Weak localization in ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$: Evidence of impurity band transport

We report the observation of negative magnetoresistance in the ferromagnetic semiconductor ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$, $x=0.05–0.08$, at low temperatures $(T<3\mathrm{K})$ and low magnetic fields $(0<B<20\mathrm{mT})$. We attribute this effect to weak localization. Observation of weak localization strongly suggests impurity band transport in these materials, since for valence band transport one expects either weak antilocalization due to strong spin-orbit interactions or total suppression of interference by intrinsic magnetization. In addition to the weak localization, we observe Altshuler-Aronov electron-electron interaction effects in this material.

Figure 1

(Color online) Temperature dependence of resistivity at $B=0$ plotted for samples with 5% Mn (solid dots) and 6.5% Mn (open dots). Triangles are measured at $B_{\perp }=30\mathrm{mT}$. In the inset the height $\left[\rho \right(30\mathrm{mT})-\rho (0\left)\right]∕\rho \left(0\right)$ (dots) and the full width at half maximum (FWHM) (triangles) of magnetoresistance peak seen in Fig. 2 are plotted as a function of temperature.

Figure 2

(Color online) Magnetoresistance in 5% Mn sample plotted at different temperatures $0.05<T<6\mathrm{K}$. Between $1.6\mathrm{K}$ and $4.2\mathrm{K}$ $\rho \left(B\right)$ is plotted at $0.2\mathrm{K}$ intervals. In the inset zero-field peak at $50\mathrm{mK}$ is enlarged. The dashed curve is a fit with $\rho \left(B\right)-\rho \left(0\right)\propto B^2$.

Figure 3

(Color online) Magnetoresistance plotted for three samples with different Mn concentrations for normal $\left(B_{\perp }\right)$ and in-plane $(B\Vert [110\left]\right)$ magnetic fields. Solid (dashed) curves are for magnetic field sweeps up (down). Data for $B_{\perp }\left(B_{\left[110\right]}\right)$ were measured at $66\mathrm{mK}\left(23\mathrm{mK}\right)$.

Figure 4

(Color online) Magnetoresistance (left panel) and planar Hall effect (right panel) shown for different orientations of in-plane magnetic field in the 6.5% Mn sample. All curves except $\alpha =90°$ are offset for clarity. Angle $\alpha =0°$ corresponds to $B\Vert \left[110\right]$, $\alpha =45°$ to $B\Vert \left[100\right]$ (the easy axis of magnetization), and $\alpha =90°$ to $B\Vert \left[1\overline{1}0\right]$. Current $I\Vert \left[110\right]$. Solid (dashed) curves are for magnetic field sweeps up (down).