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

Technical Summary: Conductance of Atomic Size Contacts of Ag and Au at High Magnetic Fields

Problem Statement
Electronic conduction at the atomic scale is typically described by Landauer's formalism, where conductance ($G$) is determined by the number of open channels ($N$) and their transmission probabilities ($T_i$). In monovalent noble metals like Gold (Au) and Silver (Ag), single-atom point contacts usually exhibit a single open channel with conductance close to the quantum of conductance ($G_0 = 2e^2/h$). While the magnetoconductivity of atomic contacts has been extensively studied in magnetic materials (e.g., Fe, Co) or systems with multiple open channels ($N \ge 1$), realizing a magnetically active conductor with a single open channel remains a significant challenge. Pure Au and Ag are non-magnetic, and previous studies at lower magnetic fields suggested their conductance is largely field-independent. The authors investigate whether high magnetic fields (up to 20 T) can induce significant changes in the conductance of single-channel Au and Ag contacts and identify the underlying mechanisms.

Methodology
The study employs a combination of experimental measurements and theoretical modeling:

• Experimental Setup: The authors utilized a cryogenic Scanning Tunneling Microscope (STM) integrated with a 20 Tesla fully superconducting magnet. Measurements were conducted at 4.2 K using 99.99% pure Au and Ag wires. To ensure clean, reproducible atomic contacts, the tip and sample were repeatedly indented to mechanically anneal the contact region. This "reset" approach at each magnetic field value prevented the tracking of a single contact over time but allowed for the statistical analysis of tens of thousands of conductance-versus-distance curves across various contact geometries. Impurity levels were verified to be negligible.
• Theoretical Modeling:
  • Structural Simulation: Classical Molecular Dynamics (CMD) using the LAMMPS package and Embedded-Atom-Model (EAM) potentials simulated the formation and rupture of nanocontacts to generate realistic dimer configurations.
  • Electronic Structure: Density Functional Theory (DFT) calculations were performed using Gaussian16 within the Unrestricted Local Spin Density Approximation (LSDA). These calculations included spin-orbit coupling and relativistic effects.
  • Transport Calculations: Non-Equilibrium Green's Functions (NEGF) were used to calculate conductance, employing a new implementation in the ANT.Gaussian code that allows for the self-consistent inclusion of a magnetic field in the z-direction.
  • Binding Energy: Universal binding curves were constructed using DFT (GGA-PBE functional with GD3BJ dispersion corrections) to analyze the interplay between elastic and magnetic forces during contact formation.

Key Results

1. Conductance Reduction in Au: In single-atom Au contacts, the authors observed a decrease in the contact conductance ($G_b$) under high magnetic fields. At 20 T, $G_b$ drops by up to approximately 15% below $G_0$ in a significant fraction of contacts. This effect is less pronounced in Ag.
2. Increase in Pre-Contact Conductance ($G_a$): The conductance immediately prior to the jump-to-contact ($G_a$) increases with the magnetic field, a trend particularly strong in Ag. This suggests a magnetic field-induced modification in the equilibrium separation distance where the bond forms.
3. Role of Residual Oxygen ($O_2$): Theoretical calculations indicate that pure Au and Ag do not exhibit strong field dependence on their own. However, the presence of residual $O_2$ molecules attached near the contact induces spin-polarized currents.
   • When an $O_2$ molecule is chemisorbed directly between the two contacting Au atoms, it creates a magnetic moment (approx. 1.74 $\mu_B$) and reduces the conductance to $\approx 0.8 G_0$ due to spin-dependent transport.
   • The authors propose that the high magnetic field induces the adsorption or "sticking" of $O_2$ molecules into the contact region by aligning their magnetic moments, thereby increasing the probability of forming these specific, conductance-reducing configurations.
4. Magnetic Anisotropy in Contact Formation: The increase in $G_a$ (and the corresponding shift in bond formation distance) is attributed to magnetic torques arising from anisotropic surface currents in the nanoscale constrictions. The magnetic field modifies the energy balance of the bonding process, particularly in Ag where the binding energy is lower, leading to a shift in the equilibrium position of the atoms by approximately 0.3 Å at 20 T.

Significance and Claims
The paper claims that single-channel atomic conductors, traditionally viewed as magnetically inert, can exhibit sizeable magnetic responses when combined with magnetically active molecular systems. The primary significance lies in demonstrating that:

• High magnetic fields can induce spin-dependent transport in noble metal atomic contacts via the mediation of adsorbed $O_2$ molecules.
• The magnetic field actively influences the atomic-scale contact formation process (the "jump to contact") through magnetic torques on surface currents, altering the equilibrium bonding distance.
• It is possible to build single-channel atomic size conductors with a significant response to magnetic fields by combining noble metals with magnetically active molecular systems, offering a pathway to control electronic transport at the atomic scale without relying on intrinsic ferromagnetism.

The authors remain modest regarding the specific mechanisms of the $O_2$ adsorption, noting that while the calculations explain the conductance reduction, the experimental observation of increased frequency of these events under high fields is attributed to field-induced alignment and sticking of the molecules. They also note that features in the conductance histograms for $G_b > G_0$ remain difficult to fully address and may relate to specific electrode shapes or multiple-atom contacts.