Image of helical local moment magnetic order in the STM spectrum

The surface tunneling microscope (STM) method probes the 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 localized electrons e.g., an incommensurate helical structure of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mn>4</a:mn><a:mi>f</a:mi></a:math> electron moments, as observed in the compound <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>GdRu</b:mi><b:mn>2</b:mn></b:msub><b:msub><b:mi>Si</b:mi><b:mn>2</b:mn></b:msub></b:mrow></b:math>. This is due to the fact that the exchange coupling of conduction states to the localized subsystem reconstructs the conduction bands which then leaves an imprint on the STM spectrum. First, we develop a theory based on this idea that shows the appearance of STM satellite peaks at the wave vector of localized moment helical order for the pure surface. Second, we derive the quasiparticle interference spectrum in the Born approximation due to the presence of surface impurities which contain information on the reconstruction process of itinerant states caused by the localized helical order. Furthermore, we show that within the full <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>T</c:mi></c:math> matrix approach, impurity bound states are also influenced by the exchange coupling to helical magnetic order.