Image of helical local moment magnetic order in the STM spectrum

The surface tunneling microscope (STM) method probes the itinerant conduction electron spectrum which is influenced by the presence of collective order parameters. It may in fact be used as a tool to obtain important information about their microscopic nature, for example the gap symmetry in unconventional superconductors. Surprisingly it has been found that the STM spectrum can also identify magnetic order of completely localised electrons, e.g., incommensurate helical structure of 4f electron moments, as observed in the compound GdRu$_2$Si$_2$. This is due to the fact that the exchange coupling of conduction states to the localised subsystem reconstructs the itinerant bands which then leaves an imprint on the STM spectrum. We develop a theory based on this idea that shows firstly the appearance of STM satellite peaks at the wave vector of localised moment helical order for the pure surface. Secondly we derive the quasiparticle interference spectrum in Born approximation due to the presence of surface impurities which contains information on the reconstruction process of itinerant states caused by the localised helical order. Furthermore we show that within full $t$-matrix approach impurity bound states are also influenced by the exchange coupling to helical magnetic order.