Evaluation of spin polarization in $p$-In${}_{0.96}$Mn${}_{0.04}$As using Andreev reflection spectroscopy including inverse proximity effect

We report on carrier transport across a superconductor/ferromagnetic semiconductor junction with a highly transparent metallic contact, Nb/$p$-In${}_{0.96}$Mn${}_{0.04}$As. Below $~$10 K, $p$-In${}_{0.96}$Mn${}_{0.04}$As becomes ferromagnetic, as evidenced by the hysteretic transverse resistance caused by the anomalous Hall effect. Below the superconducting critical temperature $T$${}_c$ of the Nb electrodes (8.2 K), a conductance reduction occurs within the bias voltage that is comparable to the Nb superconducting energy gap. A rather moderate slope in the differential conductance curves within the gap region indicates the partial suppression of the Andreev reflection caused by spin-polarized carriers in $p$-In${}_{0.96}$Mn${}_{0.04}$As. Spin polarization $P$ in $p$-In${}_{0.96}$Mn${}_{0.04}$As has been extracted by fitting the measured differential conductance curves with a newly modified Blonder-Tinkham-Klapwijk model with both spin polarization and the inverse proximity effect (mod2-BTK model). The extracted $P$ value is $P$ $=$ 0.725 at 0.5 K, and it decreases gradually with increasing temperature.

Figure 1

(a) Schematic cross-sectional view of a $p$-In${}_{0.96}$Mn${}_{0.04}$As wafer, (b) a Hall bar and measurement setup, and (c) magnetic-field dependence of Hall resistance for $p$-In${}_{0.96}$Mn${}_{0.04}$As. The applied magnetic fields range from $+90\hspace{0.5em}000$ to $-10\hspace{0.5em}000$ G.

Figure 2

(a) Measurement setup and (b) Hall resistance curves obtained from the setup shown in (a) at various temperatures.

Figure 3

(a) Measurement setup and (b) normalized $\mathit{dI}/\mathit{dV}-V$ characteristics obtained from the device shown in (a) at various temperatures.

Figure 4

Calculated probability distribution for the pair potential at the S-F interface ${\Delta }_{S0}$ assuming a Gaussian distribution $[\frac{1}{\sqrt{2\pi {\sigma }^2}}\exp (-\frac{({\Delta }_{S0}-\mu ){}^2}{2{\sigma }^2})]$ with a mean $\mu$ of 1.05 meV and a variance ${\sigma }^2$ of 0.2401. The inset shows a schematic model of the system where the pair potential in the S region decreases exponentially near the S-F interface $[\Delta (0⩽x⩽X_P)=({\Delta }_S-\frac{({\Delta }_S-{\Delta }_{S0})}{1-e})+(\frac{({\Delta }_S-{\Delta }_{S0})}{1-e})\exp (-\frac{(x-X_P)}{X_P})]$, whereas the pair potential vanishes in the F region.

Figure 5

Comparison of the measured and calculated $\mathit{dI}/\mathit{dV}-V$ characteristics at 0.5 K. The thick solid line (black) represents experimental data. The open circles (red) are calculated using the mod2-BTK model. The values used in the calculation are $Z=0.25$, $P=0.725$, ${\Delta }_S=$ 1.4 meV, $\Gamma =$ 0.15 meV, ${\xi }_S=$ 40 nm, $X_P=$ 0.6 $\mu$m, $\mu =$ 1.05 meV, and ${\sigma }^2=0.2401$. The open triangles (blue) use the mod1-BTK model with $Z=0.25$ and $P=0.745$. $\mathit{dI}/\mathit{dV}$ is normalized by the value near $V$ $=$ 2 mV.

Figure 6

Temperature dependence of spin polarization $P$ and anomalous Hall resistance terms in $p$-In${}_{0.96}$Mn${}_{0.04}$As. The solid circles (red) and left axis represent $P$. The open circles (black) and right axis represent anomalous Hall resistance terms. The $P$ values are determined by comparing the measured $\mathit{dI}/\mathit{dV}-V$ characteristics at several temperatures with those obtained from the mod2-BTK model. The anomalous Hall resistance terms are obtained from the $y$ intercept of the $R_H-H$ curves shown in Fig. 2b.

Figure 7

Calculated $\mathit{dI}/\mathit{dV}-V$ characteristics at 0.5 K obtained using the mod2-BTK model with three different $Z$ values. Open triangles (blue), open circles (red), open diamonds (green) indicate results obtained with $Z$ $=$ 0, 0.25, and 0.5, respectively. The thick solid line (black) represents experimental data obtained at 0.5 K. The $\mathit{dI}/\mathit{dV}$ values are normalized with the value obtained at a bias voltage of $V$ $=$ 2 mV. Other physical quantities used for the calculations are $P=0.725$, ${\Delta }_S=$ 1.4 meV, $\Gamma =$ 0.15 meV, ${\xi }_S=$ 40 nm, $X_P=$ 0.6 $\mu$m, $\mu =$ 1.05 meV, and ${\sigma }^2=0.2401$, as shown in the inset.

