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.
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