The Monte Carlo method in the canonical ensemble is used to investigate magnetization reversal in amorphous transition metal -rare earth multilayers. Our study is based on a model containing diluted clusters which exhibit an effective uniaxial anisotropy in competition with random magnetic anisotropy in the matrix. We simulate hysteresis loops for an abrupt profile and a diffuse one obtained from atom probe tomography analyses. Our results evidence that the atom probe tomography profile favors perpendicular magnetic anisotropy in agreement with magnetic measurements. Moreover, the hysteresis loops calculated at several temperatures qualitatively agree with the experimental ones. * Electronic address: denis.ledue@univ-rouen.fr