High-field magnetocrystalline anisotropic resistance effect in (Ga,Mn)As

Abstract

As the magnetization rotates in the ͑001͒ plane of epitaxial ͑Ga,Mn͒As films, we observe both two-and fourfold oscillations of comparable magnitude in the longitudinal resistivity. This behavior is different from the usual anisotropic magnetoresistance effect in polycrystalline films. The fourfold or cubic symmetry vanishes at the Curie temperature T C , indicating that it originates from the long-range ferromagnetic phase in single crystal films. In contrast, the twofold symmetry persists above T C , suggesting its origin to be from the alignment of spins with random orientations. However, the transverse, or planar Hall, resistivity only contains a twofold oscillation. The temperature dependence of the magnetocrystalline anisotropic resistance effect is explained by a two-component model. The anisotropic magnetoresistance ͑AMR͒ effect in ferromagnetic ͑FM͒ materials arises from the difference in the scattering rate when the magnetization direction is oriented parallel or perpendicular to an electrical current. 1 It is a convenient tool often used for characterizing the state of the magnetization in ferromagnetic metals 2 and semiconductors. 3,4 In ferromagnetic semiconductors such as GaMnAs, AMR has been linked to the intrinsic band structure properties in the presence of spin-orbit interaction. 5 For polycrystalline materials, the resistivity typically shows a twofold symmetry because the magnetocrystalline effect in the randomly oriented grains is averaged out. In single crystal films, however, also due to the spin-orbit interaction, AMR may contain higher-order terms that reflect the symmetry of the crystals. 6 Nevertheless, in many cases, the highorder terms are small and often neglected. 7,8 Here, we have conducted a series of experiments in epitaxially grown GaMnAs films and found a very strong fourfold magnetoresistance effect that is correlated with the crystalline symmetry of the films. This fourfold term is found to be connected to the long-range FM order below T C ; therefore, its temperature and field dependences reveal valuable information about the ferromagnetic ordering in the materials.We studied two Ga 1−x Mn x As samples with x = 0.039 and 0.059 which were grown on GaAs͑001͒ wafers at 250°C by molecular beam epitaxy in an As-rich environment. The samples were patterned into the standard Hall bar using photolithography and wet chemical etching. For resistivity measurements, the current flows along a ͓110͔ direction, as schematically shown in Fig. 1͑a͒, and both the longitudinal and transverse or the planar Hall dc resistivities xx and xy are measured simultaneously using the four-probe method. The measurements are performed in a superconducting magnet equipped with a rotating sample holder, which allows us to continuously change the angle between the magnetic field H and the electric current I, as illustrated in Fig. 1͑a͒. As the sample is rotated around ͓001͔, H always lies in the sample plane, and both xx and xy are recorded as angle is varied. The angular dependence is taken for different...

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