Curie temperature of ultrathin ferromagnetic layer with Dzyaloshinskii-Moriya interaction

We investigate the effect of the Dzyaloshinskii-Moriya interaction (DMI) on the Curie temperature of the ultrathin ferromagnetic layers. It has been known that the Curie temperature of the ferromagnet depends on spin wave excitation energies, and they are affected by DMI. Therefore, the ferromagnetic transition temperature of the ultrathin ferromagnetic layer must be sensitive on the DMI. We find that the Curie temperature depends on the DMI by using the double time Green's function method. Since the DMI is arisen by the inversion symmetry breaking structure, the DMI is always important in the inversion symmetry breaking ultrathin ferromagnetic layers.