Carrier localization in quaternary ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_{\mathrm{x}}{\mathrm{As}}_{1-y}{\mathrm{P}}_{\mathrm{y}}$ ferromagnetic semiconductor films

Motivated by the fact that holes in the ${\mathrm{Ga}}_{1–x}{\mathrm{Mn}}_x\mathrm{As}$ family of ferromagnetic semiconductors play a key role in determining their ferromagnetic properties, we have measured hole concentrations in a series of three ${\mathrm{Ga}}_{1–x}{\mathrm{Mn}}_x{\mathrm{As}}_{1–y}{\mathrm{P}}_y$ alloys grown by molecular beam epitaxy with varying amounts of phosphorus. This was carried out by Hall effect measurements, after eliminating the effect of the anomalous Hall term, and thus isolating the ordinary Hall term that directly provides the concentration of freely moving holes. Comparing these Hall effect results with total hole concentrations obtained from the number of acceptors and compensating donors as given by structural and magnetization measurements, we find that the number of itinerant holes (i.e., holes that contribute to the Hall effect) is significantly less than the total hole concentration. This indicates that a considerable fraction of the holes arising from Mn acceptors are localized. We find, furthermore, that the degree of such localization increases with the concentration of phosphorus in the ${\mathrm{Ga}}_{1–x}{\mathrm{Mn}}_x{\mathrm{As}}_{1–y}{\mathrm{P}}_y$ alloy. Our results indicate that the Curie temperature (and, by extension, other magnetic properties) described by the Zener model in ferromagnetic semiconductors of the ${\mathrm{Ga}}_{1–x}{\mathrm{Mn}}_x\mathrm{As}$ family are determined by the itinerant holes rather than by the total hole concentration. Finally, our results also indicate that ferromagnetism in these alloys vanishes when the total hole concentration falls below a certain Mott-like threshold, suggesting that the holes (both localized and itinerant) reside in the acceptor impurity band created by the presence of Mn acceptors.

Figure 1

(a) Hall resistivity ${\rho }_{xy}$, and (b) longitudinal resistivity ${\rho }_{xx}$ as a function of field for ${\mathrm{Ga}}_{0.94}{\mathrm{Mn}}_{0.06}{\mathrm{As}}_{0.85}{\mathrm{P}}_{0.15}$ at $T=15$ K. Field $B$ is applied normal to the sample plane, i.e., along its easy axis. Remaining samples display very similar behavior. Insets: ${\rho }_{xy}$ and ${\rho }_{xx}$ shown on expanded scale.

Figure 2

(a) Logarithmic plot of ${\rho }_{xx}$ vs ${\rho }_{xy}$ at several temperatures (3, 5, 10, 15 K) and magnetic fields (1.0–9.0 T) for ${\mathrm{Ga}}_{1–x}{\mathrm{Mn}}_x{\mathrm{As}}_{1–y}{\mathrm{P}}_y$ with $y=0.103$. (b) Magnetic field dependence of $log\left(c{M}_z\right)+0.4343B{R}_0/{\rho }_{xy}$ for the same sample, and linear fit for high-field data.

Figure 3

Schematic of Mn impurity band (Mn-IB) and the top of the valence band (VB) as a function of phosphorus content. The ${\mathrm{Ga}}_{1–x}{\mathrm{Mn}}_x\mathrm{As}$ diagram is shown for comparison. Note that even though there may be overlap between the valence and impurity bands in the case of ${\mathrm{Ga}}_{1–x}{\mathrm{Mn}}_x\mathrm{As}$, the valence band moves further from the impurity band as phosphorus concentration increases. Note also that the progression of the Fermi level $E_F$ with phosphorus content is not monotonic, since we have attempted to show the larger effect of Mn interstitials in the 15% specimen.

Figure 4

Red filled circles: Curie temperature $T_c$ as a function of ${\left(p_{\mathrm{deloc}}\right)}^{1/3}$ for our three annealed ${\mathrm{Ga}}_{1–x}{\mathrm{Mn}}_x{\mathrm{As}}_{1–y}{\mathrm{P}}_y$ samples. Black filled squares: Curie temperature $T_c$ as a function of ${\left(p_{\mathrm{deloc}}\right)}^{1/3}$ for the same samples before annealing. Open circles: $T_C$ as a function of ${\left(p_{\mathrm{tot}}\right)}^{1/3}$ for annealed samples. Open squares: $T_C$ as a function of ${\left(p_{\mathrm{tot}}\right)}^{1/3}$ for the same samples before annealing. The dashed line is from $T_{\mathrm{C}}$ vs $p^{1/3}$ as suggested in Ref. [32]. Solid line is a guide for the eye.