We present magnetotransport studies performed on an extended set of (Ga,Mn)As samples at 4.2 K with longitudinal conductivities sigma_{xx} ranging from the low- to the high-conductivity regime. The anomalous Hall conductivity sigma_{xy}^(AH) is extra
cted from the measured longitudinal and Hall resistivities. A transition from sigma_{xy}^(AH)=20 Omega^{-1}cm^{-1} due to the Berry phase effect in the high-conductivity regime to a scaling relation sigma_{xy}^(AH) proportional to sigma_{xx}^{1.6} for low-conductivity samples is observed. This scaling relation is consistent with a recently developed unified theory of the anomalous Hall effect in the framework of the Keldysh formalism. It turns out to be independent of crystallographic orientation, growth conditions, Mn concentration, and strain, and can therefore be considered universal for low-conductivity (Ga,Mn)As. The relation plays a crucial role when deriving values of the hole concentration from magnetotransport measurements in low-conductivity (Ga,Mn)As. In addition, the hole diffusion constants for the high-conductivity samples are determined from the measured longitudinal conductivities.
We present a systematic study on the influence of epitaxial strain and hole concentration on the magnetic anisotropy in (Ga,Mn)As at 4.2 K. The strain was gradually varied over a wide range from tensile to compressive by growing a series of (Ga,Mn)As
layers with 5% Mn on relaxed graded (In,Ga)As/GaAs templates with different In concentration. The hole density, the Curie temperature, and the relaxed lattice constant of the as-grown and annealed (Ga,Mn)As layers turned out to be essentially unaffected by the strain. Angle-dependent magnetotransport measurements performed at different magnetic field strengths were used to probe the magnetic anisotropy. The measurements reveal a pronounced linear dependence of the uniaxial out-of-plane anisotropy on both strain and hole density. Whereas the uniaxial and cubic in-plane anisotropies are nearly constant, the cubic out-of-plane anisotropy changes sign when the magnetic easy axis flips from in-plane to out-of-plane. The experimental results for the magnetic anisotropy are quantitatively compared with calculations of the free energy based on a mean-field Zener model. An almost perfect agreement between experiment and theory is found for the uniaxial out-of-plane and cubic in-plane anisotropy parameters of the as-grown samples. In addition, magnetostriction constants are derived from the anisotropy data.
