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We show, using a model of an ultrathin magnetic film, that when the dipole-dipole and exchange interactions are of comparable strength there exists a reorientation transition from a planar ferromagnetic phase at low temperature to either an orientationally ordered striped phase or a tetragonal phase at higher temperature. Which of these transitions occurs depends on the relative strength of the magnetic surface anisotropy. The phase diagram, as found from extensive Monte Carlo simulation, is determined as a function of temperature and magnetic surface anisotropy.
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MacIsaac et al. (1998) studied this question.
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