Anomalous Hall effect in Fe/Au multilayers

To understand the interfacial scattering effect on the anomalous Hall effect (AHE), we prepared multilayers of ${\left(\mathrm{F}{\mathrm{e}}_{\left(36/n\right)\mathrm{nm}}/\mathrm{A}{\mathrm{u}}_{(12/n)\mathrm{nm}}\right)}_n$ using an e-beam evaporator. This structure design allowed us to investigate the effect of interfacial scattering on the AHE, while keeping the samples' thickness and composition unchanged. We measured the (magneto)transport properties of the samples in a wide temperature range (10–310 K) with magnetic fields up to 50 kOe. We found that the scaling between the anomalous Hall resistivity $\left({\rho }_{\mathrm{AHE}}\right)$ and longitudinal resistivity $\left({\rho }_{xx}\right)$ can be roughly described by ${\rho }_{\mathrm{AHE}}\sim {\rho }_{xx}^{\gamma }$ with $\gamma =2.65\pm 0.10$ and 1.90 ± 0.04 for samples from $n=1$ to $n=4$ and samples from $n=4$ to $n=12$, respectively. Our quantitative analysis results showed that the interfacial scattering suppresses the contribution of the intrinsic mechanism and gives rise to a side-jump contribution.

Figure 1

Schematic diagram of sample (top view) dimensions and measurement configuration for magnetotransport properties.

Figure 2

(a) XRR spectra and (b) high-angle XRD patterns of multilayered samples from $n=1$ to $n=12$. The peaks of FeAu alloys are labeled as $\left(\nabla \right)$ AuFe(111) and (◊) $\mathrm{AuF}{\mathrm{e}}_9\left(111\right)$ in (b).

Figure 3

HRTEM images of cross sections of samples (a) $n=2$, (b) $n=6$, (c) $n=12$ and EDX depth profiles of Fe and Au elements in corresponding samples (d) $n=2$, (e) $n=6$, (f) $n=12$.

Figure 4

(a) Temperature-dependent longitudinal resistivity $\left({\rho }_{xx}\right)$ curves for all samples; (b) ${\rho }_{xx}\left(n\right)/{\rho }_{xx}\left(n=1\right)$ as a function of temperature for all samples; (c) normalized ${\rho }_{xx}\left(T\right)/{\rho }_{xx}\left(310\mathrm{K}\right)\sim T$ curves for all samples; (d) ${\rho }_{xx}\left(n\right)/{\rho }_{xx}\left(n=1\right)$ as a function of number of periods $n$ for selected temperatures.

Figure 5

(a) Field-dependent Hall resistivity $\left({\rho }_{xy}\right)$ of all samples at 10 K. (b) Field-dependent Hall resistivity $\left({\rho }_{xy}\right)$ of the $n=5$ sample at temperatures ranging from 10 to 300 K. (c) Temperature-dependent anomalous Hall resistivity $\left({\rho }_{\mathrm{AHE}}\right)$ for all samples.

Figure 6

A logarithmic plot of anomalous Hall resistivity $\left({\rho }_{\mathrm{AHE}}\right)$ versus longitudinal resistivity $\left({\rho }_{xx}\right)$ measured at 10 K for all samples. The red and blue lines are linear fits to the data.

Figure 7

MR curves of all samples measured at 10 K. $H_{//}\left(H_{\perp }\right)$ indicates that the magnetic field was parallel (perpendicular) to the measurement current. Magnetic field was applied in the sample plane during the measurement.

Figure 8

(a) ${\sigma }_{\mathrm{AHE}0}\sim {\sigma }_{xx0}$ curve measured at 10 K. The legend is also applied to (b) and (c). (b) ${\sigma }_{\mathrm{AHE}}\sim {\sigma }_{xx}^2$ curves for $n=4–12$ samples. The inset shows the intercept $\left(b\right)$ values for different $n$. (c) $b\sim {\rho }_{xx0}$ and $\beta \sim {\rho }_{xx0}$ curves. The solid lines indicate the linear fittings to each curve.