It became customary to study the stability, lifetime, dynamics, thermodynamics and transport properties of localized nanoscale magnetization particles such as skyrmionics by classical spin-lattice models with pairwise Heisenberg-type exchange interactions. The mapping of fermionic many-body systems onto a classical Heisenberg model is a nontrivial thing and by far not unique. In this presentation I motivate beyond Heisenberg multi-spin interactions [1]. I give examples, where these interactions play a decisive role [2]. I focus on MnGe in the B20- phase, which exhibits a three-dimensional spin-texture. We introduce a novel class of magnetic exchange interactions [3] – the topological-chiral interactions (TCI) rooted in the socalled topological orbital moment, which manifests as a result of finite scalar spin chirality in non-coplanar magnets. The long-wave length limit of the interactions relates to the highly acclaimed Faddeev model demonstrating that the interaction is an origin of 3D magnetization textures all the way down to hopfions.
[1] M. Hoffmann, S. Blügel, PRB 10, 024418 (2019).
[2] A. Krönlein, M. Schmitt, M. Hoffmann, J. Kemmer, N. Seubert, M. Vogt, J. Küspert, M. Böhme, B. Alonazi, J. Kügel, H. A. Albrithen, M. Bode, G. Bihlmayer, and S. Blügel, PRL 120, 207202 (2018).
[3] S. Grytsiuk, J.-P. Hanke, M. Hoffmann, J. Bouaziz, O. Gomonay, G. Bihlmayer, S. Lounis, Y. Mokrousov, S. Blügel, Nat. Commun. 11, 511 (2020).