Berry-phase contribution to the anomalous Hall effect in gadolinium

When conduction electrons are forced to follow the local spin texture, the resulting Berry phase can induce an anomalous Hall effect (AHE). In gadolinium, as in double-exchange magnets, the exchange interaction is mediated by the conduction electrons and the AHE may therefore resemble that of $\mathrm{Cr}{\mathrm{O}}_2$ and other metallic double-exchange ferromagnets. The Hall resistivity, magnetoresistance, and magnetization of single crystal gadolinium were measured in fields up to $30\mathrm{T}$. Measurements between $2\mathrm{K}$ and $400\mathrm{K}$ are consistent with previously reported data. A scaling analysis for the Hall resistivity as a function of the magnetization suggests the presence of a Berry-phase contribution to the anomalous Hall effect.

Figure 1

Gadolinium resistivity vs temperature.

Figure 2

(Color online) Gadolinium Hall resistivity vs applied magnetic field.

Figure 3

(Color online) Gadolinium reduced magnetization vs applied magnetic field.

Figure 4

(Color online) Gadolinium Hall resistivity vs reduced magnetization.

Figure 5

(Color online) Gadolinium ordinary Hall coefficient vs temperature. This represents the best fit to the data in fields below $7\mathrm{T}$. Lee and Legvold’s data are shown for comparison. (Ref. 20).

Figure 6

(Color online) Gadolinium anomalous Hall coefficient vs temperature. Previously reported data are shown for comparison (Refs. 20, 27).

Figure 7

(Color online) Gadolinium Hall resistivity vs applied magnetic field.

Figure 8

(Color online) Gadolinium reduced magnetization vs applied magnetic field.

Figure 9

(Color online) Temperature scaled Hall resistivity vs reduced magnetization.

Figure 10

Anomalous Hall coefficient vs resistivity squared. The residual resistivity has been subtracted. The ordinary Hall coefficient has been neglected when converting Lee and Legvold’s data from $R_1$ to $R_s$ (Ref. 20). The discrepancy in the plots is either due to an error in estimating the length between voltage contacts, or a systematic error in reading Lee and Legvold’s data from their log-scale plot. The line is the side-jump prediction using the experimental coefficient for iron (Refs. 1, 3, 5).

Figure 11

(Color online) Possible Berry-phase contribution vs reduced magnetization. The estimated side-jump contribution accounts for one-sixth of the Hall effect at $T_{\mathrm{C}}$.