Nonlocal anomalous Hall effect in ternary alloys based on noble metals

We present a theoretical study of the nonlocal anomalous Hall effect induced by heavy-metal impurities in dilute magnetic alloys based on noble metals. The results of our first-principles calculations are shown in comparison to those obtained within a model consideration via Matthiessen's rule. Based on the transport properties of the constituent binary alloys, we reveal optimal host-impurity combinations to enhance the phenomenon. In particular, this allows us to explain experimental findings showing a strong effect in Cu-based alloys but a vanishing effect in the case of the Au host.

Figure 1

The anomalous Hall angle of the Cu(${\mathrm{Mn}}_{1-w}{B}_w$), Ag(${\mathrm{Mn}}_{1-w}{B}_w$), and Au(${\mathrm{Mn}}_{1-w}{B}_w$) alloys divided by the spin Hall angle of the related Cu($B$), Ag($B$), and Au($B$) alloys, where $B$ denotes the nonmagnetic impurities of Table 1. The solid lines provide the results obtained by Matthiessen's rule via Eq. (3) and the dashed lines with the approximation of Eq. (5). The dots are results of straightforward ab initio transport calculations. They are performed according to the approach of Ref. [23], where Fig. 2 relates to the upper graph of this figure.

Figure 2

The anomalous Hall angle of the Cu($A_{1-w}{B}_w$) alloys divided by the spin Hall angle of the related Cu($B$) alloys, where $A$ and $B$ denote the magnetic and nonmagnetic impurities of Table 1, respectively. The solid lines provide the results obtained with Matthiessen's rule via Eq. (3) and the dashed lines with the approximation of Eq. (5). The dots are results of straightforward ab initio transport calculations according to the approach of Ref. [23].

Figure 3

The AHA of the Cu(${\mathrm{Fe}}_{1-w}{B}_w$) alloys divided by the AHA of the Cu(Fe) alloy (left) and the AHA of the Ag(${\mathrm{Fe}}_{1-w}{B}_w$) alloys (right), where $B$ denotes the nonmagnetic impurities of Table 1. The dashed lines corresponding to the approximation of Eq. (5) practically coincide with the solid lines, providing the results obtained with Matthiessen's rule via Eq. (3). The dots are results of straightforward ab initio transport calculations performed according to the approach of Ref. [23].