Scaling relation of the anomalous Hall effect in (Ga,Mn)As

Abstract

We present magnetotransport studies performed on an extended set of (Ga,Mn)As samples at 4.2 K with longitudinal conductivities σxx ranging from the low-to the high-conductivity regime. The anomalous Hall conductivity σ (AH) xy is extracted from the measured longitudinal and Hall resistivities. A transition from σ (AH) xy = 20 Ω −1 cm −1 due to the Berry phase effect in the high-conductivity regime to a scaling relation σ (AH) xy ∝ σ 1.6 xx 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.

Scaling relations between anomalous Hall and longitudinal transport coefficients in metallic (Ga,Mn)As films

“…As a result, despite the fact that particular samples may differ in magnetization values, we observe a universal scaling relation σ xy ∝ σ γ xx with γ ∼ 1.5 (or ρ xy ∝ ρ 0.5 xx based on Eq. (4)) 32 over low p range up to 10 20 cm −3 (i.e., the intermediate conductivity range, with σ xx up to 100 Ω −1 cm −1 ), in agreement with the value γ ∼ 1.5 reported by Shen et al 20 and the value γ ∼ 1.6 reported by Glunk et al 13 , and Chiba et al…”

“…However, this scaling relation breaks down rather severely in the case of higher hole concentrations (i.e., higher conductivity, σ xx > 100 Ω −1 cm −1 ), consistent with the recent experiments of Glunk et al 13 and Chiba et al 14 The above behavior agrees with a unified theory of the AHE developed by Onoda et al 33,34 , which predicts three regimes that depend on the carrier scattering time: the "clean" regime, where ρ xy ∝ ρ xx (not achievable in (Ga,Mn)As); the "intermediate" regime, where ρ xy ∝ ρ 2 xx ; and the "dirty" regime, for which this theory predicts ρ xy ∝ ρ 0.4 xx .…”

“…9 and 19 applies to both intrinsic and side-jump mechanisms, making it difficult to distinguish between the two processes; and also given the fact that Mn atoms in these materials act simultaneously as the source of magnetic moments and as acceptors, which complicates the analysis of scattering processes in this material. Furthermore, several recent studies of (Ga,Mn)As samples have reported a universal empirical scaling relation between the anomalous Hall and the longitudinal conductivities σ xy ∝ σ γ xx with γ of about 1.6, which holds over a wide range of conductivities (between 0.01 and 100 Ω −1 cm −1 ) 13,14,20 . By very simple algebra (see Sec.…”

“…It is usually assumed that AHE caused by magnetic moments embedded in a ferromagnetic metal 1 may arise from extrinsic scattering processes involving spin-orbit coupling: specifically, skew scattering 2 and/or sidejump processes 3 . Recently, however, AHE has reemerged as an active area of both theoretical 4-7 and experimental [8][9][10][11][12][13][14] research, owing to the introduction of an additional intrinsic mechanism for AHE that involves the interaction of carrier spins with the inherent spin-orbit-coupled Bloch bands 5,[15][16][17][18][19] . Despite extensive studies of this problem, the identification of the microscopic origins responsible for AHE in magnetic materials obtained by analyzing the scaling relation between the anomalous Hall and the longitudinal resistivities ρ xy ∝ ρ n xx is still a challenging task.…”

Anomalous Hall effect in ZnxFe3-xO4: Universal scaling law and electron localization below the Verwey transition

“…24 Experimentally, the scaling with exponent 1.6 has been reported, over five decades of the longitudinal conductivity (from 10 −2 up to 10 4 Ω −1 cm −1 ), for very different materials including metallic Fe ultra-thin films 25 and compounds in which the conduction regime may being varied from metallic to hopping: (La,Sr)MnO 3 , (Ti,Co)O 2 , (Ga,Mn)As. [26][27][28][29] The scaling σ xy AHE ∼ σ xx n with n = 1.6 has also been found in pure magnetite films 20 while a n = 1.69 exponent has been derived for zinc ferrites films and Fe-ZnO granular ones. 21,30 These converging experimental findings on so various materials give strong support to the universal character of the 1.6 scaling relation, even if a complete AHE theory including the insulating regime is still missing.…”