Upper bound for the $s\text{−}d$ exchange integral in $n$-(Ga,Mn)N:Si from magnetotransport studies

A series of recent magneto-optical studies pointed to contradicting values of the $s\text{−}d$ exchange energy $N_0\alpha$ in Mn-doped GaAs and GaN as well as in Fe-doped GaN. Here, a strong sensitivity of weak-localization phenomena to symmetry-breaking perturbations (such as spin-splitting and spin-disorder scattering) is exploited to evaluate the magnitude of $N_0\alpha$ for $n$-type wurtzite (Ga,Mn)N:Si films grown by metalorganic vapor phase epitaxy. Millikelvin magnetoresistance studies and their quantitative interpretation point to $N_0\alpha <40$ meV, a value at least 5 times smaller than the one found with similar measurements on, e.g., $n$-(Zn,Mn)O. It is shown that this striking difference in the values of the $s\text{−}d$ coupling between $n$-type III-V and II-VI dilute magnetic semiconductors can be explained by a theory that takes into account the acceptor character of Mn in III-V compounds.

Figure 1

Upper panels: AFM images of $(10\times 10) \mu {\mathrm{m}}^2$ scan areas for sample S0 (a), S1 (b), S2 (c), and S3 (d). Lower panels: AFM images of $(40\times 40) \mu {\mathrm{m}}^2$ scan areas for sample S0 (e), S1 (f), S2 (g), and S3 (h).

Figure 2

(a), (b) X-ray rocking curves for the symmetric (0002) and for the asymmetric $\left(10\overline{1}5\right)$ reflection, respectively. (c)–(f) Reciprocal space maps for the asymmetric $\left(10\overline{1}5\right)$ reflection of sample S0 (c), S1 (d), S2 (e), and S3 (f).

Figure 3

Hall coefficient $R_{\text{H}}=-\partial {\rho }_{xy}/\partial B$ at 50 K for the studied samples. The values of the corresponding electron concentrations are given in Table 1.

Figure 4

Dots: Measured magnetoconductivity for sample S1 at $T\le 2$ K and for sample S2 at $T=0.05$ K. Solid lines: Results of fitting within the theoretical 2D model treating $L_{\phi }\left(T\right)$ as the only fitting parameter.

Figure 5

Magnetoconductivity measured for sample S1 at $T\ge 10$ K. Bullets: Experimental data; solid lines: theoretical fitting within the 3D theory with the phase coherence length $L_{\phi }\left(T\right)$ as the only fitting parameter.

Figure 6

Magnetoconductivity measured for sample S3 at various temperatures. Dots: Experimental data; solid lines: theoretical fitting within the 3D theory with the phase coherence length $L_{\phi }\left(T\right)$ as the only fitting parameter.

Figure 7

Temperature dependence of the phase coherence length $L_{\phi }$ obtained by fitting the magnetoconductance data for (Ga,Mn)N:Si layers within the 2D and 3D models. For comparison the corresponding data for $n$-GaN:Si [37] are also presented (open symbols). Dashed line: $T^{-3/4}$ dependence. The horizontal line marks the layer thickness $d=150$ nm.

Figure 8

Dots: Magnetoconductivity measured for sample S3 at 0.3 K (a) and at 2 K (b). Solid lines: Values calculated for different magnitudes of $N_0\alpha$ taking the presence of Mn spins with concentration $x=0.06$% into account. For $N_0\alpha \gtrsim 40$ meV a positive shoulder of magnetoconductivity (shown in the inset as a hatched area) appears in the calculations.