Figure 1

Schematic of the three-terminal geometry used for measuring the anisotropy in tunneling resistance. A constant current ($I_{\mathrm{bias}}$), across the tunnel junction produces a voltage that changes when the magnetization of the magnetic layer is rotated out-of-plane. Here, $\phi$ represents the angle between a surface normal and the external field, whereas ${\phi }_M$ is the angle between the surface normal and the magnetization direction $\vec{m}$. Here, $X$ and $Z$ denote the in-plane and surface normal direction, respectively. The measured voltage V${}_{\mathrm{meas}}$, and therefore the tunnel resistance$R\left(\phi \right)=V_{\mathrm{meas}}/I_{\mathrm{bias}}$ depends on the magnetization direction.Reuse & Permissions

Figure 2

Experimental data for a $p$-Si/Al${}_2$O${}_3$/Fe junction (a) with field perpendicular (Hanle, red) and parallel to the tunnel interface (inverted Hanle, blue) and (b) the angular dependence of the measured signal at the same bias current ($I_{\mathrm{bias}}=-91.3$ $\mu$A). Data are shown after subtracting an offset signal of $V_0=-172$ mV. Labels $B_X$ and $B_Z$ in (b) represent the situations when the external field is parallel or perpendicular to the tunnel interface. Similar data set with $n$-Si/Al${}_2$O${}_3$/Fe tunnel contacts for (c) Hanle ($\phi =0^{\circ }$, red), inverted Hanle ($\phi ={90}^{\circ }$, blue) and (d) angle scan measurements at a bias voltage of $-$172 mV ($-$807 $\mu$A). In (c), $\Delta V_{\phi =0^{\circ }}$ and $\Delta V_{\phi ={90}^{\circ }}$ are the signal amplitude obtained in Hanle and inverted Hanle measurements respectively. In (d), $R(\phi$) is the resistance ($V_{\mathrm{meas}}/I_{\mathrm{bias}}$) at the respective $\phi$ value. All the measurements have been performed at 300 K. Note that (c) and (d) have different vertical scales.Reuse & Permissions

Figure 3

$\Delta R=R\left(\phi \right)-R_{\min }$ (where $R_{\min }$ is the minimum resistance) as a function of the field angle $\phi$ at $-$172 mV (a), $-$30 mV (b), 70 mv (c), and 172 mV (d), for $p$-Si/Al${}_2$O${}_3$/Fe. Similarly $\Delta$R vs $\phi$ at $-$172 mV (e), $-$30 mV (f), 70 mv (g), and 172 mV (h), for $n$-Si/Al${}_2$O${}_3$/Fe tunnel contacts. The junction resistance values at each bias are indicated in each panel. Measurements have been taken on tunnel contacts at a field of 50 kOe and a temperature of 300 K. Note the different vertical scales for $\Delta R$ in each plot. Solid lines are fits using Eq. (4) in text.Reuse & Permissions

Figure 4

Experimental data for a $p$-Si/Al${}_2$O${}_3$/Ni tunnel contact (a) with field perpendicular (Hanle, red), and parallel to the tunnel interface (inverted Hanle, blue) and (b) angular dependence of the measured signal at a bias of $-$172 mV ($-$171 $\mu$A). Similar data set for $n$-Si/Al${}_2$O${}_3$/Ni tunnel contact are shown in (c), Hanle (red), inverted Hanle (blue), and (d) angular dependence of the measured signal at a bias of $-$172 mV ($-$650 $\mu$A). Data are shown after subtracting different offset voltages. In (b) and (d), a field with constant magnitude of 50 kOe is applied.Reuse & Permissions

Figure 5

$\Delta R$ as a function of field angle $\phi$ for (a) $p$-Si/Al${}_2$O${}_3$/Ni and (b) $n$-Si/Al${}_2$O${}_3$/Ni tunnel junctions at bias voltages (in mV) indicated in each panel. The vertical axis is $\Delta R=R\left(\phi \right)-R_{\min }$, where $R_{\min }$ is the minimum resistance value. Solid lines are fits obtained through Eq. (4) in the text. Data are displaced vertically for clarity. All the measurements have been performed at 300 K and a field of 50 kOe.Reuse & Permissions

Figure 6

Bias dependence of (a) tunneling anisotropy and (b) spin resistance $\Delta R_{\mathrm{spin}}$ = $[\Delta V_{B_{\phi =0^{\circ }}}+\Delta V_{B_{\phi ={90}^{\circ }}}]/I_{\mathrm{bias}}$, shown together with (c) junction resistance for $p$-Si/Al${}_2$O${}_3$/Fe tunnel junction. $\Delta V_{B_{\phi =0^{\circ }}}$ and $\Delta V_{B_{\phi ={90}^{\circ }}}$ have been defined in Fig. 2c.Reuse & Permissions

Figure 7

Bias dependence of the (a) tunneling anisotropy, (b) spin resistance $\Delta R_{\mathrm{spin}}$, and (c) junction resistance for $n$-Si/Al${}_2$O${}_3$/Fe tunnel junction.Reuse & Permissions

Figure 8

Bias dependence of the (a) tunneling anisotropy, (b) spin resistance, and (c) junction resistance for $p$-Si/Al${}_2$O${}_3$/Ni tunnel junction.Reuse & Permissions

Figure 9

Bias dependence of the (a) tunneling anisotropy and (b) spin resistance shown together with the (c) junction resistance for $n$-Si/Al${}_2$O${}_3$/Ni tunnel junction.Reuse & Permissions

Figure 10

(a) The angle $\theta ={\phi }_M-\phi$ and (b) normalized spin accumulation $\Delta \mu$ vs field angle $\phi$ for Fe (blue) and Ni (red). In (a), at $\phi =0^{\circ }$ and 90${}^{\circ }$, field and magnetization are aligned. For intermediate values of $\phi$, the magnetization makes an angle of $\theta =({\phi }_M-\phi )$ with the field. In (b), the spin accumulation has four pronounced minima (for Fe) at indicated $\phi$ values.Reuse & Permissions

Figure 11

Fitting parameters (a) $A_1$ and (b) $A_2$ as a function of bias for $p$-Si/Al${}_2$O${}_3$/Fe tunnel contact.Reuse & Permissions

Figure 12

Fitting parameters (a) $A_1$ and (b) $A_2$ as a function of bias for $n$-Si/Al${}_2$O${}_3$/Fe tunnel contact.Reuse & Permissions

Figure 13

Parameter $A_1$ as a function of bias for (a) $p$-Si/Al${}_2$O${}_3$/Ni and (b) $n$-Si/Al${}_2$O${}_3$/Ni tunnel contacts.Reuse & Permissions