Absence of Zero-Bias Anomaly in Spin-Polarized Vacuum Tunneling in Co(0001)

In a joint experimental and theoretical study, we investigate the bias-voltage dependence of the tunnel magnetoresistance (TMR) through a vacuum barrier. The TMR observed by spin-polarized scanning tunneling microscopy between an amorphous magnetic tip and a Co(0001) sample is almost independent of the bias voltage at large tip-sample separations. Whereas qualitative understanding is achieved by means of the electronic surface structure of Co, the experimental findings are compared quantitatively with bias-voltage dependent first-principles calculations for ballistic tunneling. At small tip-sample separations, a pronounced minimum in the experimental TMR was found at $+200\mathrm{m}\mathrm{V}$ bias.

Figure 1

Tunnel magnetoresistance $\delta$ and its error of a clean Co(0001) surface vs bias voltage $U$, obtained with a magnetic tip stabilized at 1 V, 1 nA (a) and at 100 mV, 1 nA (b).

Figure 2

(a) Spin-resolved relativistic band structure of bulk hcp Co along the $\Gamma –\Delta –\mathrm{A}$ direction (i.e., ${\overrightarrow{k}}_{\parallel }=0$). The sliding grey scale of the filled circles reflects the spin polarization $P$: “majority” ($P\approx 1$) black; “minority” ($P\approx -1$) white. (b) Spin- and layer-resolved spectral density of Co(0001) at ${\overrightarrow{k}}_{\parallel }=0$ for the first four surface layers (S, S-1, …, S-3) and a bulk layer (B). The arrows mark surface states.

Figure 3

Theoretical spin-dependent tunneling through Co(0001) planar junctions. (a) Averaged conductances $G_{\mathrm{a}\mathrm{v}}$ in logarithmic scale for P (solid lines) and AP (dashed) configurations at various barrier widths $d$ (triangles: $d=2d_0$, squares: $d=3d_0$; in units of the Co interlayer distance $d_0$) vs bias voltage. (b) Tunnel magnetoresistance $\delta$ obtained from the data shown in (a).