Sensitivity of the magnetic state of a spin lattice on itinerant electron orbital phase

Spatially extended localized spins can interact via indirect exchange interaction through Friedel oscillations in the Fermi sea. In arrays of localized spins such interaction can lead to a magnetically ordered phase. Without external magnetic field such a phase is well understood via a "two-impurity" Kondo model. Here we employ non-equilibrium transport spectroscopy to investigate the role of the orbital phase of conduction electrons on the magnetic state of a spin lattice. We show experimentally, that even tiniest perpendicular magnetic field can influence the magnitude of the inter-spin magnetic exchange.