Striped phases in two-dimensional dipolar ferromagnets

A uniaxial spin system on the square lattice, where the spins are oriented perpendicular to the lattice and are coupled by both a dipole-dipole interaction and an exchange interaction, is studied. The subtle interplay of the exchange and dipolar interaction in two dimensions destabilizes the ferromagnetic ground state of the nearest-neighbor Ising model and gives rise to a sequence of striped phases. An analytic expression for the leading terms in an asymptotic expansion of the ground-state energy for the striped phase is derived for the discrete lattice. Comparison with the corresponding results for a previously proposed checkerboard state show that the striped phase is the ground state. The results are shown to be in excellent agreement with earlier numerical results. The finite-temperature phase diagram is obtained for a finite lattice using Monte Carlo simulation techniques and the corresponding structure-factor patterns discussed.