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Register a new userSpin-orbit coupling effect in (Ga,Mn)As films: anisotropic exchange interactions and magnetocrystalline anisotropy
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The magneto-crystalline anisotropy (MCA) of (Ga,Mn)As films has been studied on the basis of ab-initio electronic structure theory by performing magnetic torque calculations. An appreciable contribution to the in-plane uniaxial anisotropy can be attributed to an extended region adjacent to the surface. Calculations of the exchange tensor allow to ascribe a significant part to the MCA to the exchange anisotropy, caused either by a tetragonal distortion of the lattice or by the presence of the surface or interface.
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We show, by SQUID magnetometry, that in (Ga,Mn)As films the in-plane uniaxial magnetic easy axis is consistently associated with particular crystallographic directions and that it can be rotated from the [-110] direction to the [110] direction by low temperature annealing. We show that this behavior is hole-density-dependent and does not originate from surface anisotropy. The presence of uniaxial anisotropy as well its dependence on the hole-concentration and temperature can be explained in terms of the p-d Zener model of the ferromagnetism assuming a small trigonal distortion.
Atomic Force Microscopy and Grazing incidence X-ray diffraction measurements have revealed the presence of ripples aligned along the $[1bar{1}0]$ direction on the surface of (Ga,Mn)As layers grown on GaAs(001) substrates and buffer layers, with periodicity of about 50 nm in all samples that have been studied. These samples show the strong symmetry breaking uniaxial magnetic anisotropy normally observed in such materials. We observe a clear correlation between the amplitude of the surface ripples and the strength of the uniaxial magnetic anisotropy component suggesting that these ripples might be the source of such anisotropy.
The static and dynamic magnetic properties of tetragonally distorted Mn--Ga based alloys were investigated. Static properties are determined in magnetic fields up to 6.5~T using SQUID magnetometry. For the pure Mn$_{1.6}$Ga film, the saturation magnetisation is 0.36~MA/m and the coercivity is 0.29~T. Partial substitution of Mn by Co results in Mn$_{2.6}$Co$_{0.3}$Ga$_{1.1}$. The saturation magnetisation of those films drops to 0.2~MA/m and the coercivity is increased to 1~T. Time-resolved magneto-optical Kerr effect (TR-MOKE) is used to probe the high-frequency dynamics of Mn--Ga. The ferromagnetic resonance frequency extrapolated to zero-field is found to be 125~GHz with a Gilbert damping, $alpha$, of 0.019. The anisotropy field is determined from both SQUID and TR-MOKE to be 4.5~T, corresponding to an effective anisotropy density of 0.81~MJ/m$^3$. Given the large anisotropy field of the Mn$_{2.6}$Co$_{0.3}$Ga$_{1.1}$ film, pulsed magnetic fields up to 60~T are used to determine the field strength required to saturate the film in the plane. For this, the extraordinary Hall effect was employed as a probe of the local magnetisation. By integrating the reconstructed in--plane magnetisation curve, the effective anisotropy energy density for Mn$_{2.6}$Co$_{0.3}$Ga$_{1.1}$ is determined to be 1.23~MJ/m$^3$.
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.
We have measured the magnetoresistance in a series of Ga$_{1-x}$Mn$_x$As samples with 0.033$le x le$ 0.053 for three mutually orthogonal orientations of the applied magnetic field. The spontaneous resistivity anisotropy (SRA) in these materials is negative (i.e. the sample resistance is higher when its magnetization is perpendicular to the measuring current than when the two are parallel) and has a magnitude on the order of 5% at temperatures near 10K and below. This stands in contrast to the results for most conventional magnetic materials where the SRA is considerably smaller in magnitude for those few cases in which a negative sign is observed. The magnitude of the SRA drops from its maximum at low temperatures to zero at T$_C$ in a manner that is consistent with mean field theory. These results should provide a significant test for emerging theories of transport in this new class of materials.
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