Phase boundaries in ultrathin magnetic films

Finite-temperature phase boundaries of ultrathin magnetic films are obtained from Monte Carlo simulations as a function of the coupling strengths due to exchange (J), dipolar interaction (g), and z-axis anisotropy (K). We found three phases, corresponding to the appearance of the in-plane magnetization, the disappearance of the z magnetization, and the eventual disappearance of the in-plane magnetization. At small K-g, the transition temperature for the disappearance of the z magnetization can be well approximated by ${\mathit{T}}_{\mathit{c}}^{\mathrm{-}1}$=A+B ln[(K-g/0.120 83)/J] for constants A and B. For g=0, the magnetization disappears above the transition temperature. The constants A and B are changed only slightly (10%) as g becomes nonzero. The inverse temperature for the disappearance of the in-plane magnetization also depends linearly on ln(g/J) and only weakly on K. For a large enough K/g the magnetization never rotates onto the plane.