Interplay between localization and magnetism in (Ga,Mn)As and (In,Mn)As

Ion implantation of Mn combined with pulsed laser melting is employed to obtain two representative compounds of dilute ferromagnetic semiconductors (DFSs): $\mathrm{G}{\mathrm{a}}_{1-x}\mathrm{M}{\mathrm{n}}_x\mathrm{As}$ and $\mathrm{I}{\mathrm{n}}_{1-x}\mathrm{M}{\mathrm{n}}_x\mathrm{As}$. In contrast to films deposited by the widely used molecular beam epitaxy, neither Mn interstitials nor As antisites are present in samples prepared by the method employed here. Under these conditions the influence of localization on the hole-mediated ferromagnetism is examined in two DFSs with a differing strength of p-d coupling. On the insulating side of the transition, ferromagnetic signatures persist to higher temperatures in $\mathrm{I}{\mathrm{n}}_{1-x}\mathrm{M}{\mathrm{n}}_x\mathrm{As}$ compared to $\mathrm{G}{\mathrm{a}}_{1-x}\mathrm{M}{\mathrm{n}}_x\mathrm{As}$ with the same Mn concentration $x$. This substantiates theoretical suggestions that stronger p-d coupling results in an enhanced contribution to localization, which reduces hole-mediated ferromagnetism. Furthermore, the findings support strongly the heterogeneous model of electronic states at the localization boundary and point to the crucial role of weakly localized holes in mediating efficient spin-spin interactions even on the insulator side of the metal-insulator transition.

Figure 1

Concentration profiles of Mn in (Ga,Mn)As and (In,Mn)As determined by SIMS measurements.

Figure 2

Structural (a) and magnetic properties (b, c) of (Ga,Mn)As epilayers prepared by ion implantation and PLM. (a) A cross-sectional high-resolution TEM image of the (Ga,Mn)As sample with $1.8\%$ Mn points to high crystalline quality and excludes the presence of any extended lattice defects, amorphous inclusions, and precipitates of other crystalline phases. Temperature dependence of magnetization (b), the character of magnetic anisotropy [inset to (b)], and the magnitude of Curie temperature at given spontaneous magnetization $M_{\mathrm{S}}$ in our (Ga,Mn)As follow the trend established in optimized (Ga,Mn)As films grown by LT-MBE [26].

Figure 3

The interplay between localization and magnetism in (Ga,Mn)As in the vicinity of metal-insulator transition. Temperature dependence of remnant magnetization (lines, left axis) and sheet resistance (circles, right axis) of (Ga,Mn)As (samples G1-G5). The inset to (b) shows ZFC and FC curves for sample G2 in a field of 50 Oe. Upon increasing Mn concentration, together with the emergence of metallic conductivity, differences between spontaneous magnetization $\left(M_{\mathrm{S}}\right)$ and thermoremnant magnetization (TRM) get reduced. This indicates that the long-range global ferromagnetic order gradually replaces the mesoscopic ferromagnetic order when hole localization diminishes.

Figure 4

(a) Temperature dependence of resistivity ρ in (Ga,Mn)As in the absence of an external magnetic field. The results are shown as $ln\left(\rho \right)$ vs $T^{-1/2}$. In samples G1 and G2, the linear dependence dominates across the whole temperature range, supporting the crucial role of hopping mechanism in the electronic transport. However, in other samples with higher Mn concentrations, the conduction mechanism significantly changes, as magnified in (b).

Figure 5

Temperature- and field- dependent resistance in two (Ga,Mn)As samples. In the superparamagnetic sample G2, the resistance at 5 K gets reduced by $95\%$ in 8 T, and the effect results from the suppression of hole scattering by randomly orientated FM grains and orbital quantum localization effect. In the ferromagnetic sample G4, the critical spin-disorder scattering of itinerant holes by fluctuating Mn spins near $T_{\mathrm{C}}$ disappears when the magnetic field is increased to 1T.

Figure 6

Quantum localization-induced negative magnetoresistance in metallic (Ga,Mn)As. Negative magnetoresistance is observed at 5 K in sample G5 in the fields in which Mn spins are saturated (open squares). A remarkably good fitting (solid line) suggests that single-carrier orbital weak-localization magnetoresistance dominates at low temperatures.

Figure 7

Descriptions of the transition from the paramagnetic to ferromagnetic phases in (Ga,Mn)As. (a–d) A schematic diagram of the evolution of magnetic order in (Ga,Mn)As with increasing Mn concentration. (e) Mn-concentration dependent magnetization in the paramagnetic (circle), superparamagnetic (star), and ferromagnetic (squares) samples measured under a field of 2 T at 5 K. The normalized magnetization per Mn atom was determined by dividing the magnetization by the total number of Mn ions obtained by integrating the distribution of the Mn concentration.

Figure 8

Curie temperatures $T_{\mathrm{C}}$ (full points) and SP temperatures $T_{\sigma }$ (empty triangle) in $\mathrm{G}{\mathrm{a}}_{1-x}\mathrm{M}{\mathrm{n}}_x\mathrm{As}$. The solid line shows the prediction by the p-d Zener model for $\mathrm{G}{\mathrm{a}}_{1-x}\mathrm{M}{\mathrm{n}}_x\mathrm{As}$ assuming the absence of compensating donors. The dependence of the $T_{\mathrm{C}}\left(T_{\sigma }\right)$ on Mn content matches the Zener model prediction for both SPM and FM (Ga,Mn)As samples.

Figure 9

The transition from the PM, via SPM, to FM phase in (In,Mn)As samples at the MIT regime. Temperature dependent thermo-remnant magnetization of (In,Mn)As samples of (a) I1, (b) I2, (c) I3, and (d) I4. The inset to (b) shows the temperature dependent magnetization under a field of 30 Oe after field cooling (FC) and zero field cooling (ZFC) for sample I2.

Figure 10

Influence of the p-d coupling strength on magnetic properties of (Ga,Mn)As and (In,Mn)As. The dependence of the Curie and superparamagnetic temperature ($T_{\mathrm{C}}$ and $T_{\sigma }$, respectively) on the Mn atom density for (Ga,Mn)As and (In,Mn)As. The dashed and dotted lines are linear guides for eye for (Ga,Mn)As and (In,Mn)As, respectively. The crossing of two lines, and the higher and lower $T_{\mathrm{C}}/T_{\sigma }$ in (In,Mn)As at low and high $x$ regimes, respectively, result from weaker p-d coupling in (In,Mn)As compared to (Ga,Mn)As.