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Register a new userStrain, magnetic anisotropy, and anisotropic magnetoresistance in (Ga,Mn)As on high-index substrates: application to (113)A-oriented layers
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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 (MA) and anisotropic magnetoresistance (AMR) 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 MA and AMR 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.
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A small fraction of phosphorus (up to 10 %) was incorporated in ferromagnetic (Ga,Mn)As epilayers grown on a GaAs substrate. P incorporation allows reducing the epitaxial strain or even change its sign, resulting in strong modifications of the magnetic anisotropy. In particular a reorientation of the easy axis toward the growth direction is observed for high P concentration. It offers an interesting alternative to the metamorphic approach, in particular for magnetization reversal experiments where epitaxial defects stongly affect the domain wall propagation.
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.
Historically, comprehensive studies of dilute ferromagnetic semiconductors, e.g., $p$-type (Cd,Mn)Te and (Ga,Mn)As, paved the way for a quantitative theoretical description of effects associated with spin-orbit interactions in solids, such as crystalline magnetic anisotropy. In particular, the theory was successful in explaining {em uniaxial} magnetic anisotropies associated with biaxial strain and non-random formation of magnetic dimers in epitaxial (Ga,Mn)As layers. However, the situation appears much less settled in the case of the {em cubic} term: the theory predicts switchings of the easy axis between in-plane $langle 100rangle$ and $langle 110rangle$ directions as a function of the hole concentration, whereas only the $langle 100rangle$ orientation has been found experimentally. Here, we report on the observation of such switchings by magnetization and ferromagnetic resonance studies on a series of high-crystalline quality (Ga,Mn)As films. We describe our findings by the mean-field $p$-$d$ Zener model augmented with three new ingredients. The first one is a scattering broadening of the hole density of states, which reduces significantly the amplitude of the alternating carrier-induced contribution. This opens the way for the two other ingredients, namely the so-far disregarded single-ion magnetic anisotropy and disorder-driven non-uniformities of the carrier density, both favoring the $langle 100rangle$ direction of the apparent easy axis. However, according to our results, when the disorder gets reduced a switching to the $langle 110rangle$ orientation is possible in a certain temperature and hole concentration range.
We present an experimental and theoretical study of magnetocrystalline anisotropies in arrays of bars patterned lithographically into (Ga,Mn)As epilayers grown under compressive lattice strain. Structural properties of the (Ga,Mn)As microbars are investigated by high-resolution X-ray diffraction measurements. The experimental data, showing strong strain relaxation effects, are in good agreement with finite element simulations. SQUID magnetization measurements are performed to study the control of magnetic anisotropy in (Ga,Mn)As by the lithographically induced strain relaxation of the microbars. Microscopic theoretical modeling of the anisotropy is performed based on the mean-field kinetic-exchange model of the ferromagnetic spin-orbit coupled band structure of (Ga,Mn)As. Based on the overall agreement between experimental data and theoretical modeling we conclude that the micropatterning induced anisotropies are of the magnetocrystalline, spin-orbit coupling origin.
We report the observation of anomalies in the longitudinal magnetoresistance of tensile-strained (Ga,Mn)As epilayers with perpendicular magnetic anisotropy. Magnetoresistance measurements carried out in the planar geometry (magnetic field parallel to the current density) reveal spikes that are antisymmetric with respect to the direction of the magnetic field. These anomalies always occur during magnetization reversal, as indicated by a simultaneous change in sign of the anomalous Hall effect. The data suggest that the antisymmetric anomalies originate in anomalous Hall effect contributions to the longitudinal resistance when domain walls are located between the voltage probes. This interpretation is reinforced by carrying out angular sweeps of $vec{H}$, revealing an antisymmetric dependence on the helicity of the field sweep.
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