Magnetotransport and magnetocrystalline anisotropy in Ga1−xMnxAs epilayers

We present an analysis of the magnetic anisotropy in epitaxial Ga1−xMnx As thin films through electrical transport measurements on multiterminal microdevices. The film magnetization is manipulated in 3D space by a three-axis vector magnet. Anomalous switching patterns are observed in both longitudinal and transverse resistance data. In transverse geometry in particular we observe strong interplay between the anomalous Hall effect and the giant planar Hall effect. This allows direct electrical characterization of magnetic transitions in the 3D space. These transitions reflect a competition between cubic magnetic anisotropy and an effective out-of-plane uniaxial anisotropy, with a reversal mechanism that is distinct from the in-plane magnetization. The uniaxial anisotropy field is directly calculated with high precision and compared with theoretical predictions. (Some figures in this article are in colour only in the electronic version) Ferromagnetic semiconductors have demonstrated a variety of interesting properties arising from strong coupling between local spins and hole carriers [1]. There has been intense interest in the magnetic anisotropy in the Ga1−x Mnx As magnetic semiconductors [2–8]. A theory based on the mean-field Zener model predicts magnetic anisotropy induced by the lattice strain present in epitaxial ferromagnetic semiconductor layers [9, 10], with compressive and tensile strain inducing in-plane and out-of-plane magnetization. However, experiments to date can only provide crude estimates of the strength of the strain induced magnetic anisotropy fields and do not have sufficient resolution to validate the theoretical predictions. Furthermore, fundamental understanding of magnetic domain structures requires a more accurate knowledge of magnetic anisotropies. In this paper, we report on magnetic anisotropy studies based upon anomalous perpendicular Hall and magnetoresistance transitions in microfabricated 1 Present address: Departments of Electrical and Mechanical Engineering, Yale University, New Haven, CT 06520, USA. 0953-8984/07/165206+11$30.00 © 2007 IOP Publishing Ltd Printed in the UK 1 J. Phys.: Condens. Matter 19 (2007) 165206 H X Tang and M L Roukes Ga1−xMnx As multiterminal microdevices. The manifested magnetic transitions are interpreted based on competition between strain induced out-of-plane uniaxial anisotropy and crystalline cubic anisotropy. All relevant magnetic anisotropy fields are obtained with high precision. Ga1−x Mnx As epilayers grown on GaAs substrate are under compressive latticemismatching strain, and as a result they have strong in-plane magnetic anisotropy [1]. In a previous paper [11] we reported the enormous spontaneous Hall resistance jumps in Ga1−xMnx As microjunctions subjected to a sweeping in-plane magnetic field. This giant planar Hall effect (GPHE) was qualitatively explained by macroscopic-scale domain reversal governed by the combined effect of a dominant cubic anisotropy and a weak uniaxial in-plane anisotropy field of unknown origin. Both the cubic anisotropy field and this weak in-plane anisotropy field were derived from magnetotransport measurement data. The intriguing giant planar Hall effect in Ga1−x Mnx As encouraged us to explore the magneto-electric effect with magnetization oriented other than in-plane, such as a conventional Hall measurement where the field is applied perpendicular to the films. Sample preparation and our experimental setup were described in an earlier publication [11]. For a single-domain magnetic conductive material with the application of magnetic field H and current density j, the electrical field in the sample is given by [12, 13] E = ρ⊥j + (ρ‖ − ρ⊥)(j · m̂)m̂ + (R0H + RS4πM)× j, (1) where m̂ is a unit vector directed along the magnetization M, R0 is the normal Hall resistivity and RS is an anomalous Hall effect coefficient. In this equation, the first two terms contribute to the longitudinal magnetoresistance and the planar Hall effect observed in this material [11]. The third and the fourth term represent the normal Hall effect and anomalous Hall effect (AHE), respectively. For ferromagnets with free carriers, the anomalous coefficient RS is in many cases much greater than the ordinary coefficient R0, which is 1/pe in a hole doped magnetic semiconductor. For example, in the Ga1−x MnxAs epilayers studied in this work, the hole density is pretty high (∼1020 cm−3) and the ordinary Hall resistance is estimated to be 0.2 m Oe−1. This makes the direct influence of the external field on Hall resistance negligible in the experimental low field region; thus, for the sake of simplicity in the remainder of the paper we shall only consider the contribution of the anomalous Hall effect when sample is subject to a perpendicular field. From equation (1) the transverse and longitudinal components of the vector E are Ex = jρ⊥ + j (ρ‖ − ρ⊥) sin θ cos φ, (2) Ey = j (ρ‖ − ρ⊥) sin θ sinφ cos φ + j (R0 H⊥ + RS4πMS cos θ). (3) These expressions are made using the coordinate system shown in figure 1 where the external electric field is applied along the x direction and the polar angle θ and azimuthal angle φ specify the orientation of the magnetic moment. If the planar Hall effect is the only term to be investigated then the magnetic field is applied in the plane of the film to ensure that M⊥ is zero. The intention in this section, however, is to measure the magnetoresistance when the field is applied at some angle to the film plane. In this case M⊥ is not zero and the anomalous Hall effect has to be taken into account. 1. Out-of-plane transport measurement results Figure 2 shows the longitudinal magnetoresistance Rsheet measured at 4.2 K for a magnetic field oriented along the z direction and along two orthogonal in-plane angles (20◦ off x and y, respectively). The field sweep range is ±1 T. At higher fields there is a large overall negative magnetoresistive for all three field orientations, consistent with the suppression of localization