Spin Polarized Tunneling at Finite Bias

A mesoscopic spin valve is used to determine the dynamic spin polarization of electrons tunneling out of and into ferromagnetic (FM) transition metals at finite voltages. The dynamic polarization of electrons tunneling out of the FM slowly decreases with increasing bias but drops faster and even inverts with voltage when electrons tunnel into it. A free-electron model shows that in the former case electrons originate near the Fermi level of the FM with large polarization whereas in the latter, electrons tunnel into hot electron states for which the polarization is significantly reduced. The change in sign is ascribed to the matching of the electron wave function inside and outside the tunnel barrier.

Figure 1

(a) Scanning electron microscope image of a device and measuring scheme. (b),(c) Spin-valve effect. $V_D/I_S$ for $V_{\mathrm{dc}}=0$ and $I_S=2\mu \mathrm{A}$ as a function of $H$ at 4.2 K. The arrows on the curves indicate the field sweep direction. The arrows at the bottom of the figure represent the magnetic configuration of the leads.

Figure 2

(a) Normalized dynamic polarization $p$ for a sample at 4.2 K (main panel) and a sample at 295 K (inset). Electrons are injected out of the FM for $V_{\mathrm{dc}}<0$ and into it for $V_{\mathrm{dc}}>0$. (b) Spin-valve effect showing a sign change in the voltage switching at large positive bias (CoFe as the source). (c) Dynamic conductance of the CoFe junction at 4.2 K.

Figure 3

(a) Schematic diagram of the source tunnel junction. Parabolic $E(k)$ curves displaced in energy represent the exchange-split majority- and minority-spin bands of the ferromagnetic electrode. Top (bottom) panel: representation of negative (positive) bias. (b) Calculated dynamic polarization $p$ as a function of bias for $\varphi =1.35\mathrm{eV}$ (black) and 1.2 eV (gray). The lower inset shows the dynamic conductance of the junction for the majority (solid line) and minority band (dashed line). The upper inset shows $D/D_{\max }$ as a function of $E_B$ for different biases. In both insets, $\varphi =1.35\mathrm{eV}$.