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Register a new userScaling relation of the anomalous Hall effect in (Ga,Mn)As
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We present magnetotransport studies performed on an extended set of (Ga,Mn)As samples at 4.2 K with longitudinal conductivities sigma_{xx} ranging from the low- to the high-conductivity regime. The anomalous Hall conductivity sigma_{xy}^(AH) is extracted from the measured longitudinal and Hall resistivities. A transition from sigma_{xy}^(AH)=20 Omega^{-1}cm^{-1} due to the Berry phase effect in the high-conductivity regime to a scaling relation sigma_{xy}^(AH) proportional to sigma_{xx}^{1.6} for low-conductivity samples is observed. This scaling relation is consistent with a recently developed unified theory of the anomalous Hall effect in the framework of the Keldysh formalism. It turns out to be independent of crystallographic orientation, growth conditions, Mn concentration, and strain, and can therefore be considered universal for low-conductivity (Ga,Mn)As. The relation plays a crucial role when deriving values of the hole concentration from magnetotransport measurements in low-conductivity (Ga,Mn)As. In addition, the hole diffusion constants for the high-conductivity samples are determined from the measured longitudinal conductivities.
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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 $sigma_{xy}$ has been found in samples with the highest Curie temperatures. For more disordered channels, the scaling relation between $sigma_{xy}$ and $sigma_{xx}$, similar to the one observed previously for thicker samples, is recovered.
Mn$_{3-x}$Ga (x = 0.1, 0.4, 0.7) thin films on MgO and SrTiO$_3$ substrates were investigated with magnetic anisotropy perpendicular to the film plane. An anomalous Hall-effect was observed for the tetragonal distorted lattice in the crystallographic D0$_{22}$ phase. The Hall resistivity $varrho_{xy}$ was measured in a temperature range from 20 to 330 K. The determined skew scattering and side jump coefficients are discussed with regard to the film composition and used substrate and compared to the crystallographic and magnetic properties.
Investigating the scaling behavior of annealed Ga$_{1-x}$Mn$_{x}$As anomalous Hall coefficients, we note a universal crossover regime where the scaling behavior changes from quadratic to linear, attributed to the anomalous Hall Effect intrinsic and extrinsic origins, respectively. Furthermore, measured anomalous Hall conductivities when properly scaled by carrier concentration remain constant, equal to theoretically predicated values, spanning nearly a decade in conductivity as well as over 100 K in T$_{C}$. Both the qualitative and quantitative agreement confirms the validity of new equations of motion including the Berry phase contributions as well as tunablility of the intrinsic anomalous Hall Effect.
We study the Curie temperature and hole density of (Ga,Mn)As while systematically varying the As-antisite density. Hole compensation by As-antisites limits the Curie temperature and can completely quench long-range ferromagnetic order in the low doping regime of 1-2% Mn. Samples are grown by molecular beam epitaxy without substrate rotation in order to smoothly vary the As to Ga flux ratio across a single wafer. This technique allows for a systematic study of the effect of As stoichiometry on the structural, electronic, and magnetic properties of (Ga,Mn)As. For concentrations less than 1.5% Mn, a strong deviation from Tc ~ p^0.33 is observed. Our results emphasize that proper control of As-antisite compensation is critical for controlling the Curie temperatures in (Ga,Mn)As at the low doping limit.
The anomalous Hall effect (AHE) has been studied systematically in the low-conductivity ferromagnetic oxide Fe$_{3-x}$Zn$_x$O$_4$ with $x = 0$, 0.1, and 0.5. We used (001), (110), and (111) oriented epitaxial Fe$_{3-x}$Zn$_x$O$_4$ films grown on MgO and sapphire substrates in different oxygen partial pressure to analyze the dependence of the AHE on crystallographic orientation, Zn content, strain state, and oxygen deficiency. Despite substantial differences in the magnetic properties and magnitudes of the anomalous Hall conductivity $sigma_{xy}^{rm AHE}$ and the longitudinal conductivity $sigma_{xx}$ over several orders of magnitude, a universal scaling relation $sigma_{xy}^{rm AHE} propto sigma_{xx}^{alpha}$ with $alpha = 1.69 pm 0.08$ was found for all investigated samples. Our results are in agreement with recent theoretical and experimental findings for ferromagnetic metals in the dirty limit, where transport is by metallic conduction. We find the same scaling relation for magnetite, where hopping transport prevails. The fact that this relation is independent of crystallographic orientation, Zn content, strain state, and oxygen deficiency suggests that it is universal and particularly does not depend on the nature of the transport mechanism.
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