Thickness dependence of anomalous Hall and Nernst effects in Ni-Fe thin films

Abstract

We systematically investigate the Ni-Fe layer thickness ($t$) dependence of the anomalous Hall effect (AHE) and anomalous Nernst effect (ANE). The AHE and ANE show different behavior in the $t$ dependence; the sign of the anomalous Hall resistivity changes around $t=9\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$, whereas the anomalous Nernst coefficient (${S}_{\mathrm{ANE}}$) keeps almost constant regardless of $t$, namely, no sign change of ${S}_{\mathrm{ANE}}$ with $t$. We analyze ${S}_{\mathrm{ANE}}$ and separate it into the contribution coming from the transverse thermoelectric conductivity (${\ensuremath{\alpha}}_{xy}$) and the AHE contribution coming from the Seebeck effect. The detailed analysis for ${S}_{\mathrm{ANE}}$ concludes that the AHE contribution is negligibly small and ${\ensuremath{\alpha}}_{xy}$, which is related to the anomalous Hall conductivity (${\ensuremath{\sigma}}_{xy}$) via the Mott relation, is also independent of $t$. To gain insight into the difference in the $t$ dependence of ${\ensuremath{\sigma}}_{xy}$ and ${\ensuremath{\alpha}}_{xy}$, we clarify the origin of sign reversal in the AHE. The sign reversal in the AHE is attributed to the competing contribution of the different sources of the AHE: the extrinsic and intrinsic mechanisms. The present experimental finding of the difference between the $t$ dependence on ${\ensuremath{\sigma}}_{xy}$ and ${\ensuremath{\alpha}}_{xy}$ suggests that the relative degree between the extrinsic and intrinsic processes for the AHE is quite different from that for the ANE in the case of Ni-Fe.