Figure 8

Calculated $\mathit{dI}/\mathit{dV}-V$ characteristics at 0.5 K obtained using the mod2-BTK model with three different $P$ values. Open triangles (blue), open circles (red), open diamonds (green) indicate results obtained with $P$ $=$ 0.7, 0.725, and 0.75, respectively. The thick solid line (black) represents experimental data obtained at 0.5 K. The $\mathit{dI}/\mathit{dV}$ values are normalized with the value obtained at a bias voltage of $V$ $=$ 2 mV. Other physical quantities used for the calculations are $Z=0.25$, ${\Delta }_S=$ 1.4 meV, $\Gamma =$ 0.15 meV, ${\xi }_S=$ 40 nm, $X_P=$ 0.6 $\mu$m, $\mu =$ 1.05 meV, and ${\sigma }^2=0.2401$, as shown in the inset.

Figure 9

Calculated $\mathit{dI}/\mathit{dV}-V$ characteristics at 0.5 K obtained using the mod2-BTK model using four different combinations of $\Gamma$ and $P$ values. Open diamonds (green) indicate results obtained with $\Gamma =$ 0 meV and $P$ $=$ 0.75. Open triangles (blue), open circles (red), crosses (purple) indicate results obtained with $\Gamma =$ 0, 0.15, 0.3 meV, and $P$ $=$ 0.725, respectively. The thick solid line (black) represents experimental data obtained at 0.5 K. The $\mathit{dI}/\mathit{dV}$ values are normalized with the value obtained at a bias voltage of $V$ $=$ 2 mV. Other physical quantities used for the calculations are $Z=0.25$, ${\Delta }_S=$ 1.4 meV, ${\xi }_S=$ 40 nm, $X_P=$ 0.6 $\mu$m, $\mu =$ 1.05 meV, and ${\sigma }^2=0.2401$, as shown in the inset.

Figure 10

Calculated $\mathit{dI}/\mathit{dV}-V$ characteristics at 0.5 K obtained using the mod2-BTK model with three different $X_P$ values. Open triangles (blue), open circles (red), open diamonds (green) indicate results obtained with $X_P=$ 40 nm, 0.6 $\mu$m, and 1.2 $\mu$m, respectively. The thick solid line (black) represents experimental data obtained at 0.5 K. The $\mathit{dI}/\mathit{dV}$ values are normalized with the value obtained at a bias voltage of $V$ $=$ 2 mV. Other physical quantities used for the calculations are $Z=0.25$, $P=0.725$, ${\Delta }_S=$ 1.4 meV, $\Gamma =$ 0.15 meV, ${\xi }_S=$ 40 nm, $\mu =$ 1.05 meV, and ${\sigma }^2=0.2401$, as shown in the inset.

Figure 11

Calculated $\mathit{dI}/\mathit{dV}-V$ characteristics at 0.5 K obtained using the mod2-BTK model with three different $\mu$ values. Open triangles (blue), open circles (red), open diamonds (green) indicate results obtained with $\mu =$ 0.7, 1.05, and 1.4 meV, respectively. The thick solid line (black) represents experimental data obtained at 0.5 K. The $\mathit{dI}/\mathit{dV}$ values are normalized with the value obtained at a bias voltage of $V$ $=$ 2 mV. Other physical quantities used for the calculations are $Z=0.25$, $P=0.725$, ${\Delta }_S=$ 1.4 meV, $\Gamma =$ 0.15 meV, ${\xi }_S=$ 40 nm, $X_P=$ 0.6 $\mu$m, and ${\sigma }^2=0.2401$, as shown in the inset.

Figure 12

Calculated $\mathit{dI}/\mathit{dV}-V$ characteristics at 0.5 K obtained using the mod2-BTK model with three different ${\sigma }^2$ values. Open triangles (blue), open circles (red), open diamonds (green) indicate results obtained with ${\sigma }^2=$ 0.0882, 0.2401, and 0.49, respectively. The thick solid line (black) represents experimental data obtained at 0.5 K. The $\mathit{dI}/\mathit{dV}$ values are normalized with the value obtained at a bias voltage of $V$ $=$ 2 mV. Other physical quantities used for the calculations are $Z=0.25$, $P=0.725$, ${\Delta }_S=$ 1.4 meV, $\Gamma =$ 0.15 meV, ${\xi }_S=$ 40 nm, $X_P=$ 0.6 $\mu$m, and $\mu =$ 1.05 meV, as shown in the inset.