Evidence for the absence of electron-electron Coulomb interaction quantum correction to the anomalous Hall effect in Co2FeSi Heusler-alloy thin films

Abstract

Electrical (longitudinal) resistivity ρXX, at H=0 and H=80 kOe, anomalous Hall resistivity ρxyAH, and magnetization M, have been measured at different temperatures in the range 5-300 K on the Co2FeSi (CFS) Heusler-alloy thin films, grown on Si(111) substrate, with thickness ranging from 12 to 100 nm. At fixed fields H=0 and H=80 kOe, ρXX(T) goes through a minimum at T=Tmin (which depends on the film thickness) in all the CFS thin films. In sharp contrast, both the anomalous Hall coefficient RA and ρxyAH monotonously increase with temperature without exhibiting a minimum. Elaborate analyses of ρXX, RA, and ρxyAH establishes the following. (i) The enhanced electron-electron Coulomb interaction (EEI) quantum correction (QC) is solely responsible for the upturn in "zero-field" and "in-field" ρXX(T) at T < Tmin whereas the interband spin-flip electron-magnon (e-m) and intraband non-spin-flip electron-phonon (e-p) inelastic-scattering processes, present even at T < Tmin, overwhelm the EEI QC at temperatures above Tmin and thereby cause ρXX to increase with temperature. At all temperatures, e-m scattering contribution dominates over the e-p scattering contribution. (ii) Compared to the intrinsic (I) Berry-phase curvature mechanism, skew scattering (Sk) and side-jump (Sj) both make sizable contributions to ρxyAH(T) or RA(T) but, at any temperature in the range 5-300 K, the contribution of Sj is considerably larger than that of Sk. The observations (i) and (ii) provide a conclusive experimental evidence for the theoretical prediction that the EEI quantum corrections to anomalous Hall resistivity/coefficient vanish for both skew scattering and side-jump mechanisms even though the EEI corrections to longitudinal resistivity are finite. A strong suppression (by an order of magnitude) is observed in the anomalous Hall conductivity from the resonantly enhanced intrinsic value of 103 S/cm when the Fermi level is located near the anticrossing of band dispersions split by spin-orbit interaction. This suppression is shown to correspond to one or both of the possibilities: the resonance condition is not satisfied, or the interband spin-flip inelastic electron-magnon scattering enhances the side-jump contribution at the expense of the intrinsic contribution. We demonstrate that RA, or equivalently ρxyAH, scales with ρXXT, the temperature-dependent part of ρXX, over a considerably wide temperature range (5-300 K) only when ρxyAH is corrected for the observed temperature dependence of spontaneous magnetization and ρXX for the EEI effects.