In-Plane Anisotropy Effect to the Spin-Wave Gap in Ultrathin Ferromagnetic Films at Finite Temperatures
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In this paper, we investigate the calculated thickness- and temperature-dependent magnetization given in terms of the spin-wave gap alone for two-dimensional ultrathin ferromagnetic films with anisotropy and Zeeman energy sufficiently large to dominate over the dipolar interaction. The spin-wave gap was calculated for a magnetic field which is perpendicular to the plane. The calculated equations present a nonzero spin-wave gap at zero magnetic field which is strongly affected by anisotropies. The temperature-dependent magnetization strongly increases with decreasing thickness of the insulating spacer layer at the saturation field and at room temperature. We reported that the in-plane anisotropy strongly depends on the insulating spacer layer thickness and saturation field and overcomes the fourfold anisotropy in the spacer layers with thickness of below 0.8 nm. The results were also discussed in connection with experimental data given in Co0.9Fe0.1/MgO/C0.9Fe0.1 films.