Conductance of atomic size contacts of Ag and Au at high magnetic fields

TL;DR

The paper investigates magnetoconductance of monovalent Au and Ag atomic-size contacts under fields up to $20$ T using cryogenic STM and atomistic modeling. In the Landauer framework, conductance is given by $G=G_0\sum_i T_i$, and results show that pure Au/Ag have weak field dependence in single-channel transport, while residual $O_2$ near the contact can induce spin-polarized conduction and lower the conductance to about $0.8G_0$, with the jump-to-contact also affected by magnetic-field effects. Transport calculations with NEGF support the role of $O_2$ adsorption and SOC in producing spin-selective channels, while a universal binding-curve analysis explains how magnetic fields modify the contact geometry, especially in Ag. The results point to a route for designing single-channel spin-active atomic contacts by combining noble metals with magnetically active molecular systems, with potential implications for atomic-scale spintronics.

Abstract

Electronic conduction at the atomic scale can be described by Landauer's formalism. In single atom point contacts of noble metals like Au and Ag, there is just one channel open between both electrodes and the conductance is very close to the quantum of conductance $G \approx G_0=\frac{2e^2}{h}$, with the factor of two coming from spin degeneracy. The magnetoconductivity of atomic size contacts has been studied for numerous systems, unveiling local Kondo screening, magnetic order and spin-polarized currents. However, these have been mostly performed in elements with multiple open conduction channels where $G$ differs from $G_0$. The realization of a magnetically active conductor with a single open channel remains difficult to achieve. Here we present measurements of the electronic conductance of single channel Au and Ag atomic-size contacts in magnetic fields up to 20 Tesla. We observe a decrease in $G$ which goes up to about 15% in many Au contacts at 20 T. We perform calculations and find that pure Ag and Au do not present a strong field dependence of $G$, in agreement with previous results at smaller magnetic fields. We also find, however, that residual O$_2$ molecules attached close to the contact produce an an induced spin-polarized current, which leads to a decrease in $G$. We discuss the role of the magnetic response of the electrodes in the jump to contact. Our results suggest that single channel atomic size conductors with a sizeable response to a magnetic field can be built by combining noble metals and magnetically active molecular systems.

Figures (8)

• Figure 1: (a) Schematic representation of the variation of the single-atom point contact conductance $G_b$ normalized to the quantum of conductance $G_0$ as a function of the magnetic field in Au (dashed line and green and orange points). We show in the upper right inset a molecular junction consisting of O$_2$ (red) attached to atomic Au electrodes (depicted in yellow). (b) Schematic representation of the binding energy as a function of the distance $z$ in Ag (green and orange lines) for zero magnetic field and for 20 T. The grey disks in the upper right inset represent Ag atoms, and the equilibrium distance $z_0$ is indicated by arrows. (c-f) We show as colored lines some representative measurements of the conductance $G$ (normalized to the quantum of conductance $G_0$) versus distance $d$ in Ag and Au. Here $d=0$ is defined as the point of contact formation; for $d>0$, the characteristic exponential dependence of the tunneling regime is observed. Curves are obtained by moving the z-position of the tip from the tunneling into the contact regime (from right to left in the figure). The arrows indicate the final conductance value in the tunneling regime, $G_a$, and the conductance of the single-atom contact, $G_b$. Data are presented for zero magnetic field (panels (a) and (c)) and under a magnetic field of 20 T (panels (b) and(d)).
• Figure 2: We show two-dimensional histograms of $G_b/G_0$ vs $log(G_a/G_0)$ for various values of the magnetic field, indicated in each panel. The upper row displays the results for Au (a–e) and the bottom row (f–j) the results for Ag. The color scale shows occurrence of a certain conductance value from red (high) to blue (none) (cuts of the histogram and more details provided in Appendix D). Vertical and horizontal grey lines are visual guides. For the conductance of the single-atom point contact $G_b$ we mostly find $G_b=G_0$. In Au we observe that $G_b$ decreases below $G_0$ under applied magnetic fields, as highlighted by the green arrow. In Ag the conductance value immediately prior to the jump-to-contact event $G_a$ increases with the magnetic field, as highlighted by the orange arrow.
• Figure 3: (a) Color scale histograms of the conductance just before the jump-to-contact, $G_a$, for contacts with $G_b=1$, plotted as a function of the magnetic field for Au (top panel) and for Ag (bottom panel). White lines serve as visual guides. Red colour represents frequent occurence and the dark blue no occurrence. (b) The number of single-atom point contacts with $G_b<0.85 G_0$, as extracted from the histograms in Fig. \ref{['FigureCurvesHisto']}, is displayed as a function of the magnetic field (blue points for Au and red points for Ag).
• Figure 4: (a–d) Calculated conductance $G$ normalized to the quantum of conductance $G_0$ as a function of energy (relative to the Fermi energy) for atomic-sized Au point contacts. The solid lines represent spin-resolved conductance: red for spin-up and blue for spin-down channels. The black dashed line corresponds to the conductance of a bare single-atom Au contact at zero magnetic field, while the grey dashed line shows the same configuration under an applied magnetic field of 20 T. The green and yellow dashed lines show the conductance for single-atom Au contacts with an O$_2$ molecule adsorbed near the contact region, at zero field and 20 T respectively. The specific atomic arrangements of the O$_2$ molecule (red disks) considered in each panel are shown in the top-left insets of (a–d). The presence and position of the O$_2$ molecule leads a notable spin-dependent conductance reduction near the Fermi level when the O$_2$ molecule is directly attached to the contacting atoms.
• Figure 5: Binding energy as a function of the distance between the centers of the atoms located at the tip apex, obtained using the atomic arrangement shown in the inset. Filled circles are results of the calculation, and solid lines fits to the universal binding curve (we used the parameters given in Table \ref{['TabSupp_fit']}).