General expressions for the longitudinal and transverse resistivities of single-crystalline cubic and tetragonal ferromagnets are derived from a series expansion of the resistivity tensor with respect to the magnetization orientation. They are applied to strained (Ga,Mn)As films, grown on (001)-and (113)A-oriented GaAs substrates, where the resistivities are theoretically and experimentally studied for magnetic fields rotated within various planes parallel and perpendicular to the sample surface. We are able to model the measured angular dependences of the resistivities within the framework of a single ferromagnetic domain, calculating the field-dependent orientation of the magnetization by numerically minimizing the free-enthalpy density. Angle-dependent magnetotransport measurements are shown to be a powerful tool for probing both anisotropic magnetoresistance and magnetic anisotropy. The anisotropy parameters of the (Ga,Mn)As films inferred from the magnetotransport measurements agree with those obtained by ferromagnetic resonance measurements within a factor of two.

We present a systematic study on the influence of epitaxial strain and hole concentration on the magnetic anisotropy in ͑Ga,Mn͒As at 4.2 K. The strain was gradually varied over a wide range from tensile to compressive by growing a series of ͑Ga,Mn͒As layers with 5% Mn on relaxed graded ͑In,Ga͒As/GaAs templates with different In concentration. The hole density, the Curie temperature, and the relaxed lattice constant of the as-grown and annealed ͑Ga,Mn͒As layers turned out to be essentially unaffected by the strain. Angledependent 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. 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.

The longitudinal and transverse resistivities of differently strained ͑Ga,Mn͒As layers are theoretically and experimentally studied as a function of the magnetization orientation. The strain in the series of ͑Ga,Mn͒As layers is gradually varied from compressive to tensile using ͑In,Ga͒As templates with different In concentrations. Analytical expressions for the resistivities are derived from a series expansion of the resistivity tensor with respect to the direction cosines of the magnetization. In order to quantitatively model the experimental data, terms up to the fourth order have to be included. The expressions derived are generally valid for any single-crystalline cubic and tetragonal ferromagnet and apply to arbitrary surface orientations and current directions. The model phenomenologically incorporates the longitudinal and transverse anisotropic magnetoresistance as well as the anomalous Hall effect. The resistivity parameters obtained from a comparison between experiment and theory are found to systematically vary with the strain in the layer.

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Based on a detailed theoretical examination of the lattice distortion in high-index epilayers in terms of continuum mechanics, expressions are deduced that allow the calculation and experimental determination of the strain tensor for (hhl)-oriented (Ga,Mn)As layers. Analytical expressions are derived for the strain-dependent free-energy density and for the resistivity tensor for monoclinic and orthorhombic crystal symmetry, phenomenologically describing the magnetic anisotropy and anisotropic magnetoresistance by appropriate anisotropy and resistivity parameters, respectively. Applying the results to (113)A orientation with monoclinic crystal symmetry, the expressions are used to determine the strain tensor and the shear angle of a series of (113)A-oriented (Ga,Mn)As layers by high-resolution x-ray diffraction and to probe the magnetic anisotropy and anisotropic magnetoresistance at 4.2 K by means of angle-dependent magnetotransport. Whereas the transverse resistivity parameters are nearly unaffected by the magnetic field, the parameters describing the longitudinal resistivity are strongly field dependent.

We present magnetotransport studies performed on an extended set of (Ga,Mn)As samples at 4.2 K with longitudinal conductivities σxx ranging from the low-to the high-conductivity regime. The anomalous Hall conductivity σ (AH) xy is extracted from the measured longitudinal and Hall resistivities. A transition from σ (AH) xy = 20 Ω −1 cm −1 due to the Berry phase effect in the high-conductivity regime to a scaling relation σ (AH) xy ∝ σ 1.6 xx 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.

The lattice sites of Mn in ferromagnetic ͑Ga,Mn͒As thin films were imaged using the x-ray standing wave technique. The model-free images, obtained straightforwardly by Fourier inversion, disclose immediately that the Mn mostly substitutes the Ga with a small fraction residing on minority sites. The images further reveal variations in the Mn concentrations of the different sites upon post-growth treatments. Subsequent model refinement based on the directly reconstructed images resolves with high precision the complete Mn site distributions. It is found that post-growth annealing increases the fraction of substitutional Mn at the expense of interstitial Mn whereas hydrogenation has little influence on the Mn site distribution. Our study offers an element-specific high-resolution imaging approach for accurately determining the detailed site distributions of dilute concentrations of atoms in crystals.

We discuss the structural and electrical properties of (Ga,Mn)As layers with Mn concentrations up to 5%, grown on GaAs(311)A substrates by low-temperature molecular-beam epitaxy. High-resolution x-ray diffraction studies reveal a higher concentration of As antisites and a weaker linear increase of the relaxed lattice constant with Mn content in the (311)A layers compared to (100) reference layers. The hole densities and Curie temperatures, determined from magnetotransport measurements, are drastically reduced in the (311)A layers. The findings are explained by an enhanced incorporation of Mn atoms on nonsubstitutional and noninterstitial sites, probably as Mn–Mn or As–Mn complexes, caused by the larger amount of excess As in the (311)A layers.