Effects of surface and interface scattering on anomalous Hall effect in Co/Pd multilayers

In this paper, we report the results of surface and interface scattering on anomalous Hall effect in Co/Pd multilayers with perpendicular magnetic anisotropy. The surface scattering effect has been extracted from the total anomalous Hall effect. By scaling surface scattering contribution with ${\rho }_{AHs}\sim {\rho }_{ss}^{\gamma }$, the exponent γ has been found to decrease with the increase of surface scattering resistivity, which could account for the thickness-dependent anomalous Hall effect. Interface diffusion induced by rapid thermal annealing modifies not only the magnetization and longitudinal resistivity but also the anomalous Hall effect; a large exponent γ $\sim$ 5.7 has been attributed to interface scattering-dominated anomalous Hall effect.

Figure 1

(a) The representative Hall loops of the as-deposited [Co(3 Å)/Pd(5 Å)]${}_n$ multilayers with repetition $n$ $=$ 6, 20, 40, and 80 measured at 5 K. (b) The Hall loops of [Co/Pd]${}_{20}$ multilayers measured at 5, 150, and 325 K.

Figure 2

The temperature dependence of (a) ${\rho }_{AH}$ and (b) ${\rho }_{xx}$ for the as-deposited [Co(3 Å)/Pd(5 Å)]${}_n$ multilayers, respectively.

Figure 3

The repetition dependence of (a) ${\rho }_{xx}$ and (b) ${\rho }_{AH}$ at 5 K for the as-deposited [Co(3 Å)/Pd(5 Å)]${}_n$ multilayers, respectively.

Figure 4

The dependence of ${\rho }_{AH}$ on ${\rho }_{xx}$ at 5 K for the as-deposited [Co(3 Å)/Pd(5 Å)]${}_n$ multilayers. Inset: the plot of $\log |{\rho }_{AH}|$ vs $\log {\rho }_{xx}$.

Figure 5

${\rho }_{AH}/{\rho }_{xx}$ as a function of ${\rho }_{xx}$ for the as-deposited [Co(3 Å)/Pd(5 Å)]${}_{40}$ multilayers. The black solid line is a linear fitting for temperature dependence of the sample. Upper right insets: dependence of coefficients $a$ and $b$ on the film thickness. Lower right inset: ${\rho }_{AH}/{\rho }_{xx}$ as a function of ${\rho }_{xx}$ at 5 K for the as-deposited [Co(3 Å)/Pd(5 Å)]${}_n$ multilayers. The red solid lines are linear fittings for the data at 5 K for thickness dependence of the samples.

Figure 6

Analysis of the scaling relation by the form of $|{\rho }_{AHs}|\sim {\rho }_{ss}^{\gamma }$. The plot of $\log |{\rho }_{AHs}|$ vs $\log {\rho }_{ss}$. The dashed line is a linear fitting, yielding γ $=$ 1.17 ± 0.09. The dotted line is a guide to the eye, and the short solid lines are the tangent line at each data point. Inset: the dependence of exponent γ on ${\rho }_{ss}$.

Figure 7

Small-angle XRD patterns for as-deposited and after annealing at 350 °C for 2 min for [Co(3 Å)/Pd(5 Å)]${}_{80}$ multilayers. (Cu Kα radiation).

Figure 8

The dependence of saturation magnetization ($M_s$) and coercivity ($H_c$) on the annealing temperature for [Co(3 Å)/Pd(5 Å)]${}_{80}$ multilayers.

Figure 9

The dependence of ${\rho }_{xx}$ and ${\rho }_{AH}$ measured at 5 K on annealing temperature for [Co(3 Å)/Pd(5 Å)]${}_{80}$ multilayers.

Figure 10

The temperature dependence of (a) $M_s$, (b) ${\rho }_{xx}$, and (c) ${\rho }_{AH}$ of the [Co(3 Å)/Pd(5 Å)]${}_{80}$ multilayers before and after annealing at 150, 250, 420, and 500 °C.

Figure 11

The plot of $\log R_s$ vs $\log {\rho }_{xx}$ for the [Co(3 Å)/Pd(5 Å)]${}_{80}$ multilayers after annealing at 420 °C. The line is a linear fitting to the data. Inset: the dependence of the exponent γ on annealing temperature for [Co(3 Å)/Pd(5 Å)]${}_{80}$ multilayers.