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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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.