Transport through (Ga,Mn)As nanoislands: Coulomb blockade and temperature dependence of the conductance

We report on magnetotransport measurements of nanoconstricted (Ga,Mn)As devices showing very large resistance changes that can be controlled by both an electric and a magnetic field. Based on the bias voltage and temperature-dependent measurements down to the millikelvin range we compare the models currently used to describe transport through (Ga,Mn)As nanoconstrictions. We provide an explanation for the observed spin-valvelike behavior during a magnetic field sweep by means of the magnetization configurations in the device. Furthermore, we prove that Coulomb blockade plays a decisive role for the transport mechanism and show that modeling the constriction as a granular metal describes the temperature and bias dependence of the conductance correctly and allows to estimate the number of participating islands located in the constriction.

Figure 1

(Color) (a) Electron micrograph of the central part of a device, tilted by $40°$. (b) Polar plot of $R_{\text{sd}}$ at 1.6 K showing the strong anisotropy of $R_{\text{sd}}$ for sample A as a function of the magnetization direction. The measurement was done in a high magnetic field of 300 mT. (c) MR of sample A for $\alpha =0°$ and $\alpha =30°$ at 1.6 K. The switching fields of $\pm 28$ and $\pm 38\text{mT}$ (for $\alpha =0°$) correspond to the magnetization reversal of the broad and narrow lead, respectively. (d) Magnetization switching of the 700-nm-wide and 100-nm-wide stripe measured at 1.6 K for $\alpha =0°$ on a reference sample with additional voltage leads as shown in the sketch. Comparing the resistance values of (b) and (c) allows to deduce the magnetization alignment in the constriction. The configurations for a HR state together with the magnetization angle in the constriction is sketched in (e).

Figure 2

(Color online) (a) Temperature dependence of $R_{\text{sd}}$ for the low and high resistance state of sample A at $V_{\text{sd}}=15\text{mV}$. The inset displays the differential conductance versus $V_{\text{sd}}$ for different temperatures at $B=0$ showing insulating behavior below 30 K. (b) Temperature dependence of the MR effect observed during a magnetic field sweep at $V_{\text{sd}}=15\text{mV}$. A corresponding MR measurement is shown for 4 K in the inset.

Figure 3

(Color) (a) $I\text{−}V$ characteristics of sample B for two different gate voltages showing that the device acts as a transistor. (b) Dependence of the conductance on the gate voltage for $\alpha =0°$ and $V_{\text{sd}}=3\text{mV}$. The oscillating behavior is ascribed to a CB transport. $\Delta V_g$ stands for the average oscillation period. (c) Color plot of the conductance versus gate and source-drain voltage for $0°$ resulting in a CB diamondlike structure. (d) Polar plot of $R_{\text{sd}}$ for different gate voltages. (e) CB diamondlike structure for $\alpha =90°$ illustrating that the pattern changes for different magnetization directions. (f) $I\text{−}V$ characteristics for different magnetization directions. Gate voltage and magnetization are independent parameters which allow to tune the conductance. All measurements were carried out at $B=0.73\text{T}$ and $T=0.55\text{K}$.

Figure 4

(Color) [(a)–(b)] $\text{log}G$ versus $T^{-1/2}$ plot in a HR and LR state realized by applying a $B$ field of 730 mT along $120°$ and $90°$, respectively, showing that our experiments are not consistent with the low-field regime of the model for granular metal films. [(c)–(d)] Voltage dependence of $G$ showing a good agreement with the model for the high-field regime. From the linear fit we obtain $\text{ln}\left[G_{\infty }\left(HR\right)/{10}^{-4}{e}^2/h\right]=32\pm 2$, $V_0=\left(0.15\pm 0.01\right)\text{V}$ for $\alpha =120°$ (HR) and $\text{ln}\left[G_{\infty }\left(LR\right)/{10}^{-4}{e}^2/h\right]=18\pm 2$, $V_0=\left(0.038\pm 0.003\right)\text{V}$ for $\alpha =90°$. [(e)–(f)] Experimental data and numerical fits for the temperature dependence of $G$ for different $V_{\text{sd}}$ for HR and LR state, respectively. $N$ is the fitting parameter and indicates the number of islands which are schematically illustrated in the inset. The sensitivity of $N$ is demonstrated in (g) and (h).