Chiral multi-spin multi-site interactions*

The huge progress in the field of magnetic skyrmions and other noncollinear magnetic structures is due in large part to our understanding of the chiral Dzyaloshinskii-Moriya interaction. This illustrates the importance of identifying which magnetic interactions are present in a given material. Here, we discuss our systematic construction of a generalized spin model containing isotropic and chiral multi-site interactions [1,2]. These are motivated by a microscopic model, and their symmetry properties are established. We show that the chiral interactions arise solely from the spin-orbit interaction and that the multi-site interactions do not have to follow Moriya's rules, unlike the Dzyaloshinskii-Moriya and chiral biquadratic interactions. We then illustrate our theoretical considerations with density functional theory calculations for prototypical magnetic systems: triangular trimers made of Cr, Mn, Fe and Co on the Re(0001), Pt(111) and Au(111) surfaces, and Cr and Fe square tetramers on Pt(001).

[1] S. Brinker et al., New. J. Phys. 21, 083015 (2019)
[2] S. Brinker et al., Phys. Rev. Research 2, 033240 (2020)