Anomalous Hall Effect in Field-Effect Structures of (Ga,Mn)As

Abstract

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...

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

“…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.…”

Localization and the anomalous Hall effect in a dirty metallic ferromagnet

“…The phenomenon first attracted attention several decades ago [1][2][3][4] and still continues as an active area for theoretical [5][6][7][8][9][10] and experimental [10][11][12][13][14][15] inquiry. Calculations have identified two classes of underlying mechanisms for the AHE: "extrinsic" contributions originating from the spin-dependent scattering of carriers by impurities [2,4] and "intrinsic" ones that involve the interaction of carrier spins with the inherent crystal band structure [1,16].…”

Hole concentration dependence of the Curie temperature of (Ga,Mn)Sb in a field-effect structure

“…[1][2][3][4] The nature of hole-induced ferromagnetism enables us to control their magnetic properties by the application of gate electric fields E G through the change of hole concentration p. Electric field-effect structures with a thin ferromagnetic semiconductor channel have provided opportunities to observe novel phenomena, such as electric fieldinduced magnetic phase transition (control of the Curie temperature T C ), 5,6 modulation of coercivity and magnetic anisotropy, [6][7][8] modulation of magnetic moments, 9 and change of polarity of the anomalous Hall coefficient. 10 The electricfield effect on magnetism has also become one of the focuses in metal ferromagnetism in terms of applications as well as fundamental physics. [11][12][13][14] In order to understand the electricfield effect in a semiconducting channel, one should take into account the non-uniform distribution of carriers in the channel.…”