Substantial Magnetic Fields Arising from Ballistic Ring Currents in Single-Molecule Junctions

Abstract

When a small electric bias is applied to a single-molecule junction, current will flow through the molecule via a tunneling mechanism. In molecules with a cyclic or helical structure there may be circular currents, giving rise to a unidirectional magnetic field. Here, we implement the Biot-Savart law and calculate the magnetic field resulting from the ballistic current density for a selection of molecules. We find that three prerequisites are important for achieving a substantial magnetic field in a single-molecule junction. (1) The current must be high, (2) the ring current must be unidirectional within the bias window, and (3) the diameter of the ring current must be small. We identify both cyclic and linear molecules that potentially fulfill these requirements. In cyclic annulenes with bond-length alternation the current-induced magnetic field can approach the mT-range whereas archetypical cyclic molecules, such as benzene, are not suitable candidates for the generation of a substantial magnetic field. In linear carbon chains with circular currents due to their helical π-systems, the magnetic field is in the mT-range. When the bias window is gated closer to resonance, we show that the magnetic field can potentially reach the sub-tesla range. Our results provide proof-of-concept for achieving experimentally relevant current-induced magnetic fields in molecular wires at low bias.

Keywords: Biot−Savart law; current density; magnetism; molecular electronics; ring current; single-molecule electromagnetism; single-molecule junction.

1

(a) Ballistic current density and the resulting magnetic field computed for an aniline-terminated diyne. The current density cutoff is 5% of the maximum current density; magnetic field cutoff is 20% of the maximum field strength. (b) Schematic depiction of the linear current and circular magnetic field of the diyne as predicted by the right-hand rule. (c) Schematic depiction of the circular ring current in a meta-connected benzene and the resulting enhanced unidirectional magnetic field as predicted by the right-hand rule.

2

Current density (top row), and magnetic field (middle and bottom row) of ortho-, para-, and meta-linked benzenes. The magnetic field is plotted as a vector field (middle row) and as the point where the field is strongest (bottom row). Linkers have been removed for clarity.

3

Current density (top row), and magnetic field (middle and bottom row) of cyclic molecules with bond-length alternation. The magnetic field is plotted as a vector field (middle row) and as the point where the field is strongest (bottom row). Linkers have been removed for clarity.

4

Current density and magnetic field of aniline-terminated diyne with the end-groups rotated to 60° orientation. The magnetic field is plotted as a vector field (middle row) and as the point where the field is strongest (bottom row).

5

Current density (top row), and magnetic field (middle and bottom row) of [5]- and [4]­cumulenes. Both cumulenes are also shown with end-groups rotated into 60° orientation. Note that the functionalized [5]­cumulene has near-coplanar end groups and the functionalized [4]­cumulene has near-perpendicular end groups in their ground-state structures. The magnetic field is plotted as a vector field (middle row) and as the point where the field is strongest (bottom row).

6

Current density (top row), and magnetic field (middle and bottom row) of meta-linked benzene, dehydro[12]­annulene, [5]­cumulene and [4]­cumulene with the bias window opened up to the HOMO resonance. The magnetic field is plotted as a vector field (middle row) and as the point where the field is strongest (bottom row).