No Arabic abstract
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.
A new type of (Ga,Mn)As microstructures with laterally confined electronic and magnetic properties has been realized by growing (Ga,Mn)As films on [1-10]-oriented ridge structures with (113)A sidewalls and (001) top layers prepared on GaAs(001) substrates. The temperature- and field-dependent magnetotransport data of the overgrown structures are compared with those obtained from planar reference samples revealing the coexistence of electronic and magnetic properties specific for (001) and (113)A (Ga,Mn)As on a single sample.
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.
A modeling approach for standing spin-wave resonances based on a finite-difference formulation of the Landau-Lifshitz-Gilbert equation is presented. In contrast to a previous study [Bihler et al., Phys. Rev. B 79, 045205 (2009)], this formalism accounts for elliptical magnetization precession and magnetic properties arbitrarily varying across the layer thickness, including the magnetic anisotropy parameters, the exchange stiffness, the Gilbert damping, and the saturation magnetization. To demonstrate the usefulness of our modeling approach, we experimentally study a set of (Ga,Mn)As samples grown by low-temperature molecular-beam epitaxy by means of electrochemical capacitance-voltage measurements and angle-dependent standing spin-wave resonance spectroscopy. By applying our modeling approach, the angle dependence of the spin-wave resonance data can be reproduced in a simulation with one set of simulation parameters for all external field orientations. We find that the approximately linear gradient in the out-of-plane magnetic anisotropy is related to a linear gradient in the hole concentrations of the samples.
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.
Magnetotransport properties of ferromagnetic semiconductor (Ga,Mn)As have been investigated. Measurements at low temperature (50 mK) and high magnetic field (<= 27 T) have been employed in order to determine the hole concentration p = 3.5x10^20 cm ^-3 of a metallic (Ga0.947Mn0.053)As layer. The analysis of the temperature and magnetic field dependencies of the resistivity in the paramagnetic region was performed with the use of the above value of p, which gave the magnitude of p-d exchange energy |N0beta | ~ 1.5 eV.