Negative Nonlocal Resistance in Mesoscopic Gold Hall Bars: Absence of the Giant Spin Hall Effect

We report the observation of negative nonlocal resistances in multiterminal mesoscopic gold Hall bar structures whose characteristic dimensions are larger than the electron mean-free path. Our results can only be partially explained by a classical diffusive model of the nonlocal transport, and are not consistent with a recently proposed model based on spin Hall effects. Instead, our analysis suggests that a quasiballistic transport mechanism is responsible for the observed negative nonlocal resistance. Based on the sensitivity of our measurements and the spin Hall effect model, we find an upper limit for the spin Hall angle in gold of 0.023 at 4.5 K.

Figure 1

Schematic depiction of the physical mechanisms giving rise to (a) positive $R_{\mathrm{nl}}^c$, (b) positive $R_{\mathrm{nl}}^{\mathrm{SH}}$, and (d) negative $R_{\mathrm{nl}}$ due to quasibalistic transport as described in the text. Arrows indicate the direction of electron flow. (c) SEM image of the central region of the gold Hall bar with seven vertical wires bridged by a horizontal one.

Figure 2

Resistance of the bridging wire ($L=300\mathrm{nm}$) as a function of $T$. Lower inset: SEM image of the segment of the wire whose resistance is plotted, adapted to show the actual measurement configuration. Upper inset: Resistance of each segment of the bridging wire between adjacent vertical wires (open circles) at 4.5 K as a function of $L$. The red line is a linear fit to the data.

Figure 3

Temperature dependence of $R_{\mathrm{nl}}$ measured for wires separated by a distance $L=300\mathrm{nm}$. Lower inset: SEM image of the segment of the structure where $R_{\mathrm{nl}}$ was measured, adapted to show the actual measurement configuration. Upper inset: $R_{\mathrm{nl}}/R_{\mathrm{sq}}$ as a function of temperature.

Figure 4

(a)–(f) $R_{\mathrm{nl}}/R_{\mathrm{sq}}$ as a function of electron mean-free path for different $L$ values. Corresponding fits to Eq. (3) are shown as red lines.

Figure 5

(a) Parameter $a$ vs. $L$ (open circles) and the best exponential fit (red line) as explained in the text; (b) Parameter $b$ vs. $L$; (c) Negative $R_{\mathrm{nl}}$ vs. $L_{\mathrm{eff}}$ at 4.5 and 295 K and the corresponding fitting curves explained in the text.