Diffuson contribution to anomalous Hall effect in disordered Co < inf > 2 < /inf > FeSi thin films

Abstract

An exhaustive study of the influence of disorder on anomalous Hall (AH) resistivity (ρ xyAH ), longitudinal resistivity (ρ xx ), magnetoresistance and magnetization of Co 2 FeSi (CFS) Heusler alloy thin films of fixed (50 nm) thickness, deposited on Si (1 1 1) substrate, reveals the following. Regardless of the degree of disorder present, the side-jump mechanism gives a dominant contribution to ρ xyAH . A new and novel contribution to both ρ xx and ρ xyAH , characterized by the logarithmic temperature (-lnT) dependence at temperatures below the minimum (T < T min ), exclusive to the amorphous CFS films, originates from the scattering of conduction electrons from the diffusive hydrodynamic modes associated with the longitudinal component of magnetization, called ‘diffusons’. The electron-diffuson, e-d, scattering and weak localization (WL) mechanisms compete with the inelastic electron-magnon, e-m, scattering to produce the minimum in ρ xx (T), whereas the minimum in ρ xyAH (T) is caused by the competing contributions from the e-d and e-m scattering, as WL does not contribute to ρ xyAH . Another novel finding is that the e-d scattering contributions to ρ xyAH (T) and ρ xx (T) scale with each other. In sharp contrast, in crystalline films, enhanced electron-electron Coulomb interaction (EEI), which is basically responsible for the resistivity minimum, does not contribute to ρ xyAH with the result that no minimum in ρ xyAH (T) is observed. The conventional ρ xyAH = f(ρ xx ) scaling breaks down completely in the present case. However, when ρ xyAH (T) is corrected for the e-d contribution and ρ xx (T) for both e-d and WL contributions (only EEI) in the amorphous (crystalline) films, the AH coefficient, R A (T) = ρ xyAH (T) / 4πM s (T), (calculated from the corrected ρ xyAH and spontaneous magnetization, M s ), perfectly scales with ρ xxT , the temperature-dependent part of the corrected ρ xx , for all the CFS thin films.