Figure 1

(a) Schematic of the sample design and the experimental setup. The red and blue arrows define the plane in which the magnetic field is applied. (b) Bright-field transmission electron micrograph (TEM) of a core-shell nanowire cross section. The hexagonal core of GaAs with $\left\{11\overline{2}0\right\}$-oriented side facets is clearly distinguishable from the (Ga,Mn)As shell, which shows an epitaxial interface to the core. (c) Tilted scanning electron micrograph (SEM) of a contacted nanowire.Reuse & Permissions

Figure 2

Magnetoresistance curves at $T$ $=$ 4 K of (a) a single nanowire sample and (b) of a lithographically fabricated nanostripe array (Ref. 21) taken for different in-plane magnetic field directions between 0° (red) and 90° (blue). The field was swept from negative to positive values of $H_0$ (up sweep). The grey traces illustrate the gradual transition from the 0° to the 90° magnetoresistance trace. The small peak in (a) around ∼1 T in the topmost (blue) trace indicates that the field was not perfectly aligned along the 90° direction (accuracy of alignment: $\pm$2°).Reuse & Permissions

Figure 3

Magnetotransport data at $T$ $=$ 4 K: (a) $\vec{H}$ parallel to the nanowire axis (0°). Arrows illustrate the relative orientation of external field and magnetization. The dashed grey line is the calculated effective magnetic field $H_{\mathrm{eff}}$. The resistance jump reflects a change of the NMR as the effective magnetic field changes by 2$H_C$ at this field. (b) $\vec{H}$ perpendicular to the nanowire axis (90°). Also here the MR follows inversely the calculated effective magnetic field (dashed line). The dashed lines in (a) and (b) show $H_{\mathrm{eff}}$ as a function of $H_0$ for the two magnetic field configurations with the corresponding $y$ axis on the right side.Reuse & Permissions

Figure 4

(a) Dependence of the magnetoresistance on ${\phi }_m$ at $T=4\mathrm{K}$ and ${\mu }_0{H}_0=3\mathrm{T}$ (green dots): The resistance values are obtained from a measurement of $R\left({\phi }_H\right)$, while the corresponding values of ${\phi }_M$ are calculated by minimizing Eq. (1) for a given value of $H_0$ and ${\phi }_H$. $R\left({\phi }_M\right)$ can be well fitted by $\cos \left(2{\phi }_M\right)$ (orange curve) which describes approximately the angular dependence of the effective magnetic field. (b) Illustration of the transformation from the ${\mu }_0{H}_0$ to the ${\mu }_0{H}_{\mathrm{eff}}$ scale, by shifting $R\left({90}^{\circ }\right)$ and $R\left(0^{\circ }\right)$ by $\pm {\mu }_0{H}_A$. The resulting high field magnetoresistance at 4 K as a function of the effective magnetic field is shown in the inset. This makes the two curves directly comparable for values of the effective field of ${\mu }_0{H}_{\mathrm{eff}}>2.2\mathrm{T}$.Reuse & Permissions