Phase diagram of chiral magnets via Green's function method.

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 at zero temperature. The analysis on correlation function shows a special symmetry of transverse spin correlation, which corresponds to the skyrmion phase. The results also prove the instability of helical state and its lifetime is numerically computed. Different from 2D magnets, helical state in 3D exists in the window of a lower Zeeman energy and has a long lifetime. DM interaction also reduces Curie temperature because of the spatial symmetry breaking.