Critical Dzyaloshinskii-Moriya interaction energy density for the skyrmion states formation in ultrathin ferromagnetic layer

We investigate the condition for the skyrmion state formation in ultrathin ferromagnetic layers with the Dzyaloshinskii-Moriya interaction (DMI). By using micromagnetic simulations with DMI term, we found skyrmion state is a ground state instead of a collinear single domain when DMI is larger than a critical value. When the skyrmion arrays are formed, a specific length scale of skyrmion is governed the spin configurations. We found that the critical DMI energy density for the skyrmion state is related with not only crystalline anisotropy energy, but also the dipole-dipole interaction.