Scaling of the anomalous Hall current in Fe${}_{100-x}$(SiO${}_2$)${}_x$ films

To study the origin of the anomalous Hall effect, Fe${}_{100-x}$(SiO${}_2$)${}_x$ granular films with a volume fraction of SiO${}_2$ (0 ⩽ $x$ ⩽ 40.51) were fabricated using cosputtering. Hall and longitudinal resistivities were measured in the temperature range of 5–350 K with magnetic fields up to 5 T. As $x$ increased from 0 to 40.51, the anomalous Hall resistivity and longitudinal resistivity increased by about four and three orders in magnitude, respectively. Analysis of the results revealed that the normalized anomalous Hall conductivity is a constant for all of the samples, which may suggest a scattering-independent anomalous Hall conductivity in Fe.

Figure 1

Field-dependent Hall resistivity obtained at different temperatures for Fe${}_{100-x}$(SiO${}_2$)${}_x$ films (a) $x$ $=$ 5.36 and (b) $x$ $=$ 40.51. Field-dependent magnetization measured at different temperatures for samples with different compositions: (c) $x$ $=$ 5.36 and (d) $x$ $=$ 40.51.

Figure 2

Saturated anomalous Hall resistivity as a function of the ${\mathrm{SiO}}_2$ volume fraction at 5 K. The solid line is a guide to the eye.

Figure 3

(a) The temperature-dependent longitudinal resistivity for samples with different SiO${}_2$ volume fractions. (b) TCR as a function of the SiO${}_2$volume fraction. The solid line is a guide to the eye.

Figure 4

TEM images for Fe${}_{100-x}$(SiO${}_2$)${}_x$ films: (a) $x$ $=$ 9 and (b) $x$ $=$ 23.

Figure 5

Effective carrier concentration extracted from the ordinary Hall coefficient versus the SiO${}_2$ volume fraction.

Figure 6

The normalized anomalous Hall resistivity obtained at 5 K versus the longitudinal resistivity in a log-log scale for all of the samples. The line is a linear fit of the data, with a slope γ $=$ 2.1 ± 0.1.

Figure 7

AHE resistivity (5 K) as a function of longitudinal resistivity in a log-log scale. The solid line is a guide to the eye.