Field-dependent energy barriers in Co/CoO core-shell nanoparticles

Abstract

We perform atomistic modeling of Co/CoO nanoparticles with a diameter of a few nanometers and realistic values of the exchange and anisotropy parameters in order to study the field-dependent energy barriers under forward and backward reversal of the magnetization. The barriers are extracted from the constrained energy minimization using the integration of the Landau-Lifshitz-Gilbert equations and the Lagrange multiplier method. We show that the applied field and the interface exchange strength have opposite effects on the values of the energy barriers. In particular, while the backward (forward) energy barrier increases (decreases) linearly with the strength of the interface exchange coupling, it decreases (increases) almost quadratically with the applied magnetic field. Our results are in good agreement with the well-known Meiklejohn-Bean model of exchange bias, and allow us to analyze the limits of applicability of the macrospin approach to the study of energy barriers in core-shell Co/CoO nanoparticles.