Modeling the Training Effect in Exchange-Biased Bilayers for Large Numbers of Magnetization Reversal Cycles

The exchange bias (EB) is a unidirectional anisotropy that occurs, e.g., upon field-cooling ferromagnet/antiferromagnet systems. In many material systems, the EB field is reduced from one hysteresis loop to the next measurement. This so-called training effect (TE) has been investigated in experiments and by means of theoretical efforts by many research groups. The reduction of the EB field as a result of subsequent magnetization reversal processes is often fitted by a power law, usually with the exception of n = 1, or with an equation based on the discretized Landau–Khalatnikov equation, as first suggested by Binek. Few other models, usually with more fitting parameters, have been proposed yet. Herein, it is shown that for large numbers of subsequent magnetization reversal processes in Co/CoO thin film samples, a modified power law or a logarithmic fit can model the TE in most cases as well as the abovementioned, commonly used models.