On the Ordered States in a Two-Dimensional Heisenberg Model with Dipole-Dipole Interactions

In the two-dimensional Heisenberg model with dipole dipole interactions and uniaxial anisotropy, the ordered state is known to be an in-plane ferromagnetic state or a state with an out-of-plane stripe domain pattern. The ground-state phase diagram is approximately obtained from the fastest growing mode for the time-dependent Ginzburg-Landau equation in a continuous space approximation. A more detailed description of the ordered states is obtained by solving the Landau-Lifshitz equation numerically in the continuous space approximation. Mixed states with both in-plane ferromagnetic order and an out-of-plane stripe pattern appear between the region of the in-plane ferromagnetic state and the region of the out-of-plane stripe states in the phase diagram.