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

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.