Four-Spin Interactions as a Route to Multiple-Q Topological Magnetic Order
arXiv:2510.15158 · doi:10.1103/3njw-f1jt
Abstract
We investigate the role of four-spin interactions in stabilizing exotic multiple- topological spin textures and demonstrate their ability to realize a skyrmion crystal. While such higher-order interactions are known to be important, their intricate nature makes systematic model construction significantly challenging. To address this issue, we develop a theoretical framework that connects microscopic real-space four-spin couplings to their effective interactions in momentum space, providing a clear route to engineer target magnetic phases. Applying this framework to a frustrated Heisenberg model with designed four-spin interactions, we identify the stabilization of the zero-field skyrmion crystal with a topological number of two via simulated annealing. Furthermore, our momentum-space analysis reveals the intrinsic mechanism by which the well-known ring-exchange interaction also favors the skyrmion crystal. Our findings not only present a concrete model for a higher-order skyrmion crystal but also offer a general methodology for understanding and designing a wide range of complex multiple- magnetic orders driven by multi-spin interactions.
14 pages, 9 figures
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