Spontaneous Perpendicular Anisotropy in Ultra-thin Ferromagnetic Films

An atomistic scale study of ultra-thin ferromagnetic films was carried out using Monte Carlo simulations with Metropolis dynamics, and the simulations were performed using a Heisenberg Hamiltonian, surface and crystalline anisotropies, and dipolar interaction. We defined an 𝜖 parameter to bind the dipolar interaction with the anisotropy in order to show how the system would behave at different ratios and scale up the dipolar interaction to observe its effects on small manageable systems. The results show a strong dependency of the shape of the magnetization curves for in-plane and out-of-plane measurements with our 𝜖 parameter. We also included several measures of the magnetization direction at T = 2.5 K after a cooling process, and they show a critical thickness for an 𝜖 below which the magnetization will spontaneously beat the shape anisotropy and become perpendicular to the surface at low temperatures. As a side note, our study also shows results consistent with previous simulations that focused in a in-plane to out-of-plane transition of the magnetization when going from high temperature to low temperature.