are calculated (including for exciton $A$).