Effect of the surface anisotropy on the magnetic behavior of ultra-thin films single-domain on the spin reorientation transition regime by monte carlo simulation

Abstract

Abstract In this work, Monte Carlo simulations allowed for studying the effect of the surface anisotropy on the Spin Reorientation Transition regime for single-domain ultra-thin films. The simulations included spin moments (1), exchange constant (10 meV), magnetocrystalline anisotropy (0.5 meV), and dipolar magnetic interaction (0.05 meV). We evaluated the surface anisotropy constant for K S = 0.5, 1, and 2 meV and thicknesses ranging from 3 to 11 cells. We determined the magnetothermal and hysteresis loop in- and out-plane at different angles to the plane. Analysis of Variance allows for modeling the coercivity as a function of the thickness and the applied field direction (in- and out-plane). Under these simulation conditions, the Spin Reorientation Transitions appear only at a thickness of 7 cells with K S =1 meV. The main contribution to magnetization rises out-plane at low thicknesses and in-plane at high values. However, the dominant magnetization contribution is in-plane for the thickness of 7 cells and low surface anisotropy. The magnetization is mainly oriented, out-plane for the high surface anisotropy case. However, hysteresis loops were observed independent of the applied magnetic field direction and thickness. Analysis of Variance results suggests that the thickness and the applied magnetic field direction allowed for tunning the coercivity (hard or soft magnetic materials). Sample simulated ignoring the magnetocrystalline and the surface anisotropies produce magnetic components in- and out-plane with slight differences as angle function. The combination of dipolar interactions and magnetocrystalline anisotropy showed two magnetic behaviors, a hard magnetic phase at low angles and a soft one at high angles in-plane direction. The inverse behavior results in the out-plane component. We observed the same behavior when surface anisotropy is considered. The differences are the transition angle of 50° in the first case and 30° in the second.