Temperature dependence of the training effect in aCo∕CoOexchange-bias layer

Abstract

The temperature dependence of the training effect is studied in a $\mathrm{Co}∕\mathrm{Co}\mathrm{O}$ exchange-bias bilayer and a phenomenological theory is presented. After field cooling the sample to below its blocking temperature, the absolute value of the exchange-bias field decreases when cycling the heterostructure through consecutive hysteresis loops. This decrease is known as the training effect and is studied in the temperature range $5\ensuremath{\leqslant}T\ensuremath{\leqslant}120\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. An implicit sequence, which has been recently derived using the Landau-Khalatnikov approach of relaxation, fits the respective data set for each individual temperature. The underlying discretized dynamic equation involves an expansion of the free energy in powers of the interface magnetization of the antiferromagnetic pinning layer. The particular structure of the free energy with a leading fourth-order term is derived in a mean-field approach. The explicit temperature dependence of the leading expansion coefficient explains the temperature dependence of the training effect. The analytic approach is confirmed by the result of a best fit, which condenses the data from more than 50 measured hysteresis loops.