Anomalous Hall effect in quarternary Heusler-type Ni₅₀Mn₁₇Fe₈Ga₂₅melt-spun ribbons

The anomalous Hall effect (AHE) in quarternary Heusler-type Ni50Mn17Fe8Ga25melt-spun ribbons is investigated. Experimental correlation between saturated anomalous Hall resistivity (ρAMS) and longitudinal resistivity (ρxx) is achieved for the low-temperature martensitic phase and the high-temperature austenitic phase as ρAMS∞ ρxxn=4.2 and ρAMS∞ ρxxn=2.1, respectively. The unexpectedly large exponent of n=4.2 in the martensitic phase is found to contradict the traditional theory of AHE with n=1-2, but it can be explained by a side-jump model beyond the short-range limit as a result of the intermediate-range spin-dependent electron scattering by relatively large Mn-rich clusters instead. The restoration of the exponent back to a normal value of n=2.1 in the austenitic phase is ascribed to the domination of the electron scattering by phonons, compared to that by the Mn-rich clusters, at elevated temperatures and with phonon softening in the transverse-acoustic TA2mode.