Large extraordinary Hall effect and anomalous scaling relations between the Hall and longitudinal conductivities inε-Fe3Nnanocrystalline films

Abstract

An enhancement of extraordinary Hall coefficient over two orders of magnitude larger than that of bulk Fe is found in conductive $\ensuremath{\epsilon}{\text{-Fe}}_{3}\text{N}$ nanocrystalline films with similar and nearly temperature-independent conductivities, but extremely different structural defect content. A scaling exponential of $n=1.59$ in ${\ensuremath{\sigma}}_{xy}\ensuremath{\sim}{\ensuremath{\sigma}}_{xx}^{n}$ between the Hall and longitudinal conductivities is obtained for the well-crystallized sample, which fits well with the recent developed universal scaling theory characterized by $n=1.6$ in the dirty limit. However, no scaling relation is valid for the sample with a large amount of amorphous parts and the fitting relation of ${\ensuremath{\rho}}_{xy}\ensuremath{\propto}{\ensuremath{\rho}}_{xx}^{n}$ between the Hall and longitudinal resistivities at the lower resistivity range gives an unexpected high exponential of $n=17.6$. The anomalous scaling behavior may be qualitatively explained by the mean free path model due to the temperature-dependent scattering by spin-disordered grain boundaries and amorphous phases. Because of the large Hall coefficient, nearly temperature-independent Hall and longitudinal resistivity, and rather low Ohmic resistivity, the $\ensuremath{\epsilon}{\text{-Fe}}_{3}\text{N}$ nanocrystalline film might be a promising candidate for low-field Hall sensors.