We propose an atom-superposition-based method for simulating spin-polarized scanning tunneling microscopy (SP-STM) from first principles. Our approach provides bias-dependent STM images in high spatial resolution, with the capability of using either constant current or constant height modes of STM. In addition, topographic and magnetic contributions can clearly be distinguished, which are directly comparable to results of SP-STM experiments in the differential magnetic mode. Advantages of the proposed method are that it is computationally cheap, it is easy to parallelize, and it can employ the results of any ab initio electronic structure code. Its capabilities are illustrated for the prototype frustrated hexagonal antiferromagnetic system, Cr monolayer on Ag(111) in a noncollinear magnetic ${120}^{\ensuremath{\circ}}$ N\'eel state. We show evidence that the magnetic contrast is sensitive to the tip electronic structure, and this contrast can be reversed depending on the bias voltage.
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