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Abstract: 
The term “magnetism” subsumes a plethora of interactions originating from various physical mechanisms. Their competition often results in highly complex spin structures, such that the specific origin is masked and can only be unraveled by combining experiment and theory. For example, for an Fe monolayer on Rh(111) an up-up-down-down (↑↑↓↓) spin structure was predicted by density functional theory (DFT) [1] which was only later understood to originate from a previously unconsidered four-spin–three-site beyond-Heisenberg interaction [2]. Using spin-polarized scanning tunneling microscopy (SP-STM) we could indeed confirm this (↑↑↓↓) spin structure experimentally. Owing to the trigonal symmetry of the (111) surface, our data show the coexistence of three orientational domains. The field-dependent behavior was found to be surprisingly complex, potentially due to uncompensated spins at domain boundaries.
Another example for the complexity of spin structures formed by the competition of various magnetic interactions are transition metal oxide chains on Ir and Pt(001) [3,4]. MnO2 on Ir(001) exhibits an antiferromagnetic Mn–Mn coupling along the chain, whereas the inter-chain coupling across the non-magnetic Ir substrate is chiral with a 120° rotation between adjacent chains. Theory suggests that the inter-chain coupling is driven by a Dzyaloshinskii-Moriya-enhanced version of the well-known Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction [3]. Similar to the conventional RKKY interaction this coupling proceeds via conduction electrons of the substrate but leads to a chiral coupling, qualitatively different from the collinear cases known so far.

[1] A. Al-Zubi et al., Phys. Status Solidi B 248, 2242 (2011)
[2] A. Krönlein et al., Phys. Rev. Lett. 120, 207202 (2018)
[3] M. Schmitt et al., Nature Comm. 10, 2610 (2019)
[4] M. Schmitt et al., Phys. Rev. B 100, 054431 (2019