Non-trivial topology in 2D magnetic systems without skyrmions

The magnetic skyrmion is a kind of two-dimensional(2D) topological non-trivial spin textures which can be identified by an integer number, called topological charge. However, our study on 2D chiral magnets, however, showed that one topological charge does not necessarily correspond to one skyrmion and the non-trivial topology can be found in a disordered phase. Here, we further investigate non-trivial topology in various systems where no-skyrmion is expected in low magnetic field region. In 2D spin-frustrated systems, such thermally driven topology is dominated in a wide range of magnetic fields; In the antiferromagnetic system with staggered Dzyaloshinskii-Moriya interactions, giant response of topological charge is found in a canted spin-ordering phase. Both two systems are related to real systems so that we expect the topological properties can be observed by thermal magnon and/or anomalous Hall effect.