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In this paper, Green's function method is applied to study the ferromagnetic system with Dzyaloshinkii-Moriya (DM) interaction in both two-dimension (2D) and three-dimension chiral magnets. Relevant properties in 2D magnets are calculated, such as the susceptibility, correlation function and analytical expressions of phase boundary. Based on the theoretical results, a new phase is predicted in the window of strong DM interaction characterized by a negative winding number. In addition, helical state in pure 2D material only appears
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