Temperature dependence of the training effect in exchange bias heterostructures

Recently, the training of the exchange bias (EB) effect in antiferromagnetic (AF)/ferromagnetic (FM) heterostructures has been considered in the framework of activated spin configurational relaxation [1]. The EB field, $\mu _{0}$H$_{e}$, is determined from hysteresis loops of the magnetization which are measured by SQUID-magnetometry after field-cooling the sample below the N\'{e}el temperature of the pinning layer. The evolution of $\mu _{0}$H$_{e}$ in terms of the number of consecutively cycled loops is derived from a discretized Landau-Khalatnikov (LK) equation. Here the time parameter is replaced by the loop index n. Mapping the LK equation onto an implicit sequence allows to describe the training effect, $\mu _{0}$H$_{e}$ vs. n for all n $\ge $1, of various EB heterostructures. In the limit n$>$1, our sequence approaches the empirical $\mu _{0}$H$_{e}$(n)$\propto $1/$\surd $n behavior. The best fit of the sequence to a data set $\mu _{0}$H$_{e}$ vs. n provides the essential fitting parameter $\gamma $ which combines properties of the free energy and the damping with the exchange coupling at the AF/FM interface. We study $\gamma $ vs. T by analyzing the T-dependence of the training effect in a CoO/Co bilayer. Various data sets of $\mu _{0}$H$_{e}$ vs. n are determined from hysteresis loops after in-plane field-cooling at $\mu _{0}$H=0.3T from T=320K to temperatures 5K$<$T$<$T$_{B}\approx $150K, respectively. $\gamma $ vs. T increases with increasing temperature which provides insight into the T-dependence of the free energy. [1] Ch. Binek, Phys. Rev. B \textbf{70}, 014421 (2004).