Voltage-controlled topological spin textures in the monolayer limit

The physics of phase transitions in low-dimensional systems has long been a subject of significant research interest. Long-range magnetic order in the strict two-dimensional limit, whose discovery circumvented the Mermin-Wagner theorem, has rapidly emerged as a research focus. However, the demonstration of a non-trivial topological spin textures in two-dimensional limit has remained elusive. Here, we demonstrate the out-of-plane electric field breaks inversion symmetry while simultaneously modulating the electronic band structure, enabling electrically tunable spin-orbit interaction for creation and manipulation of topological spin textures in monolayer CrI₃. The realization of ideal two-dimensional topological spin textures may offer not only an experimental testbed for probing the Berezinskii-Kosterlitz-Thouless mechanism, but also potential insights into unresolved quantum phenomena including superconductivity and superfluidity. Moreover, voltage-controlled spin-orbit interaction offers a novel pathway to engineer two-dimensional spin textures with tailored symmetries and topologies, while opening avenues for skyrmion-based next-generation information technologies.