The anomalous Hall effect in metal-insulator-semiconductor structures having thin (Ga,Mn)As layers as a channel has been studied in a wide range of Mn and hole densities changed by the gate electric field. Strong and unanticipated temperature dependence, including a change of sign, of the anomalous Hall conductance σxy has been found in samples with the highest Curie temperatures. For more disordered channels, the scaling relation between σxy and σxx, similar to the one observed previously for thicker samples, is recovered.PACS numbers: 72.25. Dc, 73.40.Qv, 75.50.Pp, Along with anisotropic magnetoresistance, the anomalous Hall effect (AHE) results from an interplay between spin-orbit interactions and spin polarization of electric current specific to ferromagnets. It has been recently realized that for a certain region of conductivities, the anomalous Hall conductivity σ xy is a measure of the Berry phase of carrier trajectories in the k space and, thus, provides information on the hitherto inaccessible aspects of the band structure topology in the presence of various spin-orbit interactions [1,2,3,4,5]. Interestingly, the effect appears to be qualitatively immune to disorder, except for the case of linear-in-k Rashba-type Hamiltonians in two-dimensional electron systems, where the contribution to σ xy vanishes [6] unless the lifetime is spin-dependent [7]. Furthermore, a surprisingly universal empirical scaling relation between the Hall and longitudinal conductivities, σ xy ∼ σ γ xx , γ ≈ 1.6 has been found to be obeyed by a number of materials on the lower side of their conductivity values [8], where Anderson-Mott quantum localization effects should be important.In this Letter, we report on Hall resistance studies as a function of temperature and gate electric field carried out for metal-insulator-semiconductor (MIS) structures containing a thin conducting channel of ferromagnetic (Ga,Mn)As. We find out that in the σ xx range up to 10 2 S/cm, σ xy obeys a scaling relation with a similar value of the exponent γ. However, for σ xx > ∼ 10 2 S/cm the scaling relation breaks down entirely. Surprisingly, in this regime and below the Curie temperature T C , σ xy tends to decrease rather abruptly with decreasing temperature, and even reverses its sign in some cases, in the region where neither resistance R nor magnetization M vary significantly with temperature. The effect has not been observed in thicker films and appears to have no explanation within the existing theory, pointing to the importance of yet unrevealed confinement effects.The studied thin layers of tensile-strained (Ga,Mn)As have been deposited by low-temperature molecular beam epitaxy onto a buffer layer consisting of 4-nm GaAs/ 30-nm Al 0.75 Ga 0.25 As/ 500-nm In 0.15 Ga 0.85 As/30-nm GaAs grown on a semi-insulating GaAs (001) substrate. Upon growth, Hall bars having a channel of 30 or 40-µm width and ∼200-µm length are patterned by photolithography and wet etching. Subsequently, samples are annealed at 180• C for 5 min or introduced directly into an a...
The collective behavior of spins in a dilute magnetic semiconductor is determined by their mutual interactions and influenced by the underlying crystal structure. Hence, we begin with the atomic quantum-mechanical description of this system using the proposed variational-perturbation calculus, and then turn to the emerging macroscopic picture employing phenomenological constants. Within this framework we study spin waves and exchange stiffness in the p-d Zener model of (Ga,Mn)As, its thin layers and bulk crystals described by the spds* tight-binding approximation. Analyzing the anisotropic part of exchange, we find that the Dzyaloshinskii-Moriya interaction may lead to the cycloidal spin arrangement and uniaxial in-plane anisotropy in thin layers, resulting in a surface-like anisotropy in thicker films. We also derive and discuss the spin-wave contribution to magnetization and Curie temperature. Our theory reconstructs the values of stiffness determined from the temperature dependence of magnetization, but reproduces only partly those obtained from analyzing precession modes in (Ga,Mn)As thin films.Comment: 17 pages, 12 figures (added Eq. 36, replaced Fig. 10
The relativistic nature of the electron motion underlies the intrinsic part of the anomalous Hall effect, believed to dominate in ferromagnetic (Ga,Mn)As. In this paper, we concentrate on the crystal band structure as an important facet to the description of this phenomenon. Using different k.p and tight-binding computational schemes, we capture the strong effect of the bulk inversion asymmetry on the Berry curvature and the anomalous Hall conductivity. At the same time, we find it not to affect other important characteristics of (Ga,Mn)As, namely the Curie temperature and uniaxial anisotropy fields. Our results extend the established theories of the anomalous Hall effect in ferromagnetic semiconductors and shed new light on its puzzling nature.
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