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 accou
nts 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.
We present an extensive experimental and theoretical study of surface acoustic wave-driven ferromagnetic resonance. In a first modeling approach based on the Landau-Lifshitz-Gilbert equation, we derive expressions for the magnetization dynamics upon
magnetoelastic driving that are used to calculate the absorbed microwave power upon magnetic resonance as well as the spin current density generated by the precessing magnetization in the vicinity of a ferromagnet/normal metal interface. In a second modeling approach, we deal with the backaction of the magnetization dynamics on the elastic wave by solving the elastic wave equation and the Landau-Lifshitz-Gilbert equation selfconsistently, obtaining analytical solutions for the acoustic wave phase shift and attenuation. We compare both modeling approaches with the complex forward transmission of a LiNbO$_3$/Ni surface acoustic wave hybrid device recorded experimentally as a function of the external magnetic field orientation and magnitude, rotating the field within three different planes and employing three different surface acoustic wave frequencies. We find quantitative agreement of the experimentally observed power absorption and surface acoustic wave phase shift with our modeling predictions using one set of parameters for all field configurations and frequencies.
We systematically measured the DC voltage V_ISH induced by spin pumping together with the inverse spin Hall effect in ferromagnet/platinum bilayer films. In all our samples, comprising ferromagnetic 3d transition metals, Heusler compounds, ferrite sp
inel oxides, and magnetic semiconductors, V_ISH invariably has the same polarity. V_ISH furthermore scales with the magnetization precession cone angle with a universal prefactor, irrespective of the magnetic properties, the charge carrier transport mechanism or type. These findings quantitatively corroborate the present theoretical understanding of spin pumping in combination with the inverse spin Hall effect.
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.
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.
The longitudinal and transverse resistivities of differently strained (Ga,Mn)As layers are theoretically and experimentally studied as a function of the magnetization orientation. The strain in the series of (Ga,Mn)As layers is gradually varied from
compressive to tensile using (In,Ga)As 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.
